(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 57395, 1944]*) (*NotebookOutlinePosition[ 58071, 1967]*) (* CellTagsIndexPosition[ 58027, 1963]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["PRESENTACI\[CapitalOAcute]N PR\[CapitalAAcute]CTICA 5", "Title", TextAlignment->Center, TextJustification->0, FontColor->RGBColor[0, 0, 1], Background->RGBColor[0, 1, 1], FontVariations->{"CompatibilityType"->0}], Cell[CellGroupData[{ Cell[TextData[StyleBox["INTRODUCCI\[CapitalOAcute]N", FontColor->RGBColor[0, 0, 1]]], "SectionFirst", Background->RGBColor[0.8, 1, 0.4]], Cell[TextData[{ StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " dispone de funciones espec\[IAcute]ficas para calcular el polinomio \ caracter \[IAcute]stico de una matriz cuadrada, sus valores propios y sus \ vectores propios." }], "Text"], Cell[TextData[{ " \t\t ", Cell[BoxData[ RowBox[{" ", GridBox[{ { StyleBox["CharacteristicPolynomial", FontSize->14, FontWeight->"Bold"], StyleBox[\(\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(polinomio\ caracter\[IAcute]stico\ de\ \ una\ matriz\)\), FontFamily->"Times"]}, { StyleBox["Eigenvalues", FontSize->14, FontWeight->"Bold"], StyleBox[\(\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(lista\ de\ los\ \ valores\ propios\)\), FontFamily->"Times"]}, { StyleBox["Eigenvectors", FontSize->14, FontWeight->"Bold"], RowBox[{" ", StyleBox[\(lista\ vectores\ propios\), FontFamily->"Times"]}]}, { StyleBox["Eigensystem", FontSize->14, FontWeight->"Bold"], StyleBox[\(\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(valores\ y\ \ vectores\ propios\)\), FontFamily->"Times"]} }]}]], TextAlignment->Right], "\n" }], "Text"], Cell[TextData[{ "Si queremos realizar la diagonalizaci\[OAcute]n ortogonal de una matriz \ real sim\[EAcute]trica, deberemos cargar en primer lugar el paquete ", StyleBox[""Courier", FontSize->14, FontWeight->"Bold"] }], "Text"], Cell[BoxData[ StyleBox[\("Courier", FontSize->14, FontWeight->"Bold"]], "Input", CellLabel->"In[1]:=", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["EJERCICIO 5.1 (Una matriz diagonalizable en ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[DoubleStruckCapitalR]", FontColor->RGBColor[0, 0, 1]], StyleBox[" no sim\[EAcute]trica)", FontColor->RGBColor[0, 0, 1]] }], "SectionFirst", FontColor->RGBColor[1, 0, 1], Background->RGBColor[0.8, 1, 0.4]], Cell[CellGroupData[{ Cell[TextData[{ "Sea la matriz", StyleBox[":\n\t\t\t\t\t\t", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ RowBox[{"A", "=", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "3", \(-3\)}, {"6", "4", \(-6\)}, {"3", "3", \(-5\)} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]}]], TextAlignment->Left, TextJustification->1, FontFamily->"Helvetica", FontSize->14], "\n\t\t", StyleBox["\n", FontColor->RGBColor[0, 0, 1]], StyleBox["a.- ", FontColor->RGBColor[1, 0, 0]], "Hallar el polinomio caracter\[IAcute]stico de A.\n (", StyleBox["Recordar", FontColor->RGBColor[1, 0, 0]], ": ", StyleBox["p(\[Lambda])=det (A-\[Lambda]I)", FontColor->RGBColor[0, 1, 0]], ")" }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell["Cargamos la matriz A como una lista de listas.", "Text"], Cell[BoxData[ \(\(a = {{1, 3, \(-3\)}, {6, 4, \(-6\)}, {3, 3, \(-5\)}};\)\)], "Input", CellLabel->"In[1]:=", FontSize->14], Cell[BoxData[ \(p[x_] := CharacteristicPolynomial[a, x]\)], "Input", CellLabel->"In[2]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(p[x] // Factor\)], "Input", CellLabel->"In[3]:=", FontSize->14], Cell[BoxData[ \(\(-\((\(-4\) + x)\)\)\ \((2 + x)\)\^2\)], "Output", CellLabel->"Out[3]="] }, Open ]], Cell[TextData[{ "Podemos calcular el polinomio caracter\[IAcute]stico de una matriz \ calculando ", StyleBox["det (A-\[Lambda]I)", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Det[a - x\ IdentityMatrix[3]] // Factor\)], "Input", CellLabel->"In[4]:=", FontSize->14], Cell[BoxData[ \(\(-\((\(-4\) + x)\)\)\ \((2 + x)\)\^2\)], "Output", CellLabel->"Out[4]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["b.- ", FontColor->RGBColor[1, 0, 0]], "Hallar los valores propios y los subespacios propios de A, indicando una \ base de los mismos." }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell["\", "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ StyleBox["Los", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["valores", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["propios", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["de", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["la", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["matriz", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["A", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["con", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["su", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["multiplicidad", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["correspondiente", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(son : \[IndentingNewLine]\ \[Lambda]\_1 = 4\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(k\_1 = 1\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", StyleBox[\(\[Lambda]\_2 = \(-2\)\ \ \ , \ \ \ k\_2 = 2\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "Text", CellMargins->{{Inherited, 30}, {Inherited, Inherited}}, TextAlignment->Right, TextJustification->0, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"], Cell[TextData[{ "Utilizando la funci\[OAcute]n ", StyleBox["Eigenvalues", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"], " obtenemos la lista de los valores propios de una matriz con su \ multiplicidad correspondiente, pues si un valor propio es m\[UAcute]ltiplo \ aprecere en la lista de la salida correspondiente repetido tantas veces como \ su orden o multiplicidad." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Eigenvalues[a]\)], "Input", CellLabel->"In[5]:=", FontSize->14], Cell[BoxData[ \({4, \(-2\), \(-2\)}\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell[TextData[{ "La funci\[OAcute]n de ", StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["Eigenvectors", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"], " devuelve una lista de n vectores de ", Cell[BoxData[ FormBox[ StyleBox[\(\[DoubleStruckCapitalR]\^n\), FontWeight->"Bold"], TraditionalForm]]], ", siendo la matriz una matriz cuadrada de orden n. Los vectores no nulos \ de esta lista son vectores propios de la matriz linealmente independientes. \ Si todos estos vectores son no nulos, la matriz es diagonalizable y estos \ vectores constituyen una base de ", Cell[BoxData[ FormBox[ StyleBox[\(\[DoubleStruckCapitalR]\^n\), FontWeight->"Bold"], TraditionalForm]]], "formada por vectores propios de la matriz.\nSi alguno de estos vectores es \ nulo, la matriz no es diagonalizable." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Eigenvectors[a]\)], "Input", CellLabel->"In[6]:=", FontSize->14], Cell[BoxData[ \({{1, 2, 1}, {1, 0, 1}, {\(-1\), 1, 0}}\)], "Output", CellLabel->"Out[6]="] }, Open ]], Cell[TextData[{ "Tambi\[EAcute]n podemos obtener los valores y vectores propios de una \ matriz con una sola funci\[OAcute]n ", StyleBox["Eigensystem.", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Eigensystem[a]\)], "Input", CellLabel->"In[7]:=", FontSize->14], Cell[BoxData[ \({{4, \(-2\), \(-2\)}, {{1, 2, 1}, {1, 0, 1}, {\(-1\), 1, 0}}}\)], "Output", CellLabel->"Out[7]="] }, Open ]], Cell["\", "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ StyleBox["\[FivePointedStar]", FontFamily->"Helvetica", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[1, 0, 0]], StyleBox["V", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\((4)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[ScriptCapitalL] \(({\((1, 2, 1)\)})\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(B\_1 = \({\((1, 2, 1)\)}\ \ \ d\_1 = 1\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ StyleBox[ RowBox[{ RowBox[{ RowBox[{ StyleBox["\[FivePointedStar]", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox["V", FontColor->RGBColor[0, 0, 1]], StyleBox[\((\(-2\))\), FontColor->RGBColor[0, 0, 1]]}], StyleBox["=", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[ScriptCapitalL] \(({\((1, 0, 1)\), \((\(-1\), 1, 0)\)})\)\), FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0, 0, 1]], StyleBox[\(B\_2 = \({\((1, 0, 1)\), \((\(-1\), 1, 0)\)}\ \ \ d\_2 = 2\)\), FontColor->RGBColor[0, 0, 1]]}], FontFamily->"Helvetica"], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica"]}], "\[IndentingNewLine]", StyleBox[\(A\ \ es\ \(\(diagonalizable\)\(.\)\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "Text", CellMargins->{{Inherited, 26}, {Inherited, Inherited}}, TextAlignment->Right, TextJustification->0, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c.- ", FontColor->RGBColor[1, 0, 0]], "Si es posible, diagonalizar A." }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "Ya hemos justificado en el apartdo anterior que la matrzi A es \ diagonalizable.\nPara diagonalizar A necesitamos escribir una matriz D \ diagonal semejante a A y una matriz P regular tal que\n\t\t\t\t\t\t\t\t", Cell[BoxData[ RowBox[{" ", StyleBox[\(A = P\[CenterDot]D\[CenterDot]P\^\(-1\)\), FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"]}]]], "\nSabemos que la diagonal principal de D ha de estar formada por los \ valores propios de A. Recuperamos estos valores como el primer elemento de la \ lista ", StyleBox["s", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"], " obtenida en ", StyleBox["Out[7]", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"], ".\t\t\t\t\t\t\t" }], "Text"], Cell[BoxData[ \(\({valpropios, vecpropios} = Eigensystem[a];\)\)], "Input", CellLabel->"In[8]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(d = DiagonalMatrix[valpropios]\)], "Input", CellLabel->"In[9]:=", FontSize->14], Cell[BoxData[ \({{4, 0, 0}, {0, \(-2\), 0}, {0, 0, \(-2\)}}\)], "Output", CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[d]\)], "Input", CellLabel->"In[10]:=", FontSize->14], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"4", "0", "0"}, {"0", \(-2\), "0"}, {"0", "0", \(-2\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[10]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p = Transpose[vecpropios]; MatrixForm[p]\)], "Input", CellLabel->"In[11]:=", FontSize->14], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", \(-1\)}, {"2", "0", "1"}, {"1", "1", "0"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[11]//MatrixForm="] }, Open ]], Cell[TextData[{ "Aunque no es necesario comprobamos que se cumple:\n\t\t\t\t\t\t\t\t", Cell[BoxData[ RowBox[{" ", StyleBox[\(A = P\[CenterDot]D\[CenterDot]P\^\(-1\)\), FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"]}]]], "\t\t\t\t\t\t\t" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a == p . d . Inverse[p]\)], "Input", CellLabel->"In[12]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[12]="] }, Open ]], Cell[BoxData[{ RowBox[{ StyleBox[ RowBox[{"D", "=", " ", RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-2\), "0", "0"}, {"0", \(-2\), "0"}, {"0", "0", "4"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "=", RowBox[{\(P\^\(-1\)\), "\[CenterDot]", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "3", \(-3\)}, {"6", "4", \(-6\)}, {"3", "3", \(-5\)} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "\[CenterDot]", "P"}]}]}], FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[",", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["\[IndentingNewLine]", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], RowBox[{ RowBox[{ StyleBox["con", FontFamily->"Helvetica", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[" ", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["P", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]]}], StyleBox["=", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", \(-1\), "1"}, {"0", "1", "2"}, {"1", "0", "1"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], FontSize->14, FontColor->RGBColor[0, 0, 0.996109]]}]}], "\[IndentingNewLine]", RowBox[{ StyleBox["A", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["=", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "3", \(-3\)}, {"6", "4", \(-6\)}, {"3", "3", \(-5\)} }], "\[NoBreak]", ")"}], "=", RowBox[{"P", "\[CenterDot]", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-2\), "0", "0"}, {"0", \(-2\), "0"}, {"0", "0", "4"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "\[CenterDot]", \(P\^\(-1\)\)}]}], FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}]}], "Text", TextAlignment->Right, TextJustification->0, FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["d.- ", FontColor->RGBColor[1, 0, 0]], StyleBox["Hallar, si es posible, una base de ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ StyleBox[\(\[DoubleStruckCapitalR]\^3\), FontColor->RGBColor[0, 0, 1]], TraditionalForm]]], "formada por vectores propios de A", StyleBox[".", FontColor->RGBColor[0, 0, 1]] }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "Como A es una matriz diagonalizable, es posible encontrar bases de ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], "formadas por vectores propios de A. Por ejemplo:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Print", "[", RowBox[{ "\"\\"", ",", "vecpropios"}], "]"}]], "Input", CellLabel->"In[13]:=", FontSize->14], Cell[BoxData[ InterpretationBox[ RowBox[{"\", "\[InvisibleSpace]", \({{1, 2, 1}, {1, 0, 1}, {\(-1\), 1, 0}}\)}], SequenceForm[ "Una base de \!\(TraditionalForm\`\[DoubleStruckCapitalR]\^3\) formada \ por vectores propios de A, es B=", {{1, 2, 1}, {1, 0, 1}, {-1, 1, 0}}], Editable->False]], "Print", CellLabel->"From In[13]:="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["e.- ", FontColor->RGBColor[1, 0, 0]], StyleBox["Diagonalizar ortonalmente A, si es posible.", FontColor->RGBColor[0, 0, 1]] }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell["Vamos a comprobar que la matriz A no es sim\[EAcute]trica:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a \[Equal] Transpose[a]\)], "Input", CellLabel->"In[14]:=", FontSize->14], Cell[BoxData[ \(False\)], "Output", CellLabel->"Out[14]="] }, Open ]], Cell["\", "Text"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["f.- ", FontColor->RGBColor[1, 0, 0]], StyleBox["Comprobar que se cumple que\n\t\t\t\t\t\t", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ StyleBox[\(A\^n = P\[CenterDot]D\^n\[CenterDot]P\^\(-1\)\), FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"]]] }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixPower[a, n] \[Equal] p . MatrixPower[d, n] . Inverse[p]\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[15]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[16]:=", FontSize->14] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["EJERCICIO 5.2 (Una matriz real no diagonalizable)", FontColor->RGBColor[0, 0, 1]]], "SectionFirst", FontColor->RGBColor[1, 0, 1], Background->RGBColor[0.8, 1, 0.4]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Sea la matriz:\n\n\t\t\t\t\t\t", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ StyleBox[ RowBox[{"B", "=", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-3\), \(-1\), "1"}, {\(-6\), \(-2\), "6"}, {\(-7\), \(-1\), "5"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]}], FontFamily->"Helvetica"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], "\n\t\t\t\t", StyleBox["\n", FontColor->RGBColor[0, 0, 1]], StyleBox["a.- ", FontColor->RGBColor[1, 0, 0]], "Hallar los valores y subespacios propios de B, indicando una base de los \ mismos." }], "Subsubsection", CellDingbat->None, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(b = {{\(-3\), \(-1\), 1}, {\(-6\), \(-2\), 6}, {\(-7\), \(-1\), 5}};\)\), "\[IndentingNewLine]", \({valpropios, vecpropios} = Eigensystem[b]\)}], "Input", CellLabel->"In[1]:=", FontSize->14], Cell[BoxData[ \({{4, \(-2\), \(-2\)}, {{0, 1, 1}, {1, 0, 1}, {0, 0, 0}}}\)], "Output", CellLabel->"Out[2]="] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{ StyleBox["Los", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["valores", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["propios", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["de", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["la", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["matriz", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["B", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["con", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["su", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["multiplicidad", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["correspondiente", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(son : \[IndentingNewLine]\ \[Lambda]\_1 = 4\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(k\_1 = 1\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", StyleBox[\(\[Lambda]\_2 = \(-2\)\ \ \ , \ \ \ k\_2 = 2\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "Text", CellMargins->{{Inherited, 30}, {Inherited, Inherited}}, TextAlignment->Right, TextJustification->0, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"], Cell[BoxData[{ StyleBox[\(Los\ subespacios\ propios\ de\ \ B, \ son : \ son\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ StyleBox["\[FivePointedStar]", FontFamily->"Helvetica", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[1, 0, 0]], StyleBox["V", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\((4)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[ScriptCapitalL] \(({\((0, 1, 1)\)})\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(B\_1 = \({\((0, 1, 1)\)}\ \ \ d\_1 = 1\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ StyleBox[ RowBox[{ StyleBox["\[FivePointedStar]", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox["V", FontColor->RGBColor[0, 0, 1]], StyleBox[\((\(-2\))\), FontColor->RGBColor[0, 0, 1]]}], FontFamily->"Helvetica"], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[ScriptCapitalL] \(({\((1, 0, 1)\)})\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(B\_2 = \({\((1, 0, 1)\)}\ \ \ d\_2 = 1\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica"]}], "\[IndentingNewLine]", RowBox[{ StyleBox["B", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["NO", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["es", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\(diagonalizable\)\(.\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}]}], "Text", CellMargins->{{Inherited, 26}, {Inherited, Inherited}}, TextAlignment->Right, TextJustification->0, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["b.- ", FontColor->RGBColor[1, 0, 0]], "Comprobar que las matrices A (ejercicio 1.-) y B (ejercicio 2.-) tienen \ el mismo polinomio caracter\[IAcute]stico, pero NO son semejantes." }], "Subsubsection", CellDingbat->None, TextJustification->1, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell["\", "Text"], Cell[BoxData[{ \(\(a = {{1, 3, \(-3\)}, {6, 4, \(-6\)}, {3, 3, \(-5\)}};\)\), "\[IndentingNewLine]", \(\(m = {{a11, a12, a13}, {a21, a22, a23}, {a31, a32, a33}};\)\)}], "Input", CellLabel->"In[3]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(CharacteristicPolynomial[a, x] == CharacteristicPolynomial[b, x]\)], "Input", CellLabel->"In[5]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[a \[Equal] m . b . Inverse[m], Flatten[m]]\)], "Input", CellLabel->"In[6]:=", FontSize->14], Cell[BoxData[ \({}\)], "Output", CellLabel->"Out[6]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[7]:=", FontSize->14] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["EJERCICIO 5.3 (Diagonalizaci\[OAcute]n ortogonal de \ una matriz real sim\[EAcute]trica)", FontColor->RGBColor[0, 0, 1]]], "SectionFirst", TextJustification->1, FontColor->RGBColor[1, 0, 1], Background->RGBColor[0.8, 1, 0.4]], Cell[CellGroupData[{ Cell[TextData[{ "Sea la matriz sim\[EAcute]trica: ", Cell[BoxData[ StyleBox[" ", FontColor->GrayLevel[0]]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], "\n\t\t\t\t\t\t", Cell[BoxData[ RowBox[{"A", "=", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "1", "1"}, {"1", "5", "1"}, {"1", "1", "5"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]}]], TextAlignment->Left, TextJustification->1, FontFamily->"Helvetica", FontSize->14], "\n", StyleBox["a.- ", FontColor->RGBColor[1, 0, 0]], " Diagonalizar A." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell["\", "Text"], Cell[BoxData[ \(\(a = {{5, 1, 1}, {1, 5, 1}, {1, 1, 5}};\)\)], "Input", CellLabel->"In[1]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \({valpropios, vecpropios} = Eigensystem[a]\)], "Input", CellLabel->"In[2]:=", FontSize->14], Cell[BoxData[ \({{7, 4, 4}, {{1, 1, 1}, {\(-1\), 0, 1}, {\(-1\), 1, 0}}}\)], "Output", CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(d = DiagonalMatrix[valpropios]; MatrixForm[d]\)], "Input", CellLabel->"In[3]:=", FontSize->14], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"7", "0", "0"}, {"0", "4", "0"}, {"0", "0", "4"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[3]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p = Transpose[vecpropios]; MatrixForm[p]\)], "Input", CellLabel->"In[4]:=", FontSize->14], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", \(-1\), \(-1\)}, {"1", "0", "1"}, {"1", "1", "0"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[4]//MatrixForm="] }, Open ]], Cell[TextData[{ "Aunque no es necesario comprobamos que se cumple:\n\t\t\t\t\t\t\t\t", Cell[BoxData[ RowBox[{" ", StyleBox[\(A = P\[CenterDot]D\[CenterDot]P\^\(-1\)\), FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"]}]]], "\t\t\t\t\t\t\t" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a == p . d . Inverse[p]\)], "Input", CellLabel->"In[5]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{ StyleBox["Los", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["valores", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["propios", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["de", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["la", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["matriz", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["A", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["con", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["su", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["multiplicidad", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["correspondiente", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], RowBox[{ RowBox[{ StyleBox["son", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[":", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[Lambda]\_1\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["7", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(k\_1 = 1\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ StyleBox[ RowBox[{ StyleBox[\(\[Lambda]\_2\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["4", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], FontFamily->"Helvetica"], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(k\_2 = 2\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}]}], "Text", CellMargins->{{Inherited, 30}, {Inherited, Inherited}}, TextAlignment->Right, TextJustification->0, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"], Cell[BoxData[{ RowBox[{ RowBox[{ StyleBox["Los", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["subespacios", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["propios", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["de", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["A", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(son : \ son\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ StyleBox["\[FivePointedStar]", FontFamily->"Helvetica", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Helvetica", FontColor->RGBColor[1, 0, 0]], StyleBox["V", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\((7)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[ScriptCapitalL] \(({\((1, 1, 1)\)})\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(B\_1 = \({\((1, 1, 1)\)}\ \ \ d\_1 = 1\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox[ RowBox[{ StyleBox["\[FivePointedStar]", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox["V", FontColor->RGBColor[0, 0, 1]], StyleBox[\((\(-2\))\), FontColor->RGBColor[0, 0, 1]]}], FontFamily->"Helvetica"], StyleBox["=", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(\[ScriptCapitalL] \(({\((\(-1\), 0, 1)\), \((\(-1\), 1, 0)\)})\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox["\[IndentingNewLine]", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[\(B\_2 = \({\((\(-1\), 0, 1)\), \((\(-1\), 1, 0)\)}\ \ \ d\_2 = 2\)\), FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}]}], "Text", CellMargins->{{Inherited, 26}, {Inherited, Inherited}}, TextAlignment->Right, TextJustification->0, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"], Cell[BoxData[{ RowBox[{ StyleBox[ RowBox[{"D", "=", " ", RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"7", "0", "0"}, {"0", "4", "0"}, {"0", "0", "4"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "=", RowBox[{\(P\^\(-1\)\), "\[CenterDot]", TagBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "1", "1"}, {"1", "5", "1"}, {"1", "1", "5"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], (MatrixForm[ #]&)], "\[CenterDot]", "P"}]}]}], FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[",", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["\[IndentingNewLine]", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], RowBox[{ RowBox[{ StyleBox["con", FontFamily->"Helvetica", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[" ", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["P", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]]}], StyleBox["=", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", \(-1\), \(-1\)}, {"1", "0", "1"}, {"1", "1", "0"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], FontSize->14, FontColor->RGBColor[0, 0, 0.996109]]}]}], "\[IndentingNewLine]", RowBox[{ StyleBox["A", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["=", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[ RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "1", "1"}, {"1", "5", "1"}, {"1", "1", "5"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "=", RowBox[{"P", "\[CenterDot]", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"7", "0", "0"}, {"0", "4", "0"}, {"0", "0", "4"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "\[CenterDot]", \(P\^\(-1\)\)}]}], FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}]}], "Text", TextAlignment->Right, TextJustification->0, FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["b.- ", FontColor->RGBColor[1, 0, 0]], "Diagonalizar ortogonalmente la matriz A.\t\t\t" }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "Hay que ORTONORMALIZAR la base de vectores propios encontrada en ", StyleBox["Out[2]", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"], ". Si resolvieramos el problema a mano ortonormalizar\[IAcute]amos las \ bases de cada uno de los subespacios propios, pero para hacerlo con ", StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], " es m\[AAcute]s r\[AAcute]pido y c\[OAcute]modo ortonormalizar la base de \ ", StyleBox["Out[2]", FontFamily->"Courier", FontSize->14, FontWeight->"Bold"], "." }], "Text", TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman"], Cell[BoxData[ \("In[6]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(qt = GramSchmidt[vecpropios]\)], "Input", CellLabel->"In[7]:=", FontSize->14], Cell[BoxData[ \({{1\/\@3, 1\/\@3, 1\/\@3}, {\(-\(1\/\@2\)\), 0, 1\/\@2}, {\(-\(1\/\@6\)\), \@\(2\/3\), \(-\(1\/\@6\)\)}}\)], "Output",\ CellLabel->"Out[7]="] }, Open ]], Cell["\", "Text", TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell[BoxData[ \(q = Transpose[qt]; q . qt \[Equal] IdentityMatrix[3]\)], "Input", CellLabel->"In[8]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[8]="] }, Open ]], Cell[TextData[{ "Comprobamos que se cumple:\n\t\t\t\t\t\t\t\t", Cell[BoxData[ RowBox[{" ", StyleBox[\(A = Q\[CenterDot]D\[CenterDot]Q\^T\), FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"]}]]], "\t\t\t\t\t\t\t" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a \[Equal] q . d . qt\)], "Input", CellLabel->"In[9]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[9]="] }, Open ]], Cell[BoxData[{ RowBox[{ StyleBox[ RowBox[{"D", "=", " ", RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"7", "0", "0"}, {"0", "4", "0"}, {"0", "0", "4"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "=", RowBox[{\(Q\^T\), "\[CenterDot]", TagBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "1", "1"}, {"1", "5", "1"}, {"1", "1", "5"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], (MatrixForm[ #]&)], "\[CenterDot]", "Q"}]}]}], FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[",", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["\[IndentingNewLine]", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], RowBox[{ RowBox[{ StyleBox["con", FontFamily->"Helvetica", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[" ", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["Q", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]]}], StyleBox["=", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(1\/\@3\), \(-\(1\/\@2\)\), \(-\(1\/\@6\)\)}, {\(1\/\@3\), "0", \(\@\(2\/3\)\)}, {\(1\/\@3\), \(1\/\@2\), \(-\(1\/\@6\)\)} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], FontSize->14, FontColor->RGBColor[0, 0, 0.996109]]}]}], "\[IndentingNewLine]", RowBox[{ StyleBox["A", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox["=", FontFamily->"Times New Roman", FontSize->14, FontColor->RGBColor[0, 0, 0.996109]], StyleBox[ RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "1", "1"}, {"1", "5", "1"}, {"1", "1", "5"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "=", RowBox[{"Q", "\[CenterDot]", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"7", "0", "0"}, {"0", "4", "0"}, {"0", "0", "4"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], "\[CenterDot]", \(Q\^T\)}]}], FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]}]}], "Text", TextAlignment->Right, TextJustification->0, FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[10]:=", FontSize->14] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["EJERCICIO 5.4 (Una matriz real diagonalizable en \ \[DoubleStruckCapitalC])", FontColor->RGBColor[0, 0, 1]]], "SectionFirst", TextJustification->1, FontColor->RGBColor[1, 0, 1], Background->RGBColor[0.8, 1, 0.4]], Cell[CellGroupData[{ Cell[TextData[{ "Sea la matriz \n\t\t\t\t\t\t", Cell[BoxData[ RowBox[{"A", "=", TagBox[ RowBox[{"(", "\[NoBreak]\[NoBreak]", GridBox[{ {\(-1\), "1"}, {\(-1\), \(-1\)} }], ")"}], (MatrixForm[ #]&)]}]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], "\nDiagonalizar A en el cuerpo \[DoubleStruckCapitalC] de los \ n\[UAcute]meros complejos." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(\(a = {{\(-1\), 1}, {\(-1\), \(-1\)}};\)\)], "Input", CellLabel->"In[1]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \({valpropios, vecpropios} = Eigensystem[a]\)], "Input", CellLabel->"In[2]:=", FontSize->14], Cell[BoxData[ \({{\(-1\) + \[ImaginaryI], \(-1\) - \[ImaginaryI]}, \ {{\(-\[ImaginaryI]\), 1}, {\[ImaginaryI], 1}}}\)], "Output", CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(d = DiagonalMatrix[valpropios]; MatrixForm[d]\)], "Input", CellLabel->"In[3]:=", FontSize->14], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(-1\) + \[ImaginaryI]\), "0"}, {"0", \(\(-1\) - \[ImaginaryI]\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[3]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p = Transpose[vecpropios]; MatrixForm[p]\)], "Input", CellLabel->"In[4]:=", FontSize->14], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-\[ImaginaryI]\), "\[ImaginaryI]"}, {"1", "1"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[4]//MatrixForm="] }, Open ]], Cell[TextData[{ "Aunque no es necesario comprobamos que se cumple:\n\t\t\t\t\t\t\t\t", Cell[BoxData[ RowBox[{" ", StyleBox[\(A = P\[CenterDot]D\[CenterDot]P\^\(-1\)\), FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"]}]]], "\t\t\t\t\t\t\t" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a == p . d . Inverse[p]\)], "Input", CellLabel->"In[5]:=", FontSize->14], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[6]:=", FontSize->14] }, Open ]] }, Closed]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{0, 1024}, {0, 698}}, WindowSize->{748, 557}, WindowMargins->{{23, Automatic}, {Automatic, 0}}, StyleDefinitions -> "ArticleModern.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 228, 5, 90, "Title"], Cell[CellGroupData[{ Cell[2029, 62, 140, 2, 76, "SectionFirst"], Cell[2172, 66, 306, 8, 42, "Text"], Cell[2481, 76, 1315, 39, 91, "Text"], Cell[3799, 117, 293, 7, 42, "Text"], Cell[4095, 126, 193, 6, 43, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[4325, 137, 342, 9, 50, "SectionFirst"], Cell[CellGroupData[{ Cell[4692, 150, 930, 33, 153, "Subsubsection"], Cell[5625, 185, 62, 0, 24, "Text"], Cell[5690, 187, 130, 3, 43, "Input"], Cell[5823, 192, 112, 3, 43, "Input"], Cell[CellGroupData[{ Cell[5960, 199, 87, 3, 43, "Input"], Cell[6050, 204, 95, 2, 44, "Output"] }, Open ]], Cell[6160, 209, 215, 7, 26, "Text"], Cell[CellGroupData[{ Cell[6400, 220, 112, 3, 43, "Input"], Cell[6515, 225, 95, 2, 44, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[6659, 233, 280, 9, 46, "Subsubsection"], Cell[6942, 244, 320, 6, 40, "Text"], Cell[7265, 252, 3225, 95, 63, "Text"], Cell[10493, 349, 411, 10, 42, "Text"], Cell[CellGroupData[{ Cell[10929, 363, 87, 3, 43, "Input"], Cell[11019, 368, 77, 2, 42, "Output"] }, Open ]], Cell[11111, 373, 961, 26, 74, "Text"], Cell[CellGroupData[{ Cell[12097, 403, 88, 3, 43, "Input"], Cell[12188, 408, 96, 2, 42, "Output"] }, Open ]], Cell[12299, 413, 238, 7, 26, "Text"], Cell[CellGroupData[{ Cell[12562, 424, 87, 3, 43, "Input"], Cell[12652, 429, 130, 3, 42, "Output"] }, Open ]], Cell[12797, 435, 258, 5, 40, "Text"], Cell[13058, 442, 2511, 68, 120, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[15606, 515, 216, 8, 28, "Subsubsection"], Cell[15825, 525, 813, 23, 94, "Text"], Cell[16641, 550, 119, 3, 43, "Input"], Cell[CellGroupData[{ Cell[16785, 557, 103, 3, 43, "Input"], Cell[16891, 562, 101, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17029, 569, 87, 3, 43, "Input"], Cell[17119, 574, 400, 12, 84, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17556, 591, 114, 3, 43, "Input"], Cell[17673, 596, 397, 12, 84, "Output"] }, Open ]], Cell[18085, 611, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[18421, 624, 97, 3, 43, "Input"], Cell[18521, 629, 63, 2, 42, "Output"] }, Open ]], Cell[18599, 634, 2956, 85, 203, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[21592, 724, 496, 16, 29, "Subsubsection"], Cell[22091, 742, 226, 5, 24, "Text"], Cell[CellGroupData[{ Cell[22342, 751, 263, 7, 64, "Input"], Cell[22608, 760, 485, 10, 70, "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[23142, 776, 273, 9, 28, "Subsubsection"], Cell[23418, 787, 74, 0, 24, "Text"], Cell[CellGroupData[{ Cell[23517, 791, 97, 3, 43, "Input"], Cell[23617, 796, 64, 2, 70, "Output"] }, Open ]], Cell[23696, 801, 113, 3, 24, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[23846, 809, 439, 14, 47, "Subsubsection"], Cell[CellGroupData[{ Cell[24310, 827, 142, 4, 43, "Input"], Cell[24455, 833, 63, 2, 70, "Output"] }, Open ]], Cell[24533, 838, 102, 3, 43, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[24684, 847, 194, 3, 50, "SectionFirst"], Cell[CellGroupData[{ Cell[24903, 854, 882, 29, 153, "Subsubsection"], Cell[CellGroupData[{ Cell[25810, 887, 235, 5, 61, "Input"], Cell[26048, 894, 114, 2, 70, "Output"] }, Open ]], Cell[26177, 899, 3225, 95, 63, "Text"], Cell[29405, 996, 3310, 92, 139, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[32752, 1093, 352, 10, 46, "Subsubsection"], Cell[33107, 1105, 182, 4, 40, "Text"], Cell[33292, 1111, 252, 6, 61, "Input"], Cell[CellGroupData[{ Cell[33569, 1121, 144, 4, 43, "Input"], Cell[33716, 1127, 62, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33815, 1134, 121, 3, 43, "Input"], Cell[33939, 1139, 60, 2, 70, "Output"] }, Open ]], Cell[34014, 1144, 101, 3, 43, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[34164, 1153, 257, 5, 50, "SectionFirst"], Cell[CellGroupData[{ Cell[34446, 1162, 854, 32, 117, "Subsubsection"], Cell[35303, 1196, 116, 3, 24, "Text"], Cell[35422, 1201, 115, 3, 43, "Input"], Cell[CellGroupData[{ Cell[35562, 1208, 114, 3, 43, "Input"], Cell[35679, 1213, 114, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35830, 1220, 118, 3, 43, "Input"], Cell[35951, 1225, 393, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36381, 1242, 113, 3, 43, "Input"], Cell[36497, 1247, 399, 12, 70, "Output"] }, Open ]], Cell[36911, 1262, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[37247, 1275, 96, 3, 43, "Input"], Cell[37346, 1280, 62, 2, 70, "Output"] }, Open ]], Cell[37423, 1285, 4546, 137, 63, "Text"], Cell[41972, 1424, 3635, 104, 101, "Text"], Cell[45610, 1530, 3061, 89, 203, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[48708, 1624, 267, 9, 44, "Subsubsection"], Cell[48978, 1635, 705, 22, 62, "Text"], Cell[49686, 1659, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[49819, 1666, 101, 3, 43, "Input"], Cell[49923, 1671, 173, 4, 70, "Output"] }, Open ]], Cell[50111, 1678, 219, 6, 26, "Text"], Cell[CellGroupData[{ Cell[50355, 1688, 125, 3, 43, "Input"], Cell[50483, 1693, 62, 2, 70, "Output"] }, Open ]], Cell[50560, 1698, 283, 9, 44, "Text"], Cell[CellGroupData[{ Cell[50868, 1711, 94, 3, 43, "Input"], Cell[50965, 1716, 62, 2, 70, "Output"] }, Open ]], Cell[51042, 1721, 3120, 89, 283, "Text"], Cell[54165, 1812, 102, 3, 43, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[54316, 1821, 244, 5, 50, "SectionFirst"], Cell[CellGroupData[{ Cell[54585, 1830, 635, 21, 95, "Subsubsection"], Cell[55223, 1853, 113, 3, 43, "Input"], Cell[CellGroupData[{ Cell[55361, 1860, 114, 3, 43, "Input"], Cell[55478, 1865, 157, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[55672, 1873, 118, 3, 43, "Input"], Cell[55793, 1878, 400, 11, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[56230, 1894, 113, 3, 43, "Input"], Cell[56346, 1899, 381, 11, 70, "Output"] }, Open ]], Cell[56742, 1913, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[57078, 1926, 96, 3, 43, "Input"], Cell[57177, 1931, 62, 2, 70, "Output"] }, Open ]], Cell[57254, 1936, 101, 3, 43, "Input"] }, Open ]] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) Bold"], StyleBox[" ", FontWeight->"Bold"], "y utilizar estilos diferentes para cada una de las dos fucniones con \ objeto de identificarlas:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ StyleBox[\(v[x]\), FontColor->RGBColor[0, 1, 0]], ",", "vp"}], "}"}], ",", \({x, 0, 2 Pi}\), ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ StyleBox[\({Dashing[{0.04}], Thickness[0.01]}\), FontColor->RGBColor[0, 1, 0]], ",", \(Thickness[0.005]\)}], "}"}]}]}], "]"}], ";"}]], "Input", CellLabel->"In[10]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[10]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\omWI f@003ooIfMT00ol0003ofMWIomWIf@0JomWIf@03o`000?oIfMWofMWI063ofMWI00?o0000omWIfOoI fMT0S_oIfMT000oofMWI00?o0000omWIfOoIfMT06_oIfMT00ol0003ofMWIomWIf@1QomWIf@03o`00 0?oIfMWofMWI08gofMWI000?omWIf@03o`000?oIfMWofMWI01WofMWI00?o0000omWIfOoIfMT0HooI fMT00ol0003ofMWIomWIf@2omWIf@Co0000BooIfMT00ol0003ofMWI omWIf@0;omWIf@003ooIfMT2o`000:;ofMWI00?o0000omWIfOoIfMT03ooIfMT3o`0004[ofMWI00?o 0000omWIfOoIfMT02ooIfMT000oofMWI00?o0000omWIfOoIfMT0X_oIfMT00ol0003ofMWIomWIf@0? omWIf@Co0000AooIfMT00ol0003ofMWIomWIf@07ofMWI0ol0000Z omWIf@003ooIfMT00ol0003ofMWIomWIf@3RomWIf@?o0000:OoIfMT00004omWIfOl0003o0000o`00 00CofMWI0_l00005omWIf@03o`000?oIfMWofMWI0>?ofMWI0ol0000XomWIf@0000Go0000omWIfOoI fMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0i?oIfMT2 o`0002SofMWI0004omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT0 0ol0003ofMWIomWIf@3TomWIf@?o00009ooIfMT000;ofMWI0_l00003omWIf@04o`000?oIfMWofMWI o`0000CofMWI0ol0003UomWIf@?o00009_oIfMT000CofMWI00Co0000omWIfOoIfMWo00000_oIfMT0 0ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0>KofMWI0ol0000UomWIf@0000Go0000omWI fOoIfMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0iooI fMT3o`0002CofMWI00001?oIfMWo0000o`000?l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWI f@3XomWIf@;o00009?oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT?omWIf@003ooIfMT00ol0 003ofMWIomWIf@3oomWIf@oofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI 00?o0000omWIfOoIfMT0oooIfMT?omWIf@003ooIfMT2o`000?oofMWI4?oIfMT000oofMWI00?o0000 omWIfOoIfMT0oooIfMT?omWIf@003ooIfMT00ol0003ofMWIomWIf@3`omWIf@;o00007?oIfMT000oo fMWI00?o0000omWIfOoIfMT0l?oIfMT2o`0001cofMWI000?omWIf@03o`000?oIfMWofMWI0?3ofMWI 0ol0000KomWIf@003ooIfMT00ol0003ofMWIomWIf@3aomWIf@?o00006_oIfMT000oofMWI00?o0000 omWIfOoIfMT0l_oIfMT3o`0001WofMWI000?omWIf@03o`000?oIfMWofMWI0??ofMWI0ol0000HomWI f@003ooIfMT2o`000?GofMWI0_l0000HomWIf@003ooIfMT00ol0003ofMWIomWIf@3domWIf@?o0000 5ooIfMT000oofMWI00?o0000omWIfOoIfMT0mOoIfMT3o`0001KofMWI000?omWIf@03o`000?oIfMWo fMWI0?KofMWI0ol0000EomWIf@003ooIfMT00ol0003ofMWIomWIf@3gomWIf@;o00005OoIfMT000oo fMWI00?o0000omWIfOoIfMT0oooIfMT?omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@oofMWI 000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT? omWIf@003ooIfMT2o`000?oofMWI4?oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT?omWIf@00 3ooIfMT00ol0003ofMWIomWIf@3nomWIf@;o00003_oIfMT000oofMWI00?o0000omWIfOoIfMT0o_oI fMT2o`0000kofMWI000?omWIf@03o`000?oIfMWofMWI0?kofMWI0ol0000=omWIf@003ooIfMT00ol0 003ofMWIomWIf@3oomWIf@?o00003?oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT1omWIf@?o 00002ooIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT2omWIf@?o00002_oIfMT000oofMWI0_l0 003oomWIf@CofMWI0ol00009omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@CofMWI0ol00008 omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@GofMWI0ol00007omWIf@003ooIfMT00ol0003o fMWIomWIf@3oomWIf@KofMWI0_l00007omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@oofMWI 000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT? omWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.12112, \ 0.0237193, 0.241311}}] }, Open ]], Cell[TextData[{ "Aunque nos puede resultar m\[AAcute]s c\[OAcute]modo dibujrlas por \ separado con colores distintos y utilizar posteriormente la funci\[OAcute]n \ ", StyleBox["Show", FontFamily->"Courier", FontWeight->"Bold"], " para mostrar las dos gr\[AAcute]ficas juntas:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(gv = Plot[v[x], {x, 0, 2 Pi}, PlotStyle \[Rule] Thickness[0.01]];\)\)], "Input", CellLabel->"In[11]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[11]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\ omWIfA_o0000mooIfMT000oofMWI00?o0000omWIfOoIfMT01ooIfMTFo`000?7ofMWI000?omWIf@03 o`000?oIfMWofMWI01KofMWI3?l0003/omWIf@002?oIfMWoo`0001Wo0000000?omWIf@03o`000?oI fMWofMWI00GofMWI00?o0000omWIfOoIfMT01_oIfMT00ol0003ofMWIomWIf@05omWIf@03o`000?oI fMWofMWI00KofMWI00?o0000omWIfOl000002ol00003omWIf@03o`000?oIfMWofMWI00GofMWI00?o 0000omWIfOoIfMT01OoIfMT00ol0003ofMWIomWIf@06omWIf@03o`000?oIfMWofMWI00GofMWI00?o 0000omWIfOoIfMT01_oIfMT00ol0003ofMWIomWIf@05omWIf@03o`000?oIfMWofMWI00KofMWI00?o 0000omWIfOoIfMT01OoIfMT00ol0003ofMWIomWIf@05omWIf@03o`000?oIfMWofMWI00KofMWI00?o 0000omWIfOoIfMT01OoIfMT00ol0003ofMWIomWIf@06omWIf@03o`000?oIfMWofMWI00GofMWI00?o 0000omWIfOoIfMT01_oIfMT00ol0003ofMWIomWIf@05omWIf@03o`000?oIfMWofMWI00GofMWI00?o 0000omWIfOoIfMT01_oIfMT00ol0003ofMWIomWIf@05omWIf@03o`000?oIfMWofMWI00KofMWI00?o 0000omWIfOoIfMT01OoIfMT00ol0003ofMWIomWIf@06omWIf@03o`000?oIfMWofMWI00GofMWI00?o 0000omWIfOoIfMT01_oIfMT00ol0003ofMWIomWIf@05omWIf@03o`000?oIfMWofMWI00GofMWI00?o 0000omWIfOoIfMT01_oIfMT1o`00007ofMWI0OoIfMT000oofMWI00?o0000omWIfOoIfMT09ooIfMT: o`00023ofMWI00?o0000omWIfOoIfMT09ooIfMT00ol0003ofMWIomWIf@0XomWIf@03o`000?oIfMWo fMWI02OofMWI00?o0000omWIfOoIfMT09ooIfMT00ol0003ofMWIomWIf@0AomWIf@003ooIfMT00ol0 003ofMWIomWIf@0/omWIf@So0000f_oIfMT000oofMWI00?o0000omWIfOoIfMT0ooIfMT7o`000OoIfMT000oofMWI00?o0000omWIfOoIfMT0dooIfMT3o`0003SofMWI000? omWIf@03o`000?oIfMWofMWI0=CofMWI0ol0000gomWIf@003ooIfMT2o`000=KofMWI0ol0000fomWI f@003ooIfMT00ol0003ofMWIomWIf@3FomWIf@?o0000=OoIfMT000oofMWI00?o0000omWIfOoIfMT0 eooIfMT3o`0003CofMWI000?omWIf@03o`000?oIfMWofMWI0=SofMWI0ol0000comWIf@003ooIfMT0 0ol0003ofMWIomWIf@3IomWIf@?o0000<_oifmt000oofmwi00 omwif f hooifmt3o>;ofMWI0ol0000YomWIf@0000CofMWI o`000?l0003o00001?oIfMT2o`0000GofMWI00?o0000omWIfOoIfMT0hooIfMT3o`0002SofMWI0000 1Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWI omWIf@3TomWIf@;o0000:?oIfMT000CofMWI00Co0000omWIfOoIfMWo00000_oIfMT00ol0003ofMWI omWIf@02omWIf@03o`000?oIfMWofMWI0>CofMWI0ol0000WomWIf@000_oIfMT2o`0000?ofMWI00Co 0000omWIfOoIfMWo00001?oIfMT3o`000>GofMWI0ol0000VomWIf@001?oIfMT01?l0003ofMWIomWI fOl00002omWIf@03o`000?oIfMWofMWI00;ofMWI00?o0000omWIfOoIfMT0i_oIfMT3o`0002GofMWI 00001Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003o fMWIomWIf@3WomWIf@?o00009?oIfMT00004omWIfOl0003o0000o`0000CofMWI0_l00005omWIf@03 o`000?oIfMWofMWI0>SofMWI0ol0000SomWIf@003ooIfMT00ol0003ofMWIomWIf@3YomWIf@?o0000 8_oIfMT000oofMWI00?o0000omWIfOoIfMT0j_oIfMT3o`00027ofMWI000?omWIf@03o`000?oIfMWo fMWI0>_ofMWI0ol0000PomWIf@003ooIfMT00ol0003ofMWIomWIf@3/omWIf@?o00007ooIfMT000oo fMWI0_l0003^omWIf@?o00007_oIfMT000oofMWI00?o0000omWIfOoIfMT0k_oIfMT3o`0001gofMWI 000?omWIf@03o`000?oIfMWofMWI0>oofMWI0ol0000LomWIf@003ooIfMT00ol0003ofMWIomWIf@3` omWIf@;o00007?oIfMT000oofMWI00?o0000omWIfOoIfMT0l?oIfMT3o`0001_ofMWI000?omWIf@03 o`000?oIfMWofMWI0?7ofMWI0ol0000JomWIf@003ooIfMT00ol0003ofMWIomWIf@3bomWIf@?o0000 6OoIfMT000oofMWI00?o0000omWIfOoIfMT0looIfMT3o`0001SofMWI000?omWIf@;o0000mOoIfMT3 o`0001OofMWI000?omWIf@03o`000?oIfMWofMWI0?GofMWI0ol0000FomWIf@003ooIfMT00ol0003o fMWIomWIf@3fomWIf@?o00005OoIfMT000oofMWI00?o0000omWIfOoIfMT0mooIfMT3o`0001CofMWI 000?omWIf@03o`000?oIfMWofMWI0?SofMWI0ol0000ComWIf@003ooIfMT00ol0003ofMWIomWIf@3i omWIf@?o00004_oIfMT000oofMWI00?o0000omWIfOoIfMT0n_oIfMT3o`00017ofMWI000?omWIf@03 o`000?oIfMWofMWI0?_ofMWI0_l0000AomWIf@003ooIfMT00ol0003ofMWIomWIf@3komWIf@?o0000 4?oIfMT000oofMWI0_l0003momWIf@?o00003ooIfMT000oofMWI00?o0000omWIfOoIfMT0oOoIfMT3 o`0000kofMWI000?omWIf@03o`000?oIfMWofMWI0?kofMWI0_l0000>omWIf@003ooIfMT00ol0003o fMWIomWIf@3nomWIf@?o00003OoIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT3o`0000cofMWI 000?omWIf@03o`000?oIfMWofMWI0?oofMWI0OoIfMT3o`0000_ofMWI000?omWIf@03o`000?oIfMWo fMWI0?oofMWI0_oIfMT3o`0000[ofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI0ooIfMT2o`00 00[ofMWI000?omWIf@;o0000oooIfMT4omWIf@?o00002OoIfMT000oofMWI00?o0000omWIfOoIfMT0 oooIfMT4omWIf@?o00002?oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT5omWIf@?o00001ooI fMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT6omWIf@;o00001ooIfMT000oofMWI00?o0000omWI fOoIfMT0oooIfMT?omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@oofMWI000?omWIf@03o`00 0?oIfMWofMWI0?oofMWI3ooIfMT00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.10524, \ 0.0237193, 0.24114}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(gvp = Plot[vp, {x, 0, 2 Pi}, PlotStyle \[Rule] {RGBColor[0, 1, 0], Thickness[0.01]}];\)\)], "Input", CellLabel->"In[13]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[13]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\?oIfMT3o`3o0:?ofMWI000?omWIf@03o`000?oIfMWo fMWI02gofMWI0ol0o`0iomWIf@?o0?l0X_oIfMT000oofMWI00?o0000omWIfOoIfMT0;?oIfMT3o`3o 03_ofMWI0ol0o`2QomWIf@003ooIfMT00ol0003ofMWIomWIf@0[omWIf@?o0?l0?OoIfMT2o`3o0:7o fMWI000?omWIf@03o`000?oIfMWofMWI02_ofMWI0_l0o`0nomWIf@?o0?l0X?oIfMT000oofMWI0_l0 000[omWIf@?o0?l0?ooIfMT3o`3o09oofMWI000?omWIf@03o`000?oIfMWofMWI02WofMWI0ol0o`11 omWIf@;o0?l0WooIfMT000oofMWI00?o0000omWIfOoIfMT0:?oIfMT3o`3o04;ofMWI0ol0o`2NomWI f@003ooIfMT00ol0003ofMWIomWIf@0XomWIf@;o0?l0A?oIfMT3o`3o09gofMWI000?omWIf@03o`00 0?oIfMWofMWI02OofMWI0ol0o`15omWIf@;o0?l0WOoIfMT000oofMWI00?o0000omWIfOoIfMT09_oI fMT3o`3o04KofMWI0ol0o`2LomWIf@003ooIfMT2o`0002OofMWI0_l0o`18omWIf@?o0?l0VooIfMT0 00oofMWI00?o0000omWIfOoIfMT09OoIfMT3o`3o04WofMWI0_l0o`2KomWIf@003ooIfMT00ol0003o fMWIomWIf@0TomWIf@?o0?l0B_oIfMT3o`3o09[ofMWI000?omWIf@03o`000?oIfMWofMWI02CofMWI 0_l0o`1omWIf@?o0?l0V?oIfMT000[ofMWI00?o0000omWIfOoIfMT00_oIfMT0 0ol0003ofMWIomWIf@0RomWIf@;o0?l0D?oIfMT2o`3o09SofMWI000:omWIf@03o`000?oIfMWofMWI 00;ofMWI0ol0000QomWIf@?o0?l0D?oIfMT3o`3o09OofMWI0006omWIf@Co00001OoIfMT00ol0003o fMWIomWIf@0QomWIf@;o0?l0D_oIfMT3o`3o09KofMWI0006omWIf@03o`000?oIfMWofMWI00KofMWI 00?o0000omWIfOoIfMT08?oIfMT3o`3o05?ofMWI0_l0o`2FomWIf@001_oIfMT5o`0000CofMWI00?o 0000omWIfOoIfMT07ooIfMT3o`3o05CofMWI0ol0o`2EomWIf@003ooIfMT00ol0003ofMWIomWIf@0O omWIf@;o0?l0E_oIfMT2o`3o09GofMWI000?omWIf@03o`000?oIfMWofMWI01kofMWI0ol0o`1FomWI f@?o0?l0U?oIfMT000oofMWI0_l0000NomWIf@?o0?l0F?oIfMT3o`3o09?ofMWI000?omWIf@03o`00 0?oIfMWofMWI01gofMWI0_l0o`1JomWIf@;o0?l0TooIfMT000oofMWI00?o0000omWIfOoIfMT07?oI fMT3o`3o05[ofMWI0ol0o`2BomWIf@003ooIfMT00ol0003ofMWIomWIf@0LomWIf@;o0?l0G?oIfMT2 o`3o09;ofMWI000?omWIf@03o`000?oIfMWofMWI01_ofMWI0ol0o`1LomWIf@?o0?l0TOoIfMT000oo fMWI00?o0000omWIfOoIfMT06ooIfMT2o`3o05kofMWI0ol0o`2@omWIf@003ooIfMT2o`0001_ofMWI 0ol0o`1OomWIf@;o0?l0T?oIfMT000oofMWI00?o0000omWIfOoIfMT06OoIfMT3o`3o063ofMWI0ol0 o`2?omWIf@003ooIfMT00ol0003ofMWIomWIf@0IomWIf@;o0?l0H_oIfMT2o`3o08oofMWI000?omWI f@03o`000?oIfMWofMWI01SofMWI0ol0o`1RomWIf@?o0?l0S_oIfMT000oofMWI00?o0000omWIfOoI fMT06?oIfMT2o`3o06CofMWI0_l0o`2>omWIf@003ooIfMT00ol0003ofMWIomWIf@0GomWIf@?o0?l0 I?oIfMT3o`3o08gofMWI000?omWIf@;o00006?oIfMT2o`3o06KofMWI0ol0o`2omWIf@?o0?l0N?oIfMT000oofMWI 00?o0000omWIfOoIfMT00_oIfMT3o`3o08oofMWI0_l0o`1homWIf@0000CofMWIo`000?l0003o0000 0ooIfMT3o`0000GofMWI00Co0000omWIfOoIfMWofMWI0ol0o`2@omWIf@?o0?l0MooIfMT000;ofMWI 00Go0000omWIfOoIfMWofMWIo`000003omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoI fMWofMWI0_l0o`2BomWIf@;o0?l0MooIfMT000;ofMWI00?o0000omWIfOoIfMT01OoIfMT00ol0003o fMWIomWIf@02omWIf@03o`000?oIfMWofMWI00?o0?l0T_oIfMT3o`3o07KofMWI0002omWIf@03o`00 0?oIfMWofMWI00GofMWI00?o0000omWIfOoIfMT00_oIfMT3o`0000;o0?l0U?oIfMT2o`3o07KofMWI 0002omWIf@04o`000?oIfMWofMWIomWIf@Co00001OoIfMT00ol0003ofMWIo`3o0002o`3o09CofMWI 0ol0o`1eomWIf@0000?ofMWIo`000?l000000ooIfMT00ol0003ofMWIomWIf@06omWIf@04o`000?oI fMWo0?l0o`3o09KofMWI0_l0o`1eomWIf@000_oIfMT01?l0003ofMWIomWIfOoIfMT5o`0000CofMWI 00Co0000o`3o0?l0o`3o0?l0U_oIfMT3o`3o07CofMWI000?omWIf@03o`000?l0o`3o0?l009SofMWI 0_l0o`1domWIf@003ooIfMT3o`3o09SofMWI0ol0o`1comWIf@003ooIfMT2o`3o09[ofMWI0ol0o`1b omWIf@003_oIfMT3o`3o09_ofMWI0_l0o`1YomWIf@;o0?l01ooIfMT000kofMWI0_l0o`2LomWIf@?o 0?l0J?oIfMT2o`3o00OofMWI000?omWIf@03o`000?oIfMWofMWI09_ofMWI0_l0o`1WomWIf@?o0?l0 1ooIfMT000oofMWI00?o0000omWIfOoIfMT0VooIfMT3o`3o06KofMWI0_l0o`08omWIf@003ooIfMT0 0ol0003ofMWIomWIf@2LomWIf@?o0?l0I?oIfMT3o`3o00SofMWI000?omWIf@;o0000W_oIfMT2o`3o 06?ofMWI0ol0o`09omWIf@003ooIfMT00ol0003ofMWIomWIf@2MomWIf@?o0?l0H_oIfMT2o`3o00[o fMWI000?omWIf@03o`000?oIfMWofMWI09kofMWI0_l0o`1QomWIf@?o0?l02_oIfMT000oofMWI00?o 0000omWIfOoIfMT0W_oIfMT3o`3o063ofMWI0_l0o`0;omWIf@003ooIfMT00ol0003ofMWIomWIf@2O omWIf@;o0?l0GooIfMT3o`3o00_ofMWI000?omWIf@03o`000?oIfMWofMWI09oofMWI0ol0o`1MomWI f@?o0?l03?oIfMT000oofMWI0_l0002QomWIf@?o0?l0G?oIfMT2o`3o00gofMWI000?omWIf@03o`00 0?oIfMWofMWI0:7ofMWI0_l0o`1KomWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoI fMT3o`3o05[ofMWI0_l0o`0>omWIf@003ooIfMT00ol0003ofMWIomWIf@2RomWIf@;o0?l0FOoIfMT3 o`3o00kofMWI000?omWIf@03o`000?oIfMWofMWI0:;ofMWI0ol0o`1HomWIf@;o0?l03ooIfMT000oo fMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o05KofMWI0ol0o`0?omWIf@003ooIfMT2o`000:GofMWI 0_l0o`1EomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o05CofMWI0_l0 o`0AomWIf@003ooIfMT00ol0003ofMWIomWIf@2UomWIf@;o0?l0DooIfMT3o`3o017ofMWI000?omWI f@03o`000?oIfMWofMWI0:GofMWI0ol0o`1BomWIf@;o0?l04_oIfMT000Go00000ooIfMT2o`0000Go fMWI00?o0000omWIfOoIfMT0Y_oIfMT3o`3o053ofMWI0ol0o`0BomWIf@0000GofMWIo`000?oIfMWo fMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0YooIfMT2o`3o 04oofMWI0ol0o`0ComWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWIo`00 00CofMWI00?o0000omWIfOoIfMT0YooIfMT3o`3o04kofMWI0_l0o`0DomWIf@000ooIfMT01Ol0003o fMWIomWIfOoIfMWo000000;ofMWI00?o0000omWIfOoIfMT00_oIfMT3o`000:SofMWI0_l0o`1=omWI f@?o0?l05?oIfMT00005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004 omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`1;omWIf@?o0?l05OoIfMT00005o`000?oIfMWofMWI omWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:WofMWI0ol0 o`1:omWIf@;o0?l05_oIfMT00004omWIfOl0003o0000o`0000CofMWI0_l00005omWIf@03o`000?oI fMWofMWI0:[ofMWI0_l0o`19omWIf@?o0?l05_oIfMT000oofMWI00?o0000omWIfOoIfMT0Z_oIfMT3 o`3o04OofMWI0ol0o`0GomWIf@003ooIfMT00ol0003ofMWIomWIf@2[omWIf@;o0?l0A_oIfMT3o`3o 01SofMWI000?omWIf@;o0000[?oIfMT3o`3o04GofMWI0_l0o`0IomWIf@003ooIfMT00ol0003ofMWI omWIf@2/omWIf@?o0?l0@ooIfMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI0_l0 o`12omWIf@?o0?l06_oIfMT000oofMWI00?o0000omWIfOoIfMT0[OoIfMT3o`3o047ofMWI0_l0o`0K omWIf@003ooIfMT00ol0003ofMWIomWIf@2^omWIf@?o0?l0?ooIfMT3o`3o01_ofMWI000?omWIf@03 o`000?oIfMWofMWI0:oofMWI0ol0o`0momWIf@?o0?l07?oIfMT000oofMWI0_l0002aomWIf@;o0?l0 ?OoIfMT2o`3o01gofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0komWIf@?o0?l07OoI fMT000oofMWI00?o0000omWIfOoIfMT0/OoIfMT3o`3o03WofMWI0ol0o`0NomWIf@003ooIfMT00ol0 003ofMWIomWIf@2bomWIf@?o0?l0=ooIfMT3o`3o01oofMWI000?omWIf@03o`000?oIfMWofMWI0;?o fMWI0_l0o`0fomWIf@?o0?l08?oIfMT000oofMWI00?o0000omWIfOoIfMT0/ooIfMT3o`3o03CofMWI 0ol0o`0QomWIf@003ooIfMT2o`000;GofMWI0ol0o`0bomWIf@?o0?l08_oIfMT000oofMWI00?o0000 omWIfOoIfMT0]OoIfMT3o`3o033ofMWI0ol0o`0SomWIf@003ooIfMT00ol0003ofMWIomWIf@2fomWI f@?o0?l0;_oIfMT3o`3o02CofMWI000?omWIf@03o`000?oIfMWofMWI0;OofMWI1?l0o`0[omWIf@?o 0?l09OoIfMT000oofMWI00?o0000omWIfOoIfMT0^?oIfMT4o`3o02WofMWI0ol0o`0VomWIf@003ooI fMT00ol0003ofMWIomWIf@2jomWIf@?o0?l09_oIfMT4o`3o02OofMWI000?omWIf@03o`000?oIfMWo fMWI0;_ofMWI0ol0o`0TomWIf@Co0?l0:?oIfMT000oofMWI0_l0002momWIf@?o0?l08_oIfMT3o`3o 02[ofMWI000?omWIf@03o`000?oIfMWofMWI0;gofMWI1?l0o`0OomWIf@?o0?l0:ooIfMT000oofMWI 00?o0000omWIfOoIfMT0__oIfMT5o`3o01cofMWI0ol0o`0/omWIf@001Ol00002omWIf@?o00001OoI fMT00ol0003ofMWIomWIf@30omWIf@Co0?l06OoIfMT4o`3o02gofMWI00001ooIfMWo0000omWIfOoI fMWo0000omWIfOl000000ooIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0OoIfMT000oofMWI00?o0000omWIfOoIfMT0oooI fMT?omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@oofMWI000?omWIf@;o0000oooIfMT@omWI f@00oooIfMTQomWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -2.25451, \ 0.0237193, 0.161104}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[gv, gvp];\)\)], "Input", CellLabel->"In[14]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[14]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\omWIf@?o0?l0UooIfMT000oofMWI00?o0000omWIfOoIfMT08?oI fMT3o`3o043ofMWI1Ol0000=omWIf@?o0?l0U_oIfMT000oofMWI00?o0000omWIfOoIfMT07ooIfMT3 o`3o04?ofMWI1Ol0000omWIf@003ooIfMT0 0ol0003ofMWIomWIf@0GomWIf@?o0?l0G_oIfMT4o`0000;ofMWI0ol0o`2=omWIf@003ooIfMT2o`00 01OofMWI0ol0o`1PomWIf@Go000000CofMWIo`3o0?l0o`3o0?l0S?oIfMT000oofMWI00?o0000omWI fOoIfMT05_oIfMT2o`3o06?ofMWI1?l000001?oIfMWo0?l0o`3o0?l0o`2;omWIf@003ooIfMT00ol0 003ofMWIomWIf@0EomWIf@?o0?l0IOoIfMT4o`0000;o0?l0RooIfMT000oofMWI00?o0000omWIfOoI fMT05?oIfMT3o`3o06OofMWI0ol00003o`3o08[ofMWI000?omWIf@03o`000?oIfMWofMWI01?ofMWI 0ol0o`1ZomWIf@;o00000ol0o`29omWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI 00?o0000omWIfOoIfMT04_oIfMT3o`3o06cofMWI0_l00003o`3o08SofMWI0002omWIf@03o`000?oI fMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@0BomWIf@;o0?l0 KooIfMT01?l0003o0?l0o`3o0?l0o`27omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`00 0?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT04OoIfMT3o`3o073ofMWI00?o0000o`3o0?l0 o`000_l00025omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWIo`0000Co fMWI0ol0000@omWIf@?o0?l0L_oIfMT3o`3o00;o0000Q?oIfMT000;ofMWI00?o0000omWIfOoIfMT0 0_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI00oofMWI0ol0o`1domWIf@?o 0?l00ol00022omWIf@0000?ofMWIo`000?l000001?oIfMT01?l0003ofMWIomWIfOl00004omWIf@03 o`000?oIfMWofMWI00oofMWI0_l0o`1fomWIf@?o0?l00ol00021omWIf@000_oIfMT00ol0003ofMWI omWIf@03omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@0>omWIf@?o0?l0MooIfMT2o`3o0003omWI fOl0003o000000;o0000OooIfMT000oofMWI00?o0000omWIfOoIfMT03OoIfMT3o`3o07SofMWI0ol0 o`000ooIfMWo0000o`000002o`0007kofMWI000?omWIf@03o`000?oIfMWofMWI00cofMWI0ol0o`1j omWIf@?o0?l00_oIfMT4o`0007cofMWI000?omWIf@03o`000?oIfMWofMWI00cofMWI0_l0o`1lomWI f@?o0?l00_oIfMT4o`0007_ofMWI000?omWIf@03o`000?oIfMWofMWI00_ofMWI0ol0o`1momWIf@?o 0?l00ooIfMT4o`0007WofMWI000?omWIf@;o00002ooIfMT3o`3o07oofMWI0_l0o`04omWIf@Co0000 N?oIfMT000oofMWI00?o0000omWIfOoIfMT02_oIfMT2o`3o083ofMWI0ol0o`05omWIf@Co0000M_oI fMT000oofMWI00?o0000omWIfOoIfMT02OoIfMT3o`3o087ofMWI0ol0o`05omWIf@Co0000MOoIfMT0 00oofMWI00?o0000omWIfOoIfMT02?oIfMT3o`3o08?ofMWI0ol0o`06omWIf@Co0000LooIfMT000oo fMWI00?o0000omWIfOoIfMT01ooIfMT3o`3o08GofMWI0_l0o`07omWIf@Co0000L_oIfMT000oofMWI 00?o0000omWIfOoIfMT01ooIfMT2o`3o08KofMWI0ol0o`08omWIf@?o0000LOoIfMT000oofMWI00?o 0000omWIfOoIfMT01_oIfMT3o`3o08OofMWI0ol0o`08omWIf@Co0000KooIfMT000oofMWI00?o0000 omWIfOoIfMT01OoIfMT3o`3o08WofMWI0ol0o`08omWIf@Co0000K_oIfMT000oofMWI00?o0000omWI fOoIfMT01?oIfMT3o`3o08_ofMWI0_l0o`0:omWIf@Co0000K?oIfMT000oofMWI0_l00004omWIf@?o 0?l0S?oIfMT3o`3o00[ofMWI1?l0001[omWIf@003ooIfMT00ol0003ofMWIomWIf@02omWIf@?o0?l0 S_oIfMT3o`3o00_ofMWI0ol0001ZomWIf@003ooIfMT01?l0003ofMWIomWIfOoIfMT3o`3o093ofMWI 0_l0o`0omWIf@?o0000HooIfMT000kofMWI0ol0o`2IomWIf@?o0?l03_oIfMT3o`0005Wo fMWI0_l0o`07omWIf@003_oIfMT2o`3o09_ofMWI0ol0o`0>omWIf@?o0000F?oIfMT2o`3o00OofMWI 000?omWIf@03o`000?oIfMWofMWI09[ofMWI0ol0o`0>omWIf@?o0000E_oIfMT3o`3o00OofMWI000? omWIf@03o`000?oIfMWofMWI09_ofMWI0ol0o`0>omWIf@Co0000DooIfMT3o`3o00SofMWI000?omWI f@03o`000?oIfMWofMWI09cofMWI0ol0o`0>omWIf@Co0000DOoIfMT3o`3o00WofMWI000?omWIf@03 o`000?oIfMWofMWI09gofMWI0_l0o`0@omWIf@?o0000CooIfMT3o`3o00[ofMWI000?omWIf@03o`00 0?oIfMWofMWI09gofMWI0ol0o`0@omWIf@Co0000C?oIfMT3o`3o00_ofMWI000?omWIf@03o`000?oI fMWofMWI09kofMWI0ol0o`0@omWIf@Co0000B_oIfMT3o`3o00cofMWI000?omWIf@;o0000X?oIfMT3 o`3o017ofMWI0ol00019omWIf@;o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0X?oIfMT3o`3o 017ofMWI1?l00016omWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoIfMT3o`3o017o fMWI1?l00014omWIf@?o0?l03_oIfMT000oofMWI00?o0000omWIfOoIfMT0X_oIfMT3o`3o01;ofMWI 0ol00012omWIf@?o0?l03ooIfMT000oofMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o01;ofMWI1?l0 000oomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o01;ofMWI1?l0000m omWIf@?o0?l04OoIfMT000Go00000ooIfMT2o`0000GofMWI00?o0000omWIfOoIfMT0YOoIfMT3o`3o 01?ofMWI0ol0000komWIf@?o0?l04_oIfMT00005omWIfOl0003ofMWIomWIfOl000000_oIfMT01?l0 003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:KofMWI0ol0o`0ComWIf@?o0000>OoIfMT3 o`3o01?ofMWI0002omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT3 o`000:OofMWI0ol0o`0ComWIf@?o0000=ooIfMT3o`3o01CofMWI0003omWIf@05o`000?oIfMWofMWI omWIfOl000000_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`0C omWIf@?o0000=OoIfMT3o`3o01GofMWI00001Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000 omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@2YomWIf@?o0?l04ooIfMT3o`0003?ofMWI0ol0 o`0FomWIf@0000Go0000omWIfOoIfMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI 00?o0000omWIfOoIfMT0Z_oIfMT3o`3o01?ofMWI0ol0000aomWIf@?o0?l05ooIfMT00004omWIfOl0 003o0000o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI0:_ofMWI0ol0o`0ComWIf@?o0000 ;ooIfMT3o`3o01SofMWI000?omWIf@03o`000?oIfMWofMWI0:cofMWI1?l0o`0BomWIf@?o0000;OoI fMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI1?l0o`0BomWIf@?o0000:ooIfMT3 o`3o01[ofMWI000?omWIf@03o`000?oIfMWofMWI0:oofMWI0ol0o`0BomWIf@?o0000:OoIfMT3o`3o 01_ofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0BomWIf@?o00009_oIfMT4o`3o01co fMWI000?omWIf@;o0000/_oIfMT3o`3o01;ofMWI0ol0000TomWIf@Co0?l07OoIfMT000oofMWI00?o 0000omWIfOoIfMT0/_oIfMT4o`3o017ofMWI0ol0000RomWIf@?o0?l07ooIfMT000oofMWI00?o0000 omWIfOoIfMT0/ooIfMT4o`3o017ofMWI0ol0000OomWIf@Co0?l08?oIfMT000oofMWI00?o0000omWI fOoIfMT0]OoIfMT3o`3o017ofMWI0ol0000MomWIf@Co0?l08OoIfMT000oofMWI00?o0000omWIfOoI fMT0]_oIfMT3o`3o017ofMWI0ol0000JomWIf@Co0?l08ooIfMT000oofMWI00?o0000omWIfOoIfMT0 ]ooIfMT4o`3o013ofMWI0ol0000HomWIf@Co0?l09?oIfMT000oofMWI00?o0000omWIfOoIfMT0^?oI fMT4o`3o013ofMWI0ol0000FomWIf@?o0?l09_oIfMT000oofMWI00?o0000omWIfOoIfMT0^_oIfMT4 o`3o00oofMWI0ol0000ComWIf@Co0?l09ooIfMT000oofMWI0_l0002lomWIf@Co0?l03ooIfMT2o`00 017ofMWI1Ol0o`0XomWIf@003ooIfMT00ol0003ofMWIomWIf@2momWIf@Co0?l03OoIfMT3o`0000ko fMWI1Ol0o`0ZomWIf@003ooIfMT00ol0003ofMWIomWIf@2nomWIf@Ko0?l02ooIfMT3o`0000_ofMWI 1Ol0o`0/omWIf@003ooIfMT00ol0003ofMWIomWIf@30omWIf@Oo0?l02OoIfMT3o`0000SofMWI1Ol0 o`0^omWIf@003ooIfMT00ol0003ofMWIomWIf@33omWIf@Oo0?l01ooIfMT3o`0000CofMWI1_l0o`0` omWIf@003ooIfMT00ol0003ofMWIomWIf@36omWIf@[o0?l000?ofMWIo`3o0?l0o`002Ol0o`0bomWI f@003ooIfMT00ol0003ofMWIomWIf@39omWIfA3o0?l0=OoIfMT000oofMWI00?o0000omWIfOoIfMT0 c_oIfMT5o`3o0004omWIfOl0003o0000o`0003OofMWI000?omWIf@;o0000e_oIfMT3o`0003KofMWI 000?omWIf@03o`000?oIfMWofMWI0=KofMWI0ol0000eomWIf@003ooIfMT00ol0003ofMWIomWIf@3G omWIf@?o0000=?oIfMT000oofMWI00?o0000omWIfOoIfMT0f?oIfMT3o`0003?ofMWI000?omWIf@03 o`000?oIfMWofMWI0=WofMWI0ol0000bomWIf@003ooIfMT00ol0003ofMWIomWIf@3JomWIf@?o0000 3ofMWI0ol0000[omWIf@003ooIfMT00ol0003ofMWIomWIf@3Q omWIf@?o0000:_oIfMT000oofMWI00?o0000omWIfOoIfMT0h_oIfMT3o`0002WofMWI00001?oIfMWo 0000o`000?l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@3SomWIf@?o0000:?oIfMT00005 o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWo fMWI0>CofMWI0_l0000XomWIf@001?oIfMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWo fMWI00;ofMWI00?o0000omWIfOoIfMT0i?oIfMT3o`0002OofMWI0002omWIf@;o00000ooIfMT01?l0 003ofMWIomWIfOl00004omWIf@?o0000iOoIfMT3o`0002KofMWI0004omWIf@04o`000?oIfMWofMWI o`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWIomWIf@3VomWIf@?o00009OoIfMT0 0005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oI fMWofMWI0>OofMWI0ol0000TomWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI00?o 0000omWIfOoIfMT0j?oIfMT3o`0002?ofMWI000?omWIf@03o`000?oIfMWofMWI0>WofMWI0ol0000R omWIf@003ooIfMT00ol0003ofMWIomWIf@3ZomWIf@?o00008OoIfMT000oofMWI00?o0000omWIfOoI fMT0jooIfMT3o`00023ofMWI000?omWIf@03o`000?oIfMWofMWI0>cofMWI0ol0000OomWIf@003ooI fMT2o`000>kofMWI0ol0000NomWIf@003ooIfMT00ol0003ofMWIomWIf@3^omWIf@?o00007OoIfMT0 00oofMWI00?o0000omWIfOoIfMT0kooIfMT3o`0001cofMWI000?omWIf@03o`000?oIfMWofMWI0?3o fMWI0_l0000LomWIf@003ooIfMT00ol0003ofMWIomWIf@3`omWIf@?o00006ooIfMT000oofMWI00?o 0000omWIfOoIfMT0lOoIfMT3o`0001[ofMWI000?omWIf@03o`000?oIfMWofMWI0?;ofMWI0ol0000I omWIf@003ooIfMT00ol0003ofMWIomWIf@3comWIf@?o00006?oIfMT000oofMWI0_l0003eomWIf@?o 00005ooIfMT000oofMWI00?o0000omWIfOoIfMT0mOoIfMT3o`0001KofMWI000?omWIf@03o`000?oI fMWofMWI0?KofMWI0ol0000EomWIf@003ooIfMT00ol0003ofMWIomWIf@3gomWIf@?o00005?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0n?oIfMT3o`0001?ofMWI000?omWIf@03o`000?oIfMWofMWI0?Wo fMWI0ol0000BomWIf@003ooIfMT00ol0003ofMWIomWIf@3jomWIf@?o00004OoIfMT000oofMWI00?o 0000omWIfOoIfMT0nooIfMT2o`00017ofMWI000?omWIf@03o`000?oIfMWofMWI0?_ofMWI0ol0000@ omWIf@003ooIfMT2o`000?gofMWI0ol0000?omWIf@003ooIfMT00ol0003ofMWIomWIf@3momWIf@?o 00003_oIfMT000oofMWI00?o0000omWIfOoIfMT0o_oIfMT2o`0000kofMWI000?omWIf@03o`000?oI fMWofMWI0?kofMWI0ol0000=omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@?o00003?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0oooIfMT1omWIf@?o00002ooIfMT000oofMWI00?o0000omWIfOoI fMT0oooIfMT2omWIf@?o00002_oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT3omWIf@;o0000 2_oIfMT000oofMWI0_l0003oomWIf@CofMWI0ol00009omWIf@003ooIfMT00ol0003ofMWIomWIf@3o omWIf@CofMWI0ol00008omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@GofMWI0ol00007omWI f@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@KofMWI0_l00007omWIf@003ooIfMT00ol0003ofMWI omWIf@3oomWIf@oofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000 omWIfOoIfMT0oooIfMT?omWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.12112, \ 0.0237193, 0.241311}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c.- ", FontColor->RGBColor[1, 0, 0]], "Calcular ", "la norma de la funci\[OAcute]n error." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(e[x_] := v[x] - vp\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ne = Sqrt[pe[e[x], e[x]]] // N\)], "Input", CellLabel->"In[16]:=", FontSize->14], Cell[BoxData[ \(18.00250212986795`\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[17]:=", FontSize->14] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["EJERCICIO 4.6 (Un problema de ajuste exponencial)", FontColor->RGBColor[0, 0, 1]]], "SectionFirst", FontColor->RGBColor[1, 0, 1], Background->RGBColor[0.8, 1, 0.4]], Cell[CellGroupData[{ Cell[TextData[{ "Un contador Geiger da una lectura inicial de 232 unidades en 10 minutos. \ Tras introducir una muestra de indio (", Cell[BoxData[ \(\(\[InvisiblePrefixScriptBase]\^116\)In\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], "), las lecturas del contador en sucesivos intervalos de 10 minutos vienen \ reflejadas en la siguiente tabla:\n\nt(minutos)\t10\t\t20\t\t30\t\t40\t\t50\t\ \t60\n\ncontador\t20511\t\t16174\t\t13904\t\t12514\t\t10775\t\t9596\n\nEn \ general, la radiaci\[OAcute]n emitida ", Cell[BoxData[ \(R = \(R\_0\) e\^\(-\[Lambda]t\)\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], ", donde \[Lambda] es la constante de desintegraci\[OAcute]n del material. \ Se trata de ajustar una funci\[OAcute]n del tipo ", Cell[BoxData[ \(\(\(g \((t)\)\)\(=\)\(\[Alpha]e\^\[Beta]t\)\(\ \)\)\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], "a los datos ", Cell[BoxData[ \(\((t\_k\ , \ y\_k)\)\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], ", donde ", Cell[BoxData[ StyleBox[\(y\_k = contador - 232\), FontFamily->"Helvetica"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], ". \nA continuaci\[OAcute]n, deducir la vida media ", Cell[BoxData[ RowBox[{"(", RowBox[{"=", FractionBox[ StyleBox[\(ln\ 2\), FontSize->14], StyleBox["\[Lambda]", FontSize->14]]}], ")"}]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], " del indio." }], "Subsubsection", CellDingbat->None, TextAlignment->Left, TextJustification->1, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "Se trata de calcular la curva de la forma\n\t\t\t\t\t\t", Cell[BoxData[ StyleBox[\(g \((t)\) = \[Alpha]e\^\[Beta]t\), FontFamily->"Times", FontWeight->"Bold"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], "\nque mejor se ajuste a los datos ", Cell[BoxData[ StyleBox[\((t\_k\ , \ y\_k)\), FontFamily->"Times"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], ", donde ", Cell[BoxData[ StyleBox[\(y\_k = contador - 232\), FontFamily->"Times"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], ", donde ", Cell[BoxData[ \(t\_k\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], " se corresponde al riempo medido en minutos e ", Cell[BoxData[ \(\(\(y\_k\)\(=\)\)\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], " ", Cell[BoxData[ \(\[Alpha]e\^\[Beta]t\_k\)], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14], ".\n\nTenemos que reducir el problema a un ajuste lineal. Para ello, \ tomaremos logaritmos:\t\t\t\t\t\t" }], "Text", CellDingbat->None], Cell[TextData[{ Cell[BoxData[ StyleBox[\(\(y\)\(=\)\), FontWeight->"Bold"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14, FontColor->GrayLevel[0]], StyleBox[" ", FontColor->GrayLevel[0]], Cell[BoxData[ StyleBox[\(\[Alpha]e\^\[Beta]t\), FontWeight->"Bold"]], TextAlignment->Left, TextJustification->1, FontFamily->"Times New Roman", FontSize->14, FontColor->GrayLevel[0]], StyleBox[".", FontColor->GrayLevel[0]] }], "Text", CellDingbat->"\[FilledSmallCircle]", FontColor->RGBColor[0, 1, 0]], Cell[TextData[{ StyleBox["Tomando logaritmos:", FontColor->GrayLevel[0]], StyleBox[" ", FontColor->GrayLevel[0]], Cell[BoxData[ FormBox[ StyleBox[\(ln\ y = ln\ \[Alpha] + \[Beta]t\), FontSize->14, FontWeight->"Bold"], TraditionalForm]], FontColor->GrayLevel[0]], "." }], "Text", CellDingbat->"\[FilledSmallCircle]", FontColor->RGBColor[0, 1, 0]], Cell[TextData[{ StyleBox["Hallamos la recta que mejor se ajuste a los datos:", FontColor->GrayLevel[0]], StyleBox[" ", FontColor->GrayLevel[0]], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ StyleBox["(", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox[ SubscriptBox[ StyleBox["t", FontSlant->"Plain"], StyleBox["k", FontSlant->"Plain"]], FontSize->14, FontWeight->"Bold", FontSlant->"Italic"], StyleBox[" ", FontSize->14, FontWeight->"Bold"], StyleBox[",", FontSize->14, FontWeight->"Bold"], StyleBox[" ", FontSize->14, FontWeight->"Bold"], StyleBox[ SubscriptBox[ StyleBox["z", FontSlant->"Plain"], StyleBox["k", FontSlant->"Plain"]], FontSize->14, FontWeight->"Bold"]}], StyleBox[")", FontSize->14, FontWeight->"Bold"]}], StyleBox["=", FontSize->14, FontWeight->"Bold"], StyleBox[ RowBox[{"(", RowBox[{ SubscriptBox[ StyleBox["t", FontSize->14, FontWeight->"Bold", FontSlant->"Plain"], StyleBox["k", FontSlant->"Plain"]], " ", ",", " ", RowBox[{"ln", RowBox[{"(", RowBox[{ SubscriptBox["contador", StyleBox["k", FontSlant->"Plain"]], "-", "232"}], ")"}]}]}], ")"}], FontSize->14, FontWeight->"Bold"]}], TraditionalForm]], FontColor->GrayLevel[0]], ":\n\t\t\t\t\t\t\t", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["z", FontSlant->"Plain"], "=", RowBox[{ StyleBox["a", FontSlant->"Plain"], "+", "ct"}]}], TraditionalForm]], FontSize->16, FontWeight->"Bold", FontColor->GrayLevel[0]], "\ncon \t\t\t\t\t\t" }], "Text", CellDingbat->"\[FilledSmallCircle]", FontColor->RGBColor[0, 1, 0]], Cell["\", "Text", CellDingbat->None], Cell[BoxData[{ \(\(A = {{1, 10}, {1, 20}, {1, 30}, {1, 40}, {1, 50}, {1, 60}};\)\), "\[IndentingNewLine]", \(\(tiempos = {10, 20, 30, 40, 50, 60};\)\), "\[IndentingNewLine]", \(\(bt = {20511, 16174, 13904, 12514, 10775, 9596};\)\), "\[IndentingNewLine]", \(\(b = Log[bt - 232. ];\)\)}], "Input", CellLabel->"In[1]:=", FontSize->14], Cell["\", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(diagramadedispersion = Table[{tiempos[\([i]\)], bt[\([i]\)] - 232}, {i, 6}];\)\), "\[IndentingNewLine]", \(\(g1 = ListPlot[diagramadedispersion, PlotStyle \[Rule] {PointSize[0.02], RGBColor[1, 0, 0]}];\)\)}], "Input", CellLabel->"In[7]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[7]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {3.28438, 8277.64, 0.201972, \ 71.3399}}] }, Open ]], Cell["\", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(solucion = Inverse[Transpose[A] . A] . \((Transpose[A] . b)\) // N\)], "Input", CellLabel->"In[9]:=", FontSize->14], Cell[BoxData[ \({10.011275690734983`, \(-0.01488933363202305`\)}\)], "Output", CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(alpha = Exp[solucion[\([1]\)]]\)], "Input", CellLabel->"In[10]:=", FontSize->14], Cell[BoxData[ \(22276.23492450111`\)], "Output", CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(beta = solucion[\([2]\)]\)], "Input", CellLabel->"In[11]:=", FontSize->14], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[11]:="], Cell[BoxData[ \(\(-0.01488933363202305`\)\)], "Output", CellLabel->"Out[11]="] }, Open ]], Cell["Luego la curva pedida es:", "Text"], Cell[BoxData[ \(\(g[t_] := Exp[solucion[\([1]\)]]*Exp[solucion[\([2]\)]*t];\)\)], "Input", CellLabel->"In[12]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(Print["\", g[t]]\)], "Input", CellLabel->"In[13]:=", FontSize->14], Cell[BoxData[ InterpretationBox[\("la curva exponencial que mejor se ajusta a los datos \ es g(t)="\[InvisibleSpace]\(22276.23492450111`\ \ \[ExponentialE]\^\(\(-0.01488933363202305`\)\ t\)\)\), SequenceForm[ "la curva exponencial que mejor se ajusta a los datos es g(t)=", Times[ 22276.23492450111, Power[ E, Times[ -0.01488933363202305, t]]]], Editable->False]], "Print", CellLabel->"From In[13]:="] }, Open ]], Cell["\", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(g2 = Plot[g[t], {t, 0, 65}, PlotStyle \[Rule] {Thickness[0.01], RGBColor[0, 1, 0]}];\)\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[15]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\?oIfMT0027ofMWI0_l0002m omWIf@Ko0?l0>_oIfMT0027ofMWI00?o0000omWIfOoIfMT0^OoIfMT7o`3o03cofMWI000QomWIf@03 o`000?oIfMWofMWI0;KofMWI1ol0o`0oomWIf@008OoIfMT00ol0003ofMWIomWIf@2domWIf@Ko0?l0 @_oIfMT0027ofMWI00?o0000omWIfOoIfMT0/_oIfMT5o`3o04GofMWI000QomWIf@03o`000?oIfMWo fMWI0;3ofMWI1Ol0o`17omWIf@008OoIfMT2o`000:oofMWI1Ol0o`19omWIf@008OoIfMT00ol0003o fMWIomWIf@2/omWIf@Go0?l0BooIfMT0027ofMWI00?o0000omWIfOoIfMT0Z_oIfMT5o`3o04gofMWI 000QomWIf@03o`000?oIfMWofMWI0:SofMWI1Ol0o`1?omWIf@008OoIfMT00ol0003ofMWIomWIf@2V omWIf@Go0?l0DOoIfMT0027ofMWI0_l0002UomWIf@Go0?l0DooIfMT0027ofMWI00?o0000omWIfOoI fMT0X_oIfMT5o`3o05GofMWI000QomWIf@03o`000?oIfMWofMWI0:3ofMWI1Ol0o`1GomWIf@0000Co fMWIo`000?l0003o00000_oIfMT5o`0000?ofMWI0_l00004omWIf@;o00001?oIfMT2o`0000GofMWI 00?o0000omWIfOoIfMT0W_oIfMT5o`3o05WofMWI0002omWIf@03o`000?oIfMWofMWI00;ofMWI00Co 0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`00 00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@2LomWIf@Go0?l0FooIfMT0 00;ofMWI00?o0000omWIfOoIfMT00ooIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWI o`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`00 0?oIfMWofMWI09[ofMWI1Ol0o`1MomWIf@000_oIfMT00ol0003ofMWIomWIf@04omWIf@05o`000?oI fMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`00 00;ofMWI00?o0000omWIfOoIfMT00_oIfMT2o`0009WofMWI1Ol0o`1OomWIf@000_oIfMT01Ol0003o fMWIomWIfOoIfMWo000000?ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl0 0002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWI omWIf@2FomWIf@Go0?l0HOoIfMT00003omWIfOl0003o000000?ofMWI00Go0000omWIfOoIfMWofMWI o`000002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0 003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI09CofMWI1Ol0o`1SomWIf@000_oIfMT00ol0 003ofMWIomWIf@02omWIf@?o00001?oIfMT2o`0000CofMWI0_l00004omWIf@;o00001OoIfMT00ol0 003ofMWIomWIf@2BomWIf@Go0?l0IOoIfMT0027ofMWI00?o0000omWIfOoIfMT0TOoIfMT4o`3o06Oo fMWI000QomWIf@;o0000T?oIfMT4o`3o06WofMWI000QomWIf@03o`000?oIfMWofMWI08gofMWI1Ol0 o`1ZomWIf@008OoIfMT00ol0003ofMWIomWIf@2;omWIf@Go0?l0K?oIfMT0027ofMWI00?o0000omWI fOoIfMT0ROoIfMT5o`3o06kofMWI000QomWIf@03o`000?oIfMWofMWI08SofMWI1?l0o`1`omWIf@00 8OoIfMT00ol0003ofMWIomWIf@26omWIf@Co0?l0L_oIfMT0027ofMWI0_l00025omWIf@Go0?l0LooI fMT0027ofMWI00?o0000omWIfOoIfMT0PooIfMT4o`3o07GofMWI000QomWIf@03o`000?oIfMWofMWI 087ofMWI1?l0o`1gomWIf@008OoIfMT00ol0003ofMWIomWIf@1oomWIf@Go0?l0N?oIfMT0027ofMWI 00?o0000omWIfOoIfMT0OOoIfMT5o`3o07[ofMWI000QomWIf@;o0000OOoIfMT4o`3o07cofMWI000Q omWIf@03o`000?oIfMWofMWI07[ofMWI1?l0o`1nomWIf@008OoIfMT00ol0003ofMWIomWIf@1homWI f@Go0?l0OooIfMT00004omWIfOl0003o0000o`0000CofMWI0ol00003omWIf@;o00001?oIfMT2o`00 00CofMWI0_l00005omWIf@03o`000?oIfMWofMWI07KofMWI1Ol0o`21omWIf@000_oIfMT00ol0003o fMWIomWIf@04omWIf@05o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002 omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWIomWI f@1eomWIf@Co0?l0PooIfMT000;ofMWI00Co0000omWIfOoIfMWofMWI1Ol00002omWIf@04o`000?oI fMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00004omWI f@03o`000?oIfMWofMWI07?ofMWI1?l0o`25omWIf@000_oIfMT01Ol0003ofMWIomWIfOoIfMWo0000 00;ofMWI00Go0000omWIfOoIfMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co 0000omWIfOoIfMWo00000_oIfMT00ol0003ofMWIomWIf@02omWIf@;o0000LooIfMT4o`3o08KofMWI 0002omWIf@03o`000?oIfMWofMWI00;ofMWI00?o0000omWIfOl000000ooIfMT01?l0003ofMWIomWI fOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0 003ofMWIomWIf@1`omWIf@Co0?l0R?oIfMT00003omWIfOl0003o000000GofMWI0_l00003omWIf@04 o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl0 0004omWIf@03o`000?oIfMWofMWI06oofMWI1?l0o`29omWIf@000_oIfMT00ol0003ofMWIomWIf@04 omWIf@03o`000?oIfMWofMWI00;ofMWI0_l00004omWIf@;o00001?oIfMT2o`0000GofMWI00?o0000 omWIfOoIfMT0KOoIfMT4o`3o08_ofMWI000QomWIf@03o`000?oIfMWofMWI06_ofMWI1Ol0o`2omWIf@008OoIfMT00ol0003ofMWIomWIf@1XomWIf@Co0?l0 T?oIfMT0027ofMWI00?o0000omWIfOoIfMT0I_oIfMT4o`3o09;ofMWI000QomWIf@03o`000?oIfMWo fMWI06CofMWI1Ol0o`2ComWIf@008OoIfMT00ol0003ofMWIomWIf@1RomWIf@Go0?l0UOoIfMT0027o fMWI00?o0000omWIfOoIfMT0HOoIfMT4o`3o09OofMWI000QomWIf@;o0000H?oIfMT4o`3o09WofMWI 000QomWIf@03o`000?oIfMWofMWI05kofMWI1?l0o`2JomWIf@008OoIfMT00ol0003ofMWIomWIf@1M omWIf@?o0?l0W?oIfMT0027ofMWI00?o0000omWIfOoIfMT0FooIfMT4o`3o09gofMWI000QomWIf@03 o`000?oIfMWofMWI05[ofMWI1?l0o`2NomWIf@008OoIfMT2o`0005WofMWI1?l0o`2PomWIf@008OoI fMT00ol0003ofMWIomWIf@1GomWIf@Co0?l0XOoIfMT0027ofMWI00?o0000omWIfOoIfMT0EOoIfMT4 o`3o0:?ofMWI000QomWIf@03o`000?oIfMWofMWI05CofMWI1?l0o`2TomWIf@0000CofMWIo`000?l0 003o00000ooIfMT3o`0000CofMWI0_l00004omWIf@;o00001?oIfMT2o`0000GofMWI00?o0000omWI fOoIfMT0DooIfMT3o`3o0:KofMWI0002omWIf@05o`000?oIfMWofMWIomWIfOl000000ooIfMT01?l0 003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo0000 0_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI057ofMWI1?l0o`2WomWIf@000_oI fMT01Ol0003ofMWIomWIfOoIfMWo000000?ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003o fMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT2 o`00057ofMWI1?l0o`2XomWIf@000_oIfMT01?l0003ofMWIomWIfOoIfMT4o`0000?ofMWI00Co0000 omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000Co fMWI00?o0000omWIfOoIfMT0C_oIfMT4o`3o0:[ofMWI0002omWIf@05o`000?oIfMWofMWIomWIfOl0 00001_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000 omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@1=omWIf@Co0?l0ZooIfMT00003omWIfOl0003o 000000CofMWI00?o0000omWIfOoIfMT00ooIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oI fMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@1;ofMWI0003 omWIf@05o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`00 0?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT00ol0003ofMWIomWIf@02omWI f@03o`000?oIfMWofMWI01KofMWI0ol0o`3SomWIf@0000Go0000omWIfOoIfMWofMWIo`000002omWI f@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWI fOl00002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT05OoIfMT3o`3o0>Co fMWI00001Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0 003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo0000 1?oIfMT00ol0003ofMWIomWIf@0DomWIf@?o0?l0iOoIfMT00004omWIfOl0003o0000o`0000CofMWI 0_l00004omWIf@;o00001?oIfMT2o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI01?ofMWI 0ol0o`3VomWIf@008OoIfMT00ol0003ofMWIomWIf@0BomWIf@?o0?l0iooIfMT0027ofMWI0_l0000A omWIf@Co0?l0j?oIfMT0027ofMWI00?o0000omWIfOoIfMT03ooIfMT4o`3o0>WofMWI000QomWIf@03 o`000?oIfMWofMWI00kofMWI0ol0o`3[omWIf@008OoIfMT00ol0003ofMWIomWIf@0=omWIf@?o0?l0 k?oIfMT0027ofMWI00?o0000omWIfOoIfMT03?oIfMT3o`3o0>gofMWI000QomWIf@;o00003?oIfMT3 o`3o0>kofMWI000QomWIf@03o`000?oIfMWofMWI00[ofMWI0ol0o`3_omWIf@008OoIfMT00ol0003o fMWIomWIf@09omWIf@?o0?l0l?oIfMT0027ofMWI00?o0000omWIfOoIfMT02?oIfMT3o`3o0?7ofMWI 000QomWIf@03o`000?oIfMWofMWI00OofMWI0ol0o`3bomWIf@008OoIfMT00ol0003ofMWIomWIf@06 omWIf@?o0?l0looIfMT0027ofMWI0_l00006omWIf@?o0?l0m?oIfMT0027ofMWI00?o0000omWIfOoI fMT01?oIfMT3o`3o0?GofMWI000QomWIf@03o`000?oIfMWofMWI00?ofMWI0ol0o`3fomWIf@001Ol0 00000ooIfMWo0000o`000003o`0000?ofMWI0_l00004omWIf@;o00001?oIfMT2o`0000GofMWI00?o 0000omWIfOoIfMT00_oIfMT3o`3o0?OofMWI00001OoIfMWo0000omWIfOoIfMWo000000;ofMWI00Co 0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`00 00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT01?l0003ofMWIomWIfOoIfMT3o`3o0?SofMWI0002 omWIf@03o`000?oIfMWofMWI00?ofMWI00?o0000omWIfOoIfMT00_oIfMT01?l0003ofMWIomWIfOl0 0002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT2o`000004 omWIfOl0o`3o0?l0o`3o0?WofMWI0003omWIf@03o`000?oIfMWofMWI00?ofMWI00Go0000omWIfOoI fMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oI fMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWo0?l000;o0?l0n_oIfMT00007o`000?oIfMWo fMWIomWIfOl0003ofMWIo`000003omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoI fMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000 o`3o0?l0o`3o0?l0nooIfMT00007o`000?oIfMWofMWIomWIfOl0003ofMWIo`000003omWIf@04o`00 0?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002 omWIf@03o`000?oIfMWofMWI00;ofMWI0ol0o`3lomWIf@0000CofMWIo`000?l0003o00000ooIfMT3 o`0000CofMWI0_l00004omWIf@;o00001?oIfMT2o`0000CofMWI0ol0o`3momWIf@008?oIfMT2o`3o 0?kofMWI000QomWIf@;o0000oOoIfMT0027ofMWI00?o0000omWIfOoIfMT0o?oIfMT00?oofMWI8OoI fMT00?oofMWI8OoIfMT00?oofMWI8OoIfMT00?oofMWI8OoIfMT00?oofMWI8OoIfMT00?oofMWI8OoI fMT00?oofMWI8OoIfMT00?oofMWI8OoIfMT00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-8.73034, 7382.5, 0.262564, \ 90.2821}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[g1, g2];\)\)], "Input", CellLabel->"In[16]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[16]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\?oIfMT0027ofMWI0_l0002jomWIf@?oo`001_l0o`0jomWIf@008OoIfMT00ol0 003ofMWIomWIf@2iomWIf@Oo0?l0??oIfMT0027ofMWI00?o0000omWIfOoIfMT0]_oIfMT7o`3o0003 ool00?oIfMWofMWI03cofMWI000QomWIf@03o`000?oIfMWofMWI0;CofMWI1_l0o`03ool003oofMWI 000QomWIf@03o`000?oIfMWofMWI0;;ofMWI1Ol0o`15omWIf@008OoIfMT00ol0003ofMWIomWIf@2` omWIf@Go0?l0AooIfMT0027ofMWI0_l0002_omWIf@Go0?l0BOoIfMT0027ofMWI00?o0000omWIfOoI fMT0[?oIfMT5o`3o04_ofMWI000QomWIf@03o`000?oIfMWofMWI0:[ofMWI1Ol0o`1=omWIf@008OoI fMT00ol0003ofMWIomWIf@2XomWIf@Go0?l0CooIfMT0027ofMWI00?o0000omWIfOoIfMT0Y_oIfMT5 o`3o057ofMWI000QomWIf@;o0000YOoIfMT5o`3o05?ofMWI000QomWIf@03o`000?oIfMWofMWI0:;o fMWI1Ol0o`1EomWIf@008OoIfMT00ol0003ofMWIomWIf@2PomWIf@Go0?l0EooIfMT00004omWIfOl0 003o0000o`0000;ofMWI1Ol00003omWIf@;o00001?oIfMT2o`0000CofMWI0_l00005omWIf@03o`00 0?oIfMWofMWI09kofMWI1Ol0o`1IomWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oI fMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWI f@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0W?oIfMT5o`3o05_ofMWI0002omWI f@03o`000?oIfMWofMWI00?ofMWI00?o0000omWIfOoIfMT00_oIfMT01?l0003ofMWIomWIfOl00002 omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWI omWIf@2JomWIf@Go0?l0GOoIfMT000;ofMWI00?o0000omWIfOoIfMT01?oIfMT01Ol0003ofMWIomWI fOoIfMWo000000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWI f@03o`000?oIfMWofMWI00;ofMWI0_l0002IomWIf@Go0?l0GooIfMT000;ofMWI00Go0000omWIfOoI fMWofMWIo`000003omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oI fMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWofMWI00;ofMWI00?o0000omWIfOoIfMT0 U?oIfMT2ool000Go0?l0HOoIfMT00003omWIfOl0003o000000?ofMWI00Go0000omWIfOoIfMWofMWI o`000002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0 003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI09?ofMWI00?oo`00o`3o0?l0o`000ol0o`1S omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@?o00001?oIfMT2o`0000CofMWI0_l00004omWI f@;o00001OoIfMT00ol0003ofMWIomWIf@2BomWIf@Go0?l000?oo`00omWIfOoIfMT0H_oIfMT0027o fMWI00?o0000omWIfOoIfMT0TOoIfMT4o`3o00?oo`00I?oIfMT0027ofMWI0_l0002@omWIf@Co0?l0 00CofMWIool00?oo003oo`00IOoIfMT0027ofMWI00?o0000omWIfOoIfMT0SOoIfMT5o`3o06[ofMWI 000QomWIf@03o`000?oIfMWofMWI08_ofMWI1Ol0o`1/omWIf@008OoIfMT00ol0003ofMWIomWIf@29 omWIf@Go0?l0K_oIfMT0027ofMWI00?o0000omWIfOoIfMT0R?oIfMT4o`3o073ofMWI000QomWIf@03 o`000?oIfMWofMWI08KofMWI1?l0o`1bomWIf@008OoIfMT2o`0008GofMWI1Ol0o`1comWIf@008OoI fMT00ol0003ofMWIomWIf@23omWIf@Co0?l0MOoIfMT0027ofMWI00?o0000omWIfOoIfMT0POoIfMT4 o`3o07OofMWI000QomWIf@03o`000?oIfMWofMWI07oofMWI1Ol0o`1homWIf@008OoIfMT00ol0003o fMWIomWIf@1momWIf@Go0?l0N_oIfMT0027ofMWI0_l0001_omWIf@?oo`002ooIfMT4o`3o07cofMWI 000QomWIf@03o`000?oIfMWofMWI06gofMWI1Ooo0008omWIf@Co0?l0O_oIfMT0027ofMWI00?o0000 omWIfOoIfMT0KOoIfMT5ool000KofMWI1Ol0o`1oomWIf@0000CofMWIo`000?l0003o00001?oIfMT3 o`0000?ofMWI0_l00004omWIf@;o00001?oIfMT2o`0000GofMWI00?o0000omWIfOoIfMT0KOoIfMT5 ool000CofMWI1Ol0o`21omWIf@000_oIfMT00ol0003ofMWIomWIf@04omWIf@05o`000?oIfMWofMWI omWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI 00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWIomWIf@1^omWIf@?oo`001?oIfMT4o`3o08?ofMWI 0002omWIf@04o`000?oIfMWofMWIomWIf@Go00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04 o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@1c omWIf@Co0?l0QOoIfMT000;ofMWI00Go0000omWIfOoIfMWofMWIo`000002omWIf@05o`000?oIfMWo fMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;o fMWI00?o0000omWIfOoIfMT00_oIfMT2o`0007?ofMWI1?l0o`26omWIf@000_oIfMT00ol0003ofMWI omWIf@02omWIf@03o`000?oIfMWo000000?ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003o fMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0L?oIfMT4 o`3o08SofMWI00000ooIfMWo0000o`000005omWIf@;o00000ooIfMT01?l0003ofMWIomWIfOl00002 omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWI omWIf@1_omWIf@Co0?l0ROoIfMT000;ofMWI00?o0000omWIfOoIfMT01?oIfMT00ol0003ofMWIomWI f@02omWIf@;o00001?oIfMT2o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI06gofMWI1?l0 o`2;omWIf@008OoIfMT00ol0003ofMWIomWIf@1[omWIf@Go0?l0S?oIfMT0027ofMWI0_l0001ZomWI f@Go0?l0S_oIfMT0027ofMWI00?o0000omWIfOoIfMT0J?oIfMT4o`3o093ofMWI000QomWIf@03o`00 0?oIfMWofMWI06KofMWI1?l0o`2BomWIf@008OoIfMT00ol0003ofMWIomWIf@1TomWIf@Go0?l0TooI fMT0027ofMWI00?o0000omWIfOoIfMT0H_oIfMT5o`3o09GofMWI000QomWIf@03o`000?oIfMWofMWI 067ofMWI1?l0o`2GomWIf@008OoIfMT2o`00063ofMWI1?l0o`2IomWIf@008OoIfMT00ol0003ofMWI omWIf@1NomWIf@Co0?l0V_oIfMT0027ofMWI00?o0000omWIfOoIfMT0GOoIfMT3o`3o09cofMWI000Q omWIf@03o`000?oIfMWofMWI05_ofMWI1?l0o`2MomWIf@008OoIfMT00ol0003ofMWIomWIf@1JomWI f@Co0?l0W_oIfMT0027ofMWI0_l0001IomWIf@Co0?l0X?oIfMT0027ofMWI00?o0000omWIfOoIfMT0 EooIfMT4o`3o0:7ofMWI000QomWIf@03o`000?oIfMWofMWI05GofMWI1?l0o`2SomWIf@008OoIfMT0 0ol0003ofMWIomWIf@18omWIf@?oo`002OoIfMT4o`3o0:CofMWI00001?oIfMWo0000o`000?l00003 omWIf@?o00001?oIfMT2o`0000CofMWI0_l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@17 omWIf@Goo`001ooIfMT3o`3o0:KofMWI0002omWIf@05o`000?oIfMWofMWIomWIfOl000000ooIfMT0 1?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo 00000_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI04OofMWI1Ooo0005omWIf@Co 0?l0YooIfMT000;ofMWI00Go0000omWIfOoIfMWofMWIo`000003omWIf@04o`000?oIfMWofMWIo`00 00;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oI fMWofMWI00;ofMWI0_l00018omWIf@Goo`001?oIfMT4o`3o0:SofMWI0002omWIf@04o`000?oIfMWo fMWIomWIf@Co00000ooIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;o fMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@18omWIf@?oo`000ooIfMT4o`3o 0:[ofMWI0002omWIf@05o`000?oIfMWofMWIomWIfOl000001_oIfMT01?l0003ofMWIomWIfOl00002 omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWI omWIf@1=omWIf@Co0?l0ZooIfMT00003omWIfOl0003o000000CofMWI00?o0000omWIfOoIfMT00ooI fMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoI fMWo00001?oIfMT00ol0003ofMWIomWIf@1;ofMWI0003omWIf@05o`000?oIfMWofMWIomWIfOl00000 0_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWI fOoIfMWo00000_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI01KofMWI0ol0o`09 omWIf@?oo`00eooIfMT00005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl0 0002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003o fMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI01GofMWI0ol0o`09omWIf@Goo`00e_oIfMT00005 o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWo fMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03 o`000?oIfMWofMWI01CofMWI0ol0o`0:omWIf@Goo`00e_oIfMT00004omWIfOl0003o0000o`0000Co fMWI0_l00004omWIf@;o00001?oIfMT2o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI01?o fMWI0ol0o`0;omWIf@Goo`00e_oIfMT0027ofMWI00?o0000omWIfOoIfMT04_oIfMT3o`3o00gofMWI 0ooo003GomWIf@008OoIfMT2o`00017ofMWI1?l0o`3XomWIf@008OoIfMT00ol0003ofMWIomWIf@0? omWIf@Co0?l0jOoIfMT0027ofMWI00?o0000omWIfOoIfMT03_oIfMT3o`3o0>_ofMWI000QomWIf@03 o`000?oIfMWofMWI00gofMWI0ol0o`3/omWIf@008OoIfMT00ol0003ofMWIomWIf@0oofMWI000QomWIf@03o`000?oIfMWofMWI00WofMWI0ol0o`3`omWIf@008OoIfMT00ol0003o fMWIomWIf@08omWIf@?o0?l0lOoIfMT0027ofMWI00?o0000omWIfOoIfMT01ooIfMT3o`3o0?;ofMWI 000QomWIf@03o`000?oIfMWofMWI00KofMWI0ol0o`3comWIf@008OoIfMT2o`0000KofMWI0ol0o`3d omWIf@008OoIfMT00ol0003ofMWIomWIf@04omWIf@?o0?l0mOoIfMT0027ofMWI00?o0000omWIfOoI fMT00ooIfMT3o`3o0?KofMWI0005o`000003omWIfOl0003o000000?o00000ooIfMT2o`0000CofMWI 0_l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@02omWIf@?o0?l0mooIfMT00005omWIfOl0 003ofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`00 00;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@04o`000?oI fMWofMWIomWIf@?o0?l0n?oIfMT000;ofMWI00?o0000omWIfOoIfMT00ooIfMT00ol0003ofMWIomWI f@02omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003o fMWIomWIfOl00004omWIf@;o000000CofMWIo`3o0?l0o`3o0?l0nOoIfMT000?ofMWI00?o0000omWI fOoIfMT00ooIfMT01Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000omWIfOoIfMWo00000_oI fMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWofMWI00;ofMWI00?o0000omWIfOl0o`00 0_l0o`3jomWIf@0000Oo0000omWIfOoIfMWofMWIo`000?oIfMWo000000?ofMWI00Co0000omWIfOoI fMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o 0000omWIfOoIfMT00_oIfMT01?l0003o0?l0o`3o0?l0o`3komWIf@0000Oo0000omWIfOoIfMWofMWI o`000?oIfMWo000000?ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002 omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT3o`3o0?cofMWI0000 1?oIfMWo0000o`000?l00003omWIf@?o00001?oIfMT2o`0000CofMWI0_l00004omWIf@;o00001?oI fMT3o`3o0?gofMWI000PomWIf@;o0?l0o_oIfMT0027ofMWI0_l0003momWIf@008OoIfMT00ol0003o fMWIomWIf@3lomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWI f@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-8.73034, 7382.5, 0.262564, \ 90.2821}}] }, Open ]], Cell["\", "Text"], Cell[BoxData[ \("In[17]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[{ \(\(a1 = \(Transpose[A]\)[\([1]\)];\)\), "\[IndentingNewLine]", \(\(a2 = \(Transpose[A]\)[\([2]\)];\)\), "\[IndentingNewLine]", \(o = GramSchmidt[{a1, a2}]\)}], "Input", CellLabel->"In[18]:=", FontSize->14], Cell[BoxData[ \({{1\/\@6, 1\/\@6, 1\/\@6, 1\/\@6, 1\/\@6, 1\/\@6}, {\(-\@\(5\/14\)\), \(-\(3\/\@70\)\), \(-\(1\/\@70\)\), 1\/\@70, 3\/\@70, \@\(5\/14\)}}\)], "Output", CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(bp = Sum[Projection[b, o[\([i]\)]], {i, 2}] // N\)], "Input", CellLabel->"In[21]:=", FontSize->14], Cell[BoxData[ \({9.862382354414756`, 9.713489018094522`, 9.56459568177429`, 9.415702345454058`, 9.266809009133825`, 9.117915672813591`}\)], "Output",\ CellLabel->"Out[21]="] }, Open ]], Cell[TextData[{ "Aunque nos puede resultar m\[AAcute]s c\[OAcute]modo dibujrlas por \ separado con colores distintos y utilizar posteriormente la funci\[OAcute]n \ ", StyleBox["Show", FontFamily->"Courier", FontWeight->"Bold"], " para mostrar las dos gr\[AAcute]ficas juntas:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(sistema = Table[l\[Alpha]*a1[\([i]\)] + \[Beta]*a2[\([i]\)] \[Equal] bp[\([i]\)], {i, Length[a1]}];\)\), "\[IndentingNewLine]", \(Solve[sistema, {l\[Alpha], \[Beta]}]\)}], "Input", CellLabel->"In[26]:=", FontSize->14], Cell[BoxData[ \({{l\[Alpha] \[Rule] 10.011275690734989`, \[Beta] \[Rule] \ \(-0.01488933363202328`\)}}\)], "Output", CellLabel->"Out[27]="] }, Open ]], Cell["La curva pedida es:", "Text"], Cell[BoxData[ \(\(ng[ t_] := \((Exp[ l\[Alpha]] /. {\(%27[\([1]\)]\)[\([1]\)]})\)*\((Exp[\[Beta]* t])\) /. {\[Beta] \[Rule] \(%27[\([1]\)]\)[\([2]\)]};\)\)], \ "Input", CellLabel->"In[42]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ng[t]\)], "Input", CellLabel->"In[43]:="], Cell[BoxData[ \(22276.23492450123`\ \[ExponentialE]\^\(t\ \((\[Beta] \[Rule] \ \(-0.01488933363202328`\))\)\)\)], "Output", CellLabel->"Out[43]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Exp[l\[Alpha]] /. {\(%27[\([1]\)]\)[\([1]\)]}\)], "Input", CellLabel->"In[37]:="], Cell[BoxData[ \(22276.23492450123`\)], "Output", CellLabel->"Out[37]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(gvp = Plot[vp, {x, 0, 2 Pi}, PlotStyle \[Rule] {RGBColor[0, 1, 0], Thickness[0.01]}];\)\)], "Input", CellLabel->"In[13]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[13]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\?oIfMT3o`3o0:?ofMWI000?omWIf@03o`000?oIfMWo fMWI02gofMWI0ol0o`0iomWIf@?o0?l0X_oIfMT000oofMWI00?o0000omWIfOoIfMT0;?oIfMT3o`3o 03_ofMWI0ol0o`2QomWIf@003ooIfMT00ol0003ofMWIomWIf@0[omWIf@?o0?l0?OoIfMT2o`3o0:7o fMWI000?omWIf@03o`000?oIfMWofMWI02_ofMWI0_l0o`0nomWIf@?o0?l0X?oIfMT000oofMWI0_l0 000[omWIf@?o0?l0?ooIfMT3o`3o09oofMWI000?omWIf@03o`000?oIfMWofMWI02WofMWI0ol0o`11 omWIf@;o0?l0WooIfMT000oofMWI00?o0000omWIfOoIfMT0:?oIfMT3o`3o04;ofMWI0ol0o`2NomWI f@003ooIfMT00ol0003ofMWIomWIf@0XomWIf@;o0?l0A?oIfMT3o`3o09gofMWI000?omWIf@03o`00 0?oIfMWofMWI02OofMWI0ol0o`15omWIf@;o0?l0WOoIfMT000oofMWI00?o0000omWIfOoIfMT09_oI fMT3o`3o04KofMWI0ol0o`2LomWIf@003ooIfMT2o`0002OofMWI0_l0o`18omWIf@?o0?l0VooIfMT0 00oofMWI00?o0000omWIfOoIfMT09OoIfMT3o`3o04WofMWI0_l0o`2KomWIf@003ooIfMT00ol0003o fMWIomWIf@0TomWIf@?o0?l0B_oIfMT3o`3o09[ofMWI000?omWIf@03o`000?oIfMWofMWI02CofMWI 0_l0o`1omWIf@?o0?l0V?oIfMT000[ofMWI00?o0000omWIfOoIfMT00_oIfMT0 0ol0003ofMWIomWIf@0RomWIf@;o0?l0D?oIfMT2o`3o09SofMWI000:omWIf@03o`000?oIfMWofMWI 00;ofMWI0ol0000QomWIf@?o0?l0D?oIfMT3o`3o09OofMWI0006omWIf@Co00001OoIfMT00ol0003o fMWIomWIf@0QomWIf@;o0?l0D_oIfMT3o`3o09KofMWI0006omWIf@03o`000?oIfMWofMWI00KofMWI 00?o0000omWIfOoIfMT08?oIfMT3o`3o05?ofMWI0_l0o`2FomWIf@001_oIfMT5o`0000CofMWI00?o 0000omWIfOoIfMT07ooIfMT3o`3o05CofMWI0ol0o`2EomWIf@003ooIfMT00ol0003ofMWIomWIf@0O omWIf@;o0?l0E_oIfMT2o`3o09GofMWI000?omWIf@03o`000?oIfMWofMWI01kofMWI0ol0o`1FomWI f@?o0?l0U?oIfMT000oofMWI0_l0000NomWIf@?o0?l0F?oIfMT3o`3o09?ofMWI000?omWIf@03o`00 0?oIfMWofMWI01gofMWI0_l0o`1JomWIf@;o0?l0TooIfMT000oofMWI00?o0000omWIfOoIfMT07?oI fMT3o`3o05[ofMWI0ol0o`2BomWIf@003ooIfMT00ol0003ofMWIomWIf@0LomWIf@;o0?l0G?oIfMT2 o`3o09;ofMWI000?omWIf@03o`000?oIfMWofMWI01_ofMWI0ol0o`1LomWIf@?o0?l0TOoIfMT000oo fMWI00?o0000omWIfOoIfMT06ooIfMT2o`3o05kofMWI0ol0o`2@omWIf@003ooIfMT2o`0001_ofMWI 0ol0o`1OomWIf@;o0?l0T?oIfMT000oofMWI00?o0000omWIfOoIfMT06OoIfMT3o`3o063ofMWI0ol0 o`2?omWIf@003ooIfMT00ol0003ofMWIomWIf@0IomWIf@;o0?l0H_oIfMT2o`3o08oofMWI000?omWI f@03o`000?oIfMWofMWI01SofMWI0ol0o`1RomWIf@?o0?l0S_oIfMT000oofMWI00?o0000omWIfOoI fMT06?oIfMT2o`3o06CofMWI0_l0o`2>omWIf@003ooIfMT00ol0003ofMWIomWIf@0GomWIf@?o0?l0 I?oIfMT3o`3o08gofMWI000?omWIf@;o00006?oIfMT2o`3o06KofMWI0ol0o`2omWIf@?o0?l0N?oIfMT000oofMWI 00?o0000omWIfOoIfMT00_oIfMT3o`3o08oofMWI0_l0o`1homWIf@0000CofMWIo`000?l0003o0000 0ooIfMT3o`0000GofMWI00Co0000omWIfOoIfMWofMWI0ol0o`2@omWIf@?o0?l0MooIfMT000;ofMWI 00Go0000omWIfOoIfMWofMWIo`000003omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoI fMWofMWI0_l0o`2BomWIf@;o0?l0MooIfMT000;ofMWI00?o0000omWIfOoIfMT01OoIfMT00ol0003o fMWIomWIf@02omWIf@03o`000?oIfMWofMWI00?o0?l0T_oIfMT3o`3o07KofMWI0002omWIf@03o`00 0?oIfMWofMWI00GofMWI00?o0000omWIfOoIfMT00_oIfMT3o`0000;o0?l0U?oIfMT2o`3o07KofMWI 0002omWIf@04o`000?oIfMWofMWIomWIf@Co00001OoIfMT00ol0003ofMWIo`3o0002o`3o09CofMWI 0ol0o`1eomWIf@0000?ofMWIo`000?l000000ooIfMT00ol0003ofMWIomWIf@06omWIf@04o`000?oI fMWo0?l0o`3o09KofMWI0_l0o`1eomWIf@000_oIfMT01?l0003ofMWIomWIfOoIfMT5o`0000CofMWI 00Co0000o`3o0?l0o`3o0?l0U_oIfMT3o`3o07CofMWI000?omWIf@03o`000?l0o`3o0?l009SofMWI 0_l0o`1domWIf@003ooIfMT3o`3o09SofMWI0ol0o`1comWIf@003ooIfMT2o`3o09[ofMWI0ol0o`1b omWIf@003_oIfMT3o`3o09_ofMWI0_l0o`1YomWIf@;o0?l01ooIfMT000kofMWI0_l0o`2LomWIf@?o 0?l0J?oIfMT2o`3o00OofMWI000?omWIf@03o`000?oIfMWofMWI09_ofMWI0_l0o`1WomWIf@?o0?l0 1ooIfMT000oofMWI00?o0000omWIfOoIfMT0VooIfMT3o`3o06KofMWI0_l0o`08omWIf@003ooIfMT0 0ol0003ofMWIomWIf@2LomWIf@?o0?l0I?oIfMT3o`3o00SofMWI000?omWIf@;o0000W_oIfMT2o`3o 06?ofMWI0ol0o`09omWIf@003ooIfMT00ol0003ofMWIomWIf@2MomWIf@?o0?l0H_oIfMT2o`3o00[o fMWI000?omWIf@03o`000?oIfMWofMWI09kofMWI0_l0o`1QomWIf@?o0?l02_oIfMT000oofMWI00?o 0000omWIfOoIfMT0W_oIfMT3o`3o063ofMWI0_l0o`0;omWIf@003ooIfMT00ol0003ofMWIomWIf@2O omWIf@;o0?l0GooIfMT3o`3o00_ofMWI000?omWIf@03o`000?oIfMWofMWI09oofMWI0ol0o`1MomWI f@?o0?l03?oIfMT000oofMWI0_l0002QomWIf@?o0?l0G?oIfMT2o`3o00gofMWI000?omWIf@03o`00 0?oIfMWofMWI0:7ofMWI0_l0o`1KomWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoI fMT3o`3o05[ofMWI0_l0o`0>omWIf@003ooIfMT00ol0003ofMWIomWIf@2RomWIf@;o0?l0FOoIfMT3 o`3o00kofMWI000?omWIf@03o`000?oIfMWofMWI0:;ofMWI0ol0o`1HomWIf@;o0?l03ooIfMT000oo fMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o05KofMWI0ol0o`0?omWIf@003ooIfMT2o`000:GofMWI 0_l0o`1EomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o05CofMWI0_l0 o`0AomWIf@003ooIfMT00ol0003ofMWIomWIf@2UomWIf@;o0?l0DooIfMT3o`3o017ofMWI000?omWI f@03o`000?oIfMWofMWI0:GofMWI0ol0o`1BomWIf@;o0?l04_oIfMT000Go00000ooIfMT2o`0000Go fMWI00?o0000omWIfOoIfMT0Y_oIfMT3o`3o053ofMWI0ol0o`0BomWIf@0000GofMWIo`000?oIfMWo fMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0YooIfMT2o`3o 04oofMWI0ol0o`0ComWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWIo`00 00CofMWI00?o0000omWIfOoIfMT0YooIfMT3o`3o04kofMWI0_l0o`0DomWIf@000ooIfMT01Ol0003o fMWIomWIfOoIfMWo000000;ofMWI00?o0000omWIfOoIfMT00_oIfMT3o`000:SofMWI0_l0o`1=omWI f@?o0?l05?oIfMT00005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004 omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`1;omWIf@?o0?l05OoIfMT00005o`000?oIfMWofMWI omWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:WofMWI0ol0 o`1:omWIf@;o0?l05_oIfMT00004omWIfOl0003o0000o`0000CofMWI0_l00005omWIf@03o`000?oI fMWofMWI0:[ofMWI0_l0o`19omWIf@?o0?l05_oIfMT000oofMWI00?o0000omWIfOoIfMT0Z_oIfMT3 o`3o04OofMWI0ol0o`0GomWIf@003ooIfMT00ol0003ofMWIomWIf@2[omWIf@;o0?l0A_oIfMT3o`3o 01SofMWI000?omWIf@;o0000[?oIfMT3o`3o04GofMWI0_l0o`0IomWIf@003ooIfMT00ol0003ofMWI omWIf@2/omWIf@?o0?l0@ooIfMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI0_l0 o`12omWIf@?o0?l06_oIfMT000oofMWI00?o0000omWIfOoIfMT0[OoIfMT3o`3o047ofMWI0_l0o`0K omWIf@003ooIfMT00ol0003ofMWIomWIf@2^omWIf@?o0?l0?ooIfMT3o`3o01_ofMWI000?omWIf@03 o`000?oIfMWofMWI0:oofMWI0ol0o`0momWIf@?o0?l07?oIfMT000oofMWI0_l0002aomWIf@;o0?l0 ?OoIfMT2o`3o01gofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0komWIf@?o0?l07OoI fMT000oofMWI00?o0000omWIfOoIfMT0/OoIfMT3o`3o03WofMWI0ol0o`0NomWIf@003ooIfMT00ol0 003ofMWIomWIf@2bomWIf@?o0?l0=ooIfMT3o`3o01oofMWI000?omWIf@03o`000?oIfMWofMWI0;?o fMWI0_l0o`0fomWIf@?o0?l08?oIfMT000oofMWI00?o0000omWIfOoIfMT0/ooIfMT3o`3o03CofMWI 0ol0o`0QomWIf@003ooIfMT2o`000;GofMWI0ol0o`0bomWIf@?o0?l08_oIfMT000oofMWI00?o0000 omWIfOoIfMT0]OoIfMT3o`3o033ofMWI0ol0o`0SomWIf@003ooIfMT00ol0003ofMWIomWIf@2fomWI f@?o0?l0;_oIfMT3o`3o02CofMWI000?omWIf@03o`000?oIfMWofMWI0;OofMWI1?l0o`0[omWIf@?o 0?l09OoIfMT000oofMWI00?o0000omWIfOoIfMT0^?oIfMT4o`3o02WofMWI0ol0o`0VomWIf@003ooI fMT00ol0003ofMWIomWIf@2jomWIf@?o0?l09_oIfMT4o`3o02OofMWI000?omWIf@03o`000?oIfMWo fMWI0;_ofMWI0ol0o`0TomWIf@Co0?l0:?oIfMT000oofMWI0_l0002momWIf@?o0?l08_oIfMT3o`3o 02[ofMWI000?omWIf@03o`000?oIfMWofMWI0;gofMWI1?l0o`0OomWIf@?o0?l0:ooIfMT000oofMWI 00?o0000omWIfOoIfMT0__oIfMT5o`3o01cofMWI0ol0o`0/omWIf@001Ol00002omWIf@?o00001OoI fMT00ol0003ofMWIomWIf@30omWIf@Co0?l06OoIfMT4o`3o02gofMWI00001ooIfMWo0000omWIfOoI fMWo0000omWIfOl000000ooIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0OoIfMT000oofMWI00?o0000omWIfOoIfMT0oooI fMT?omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@oofMWI000?omWIf@;o0000oooIfMT@omWI f@00oooIfMTQomWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -2.25451, \ 0.0237193, 0.161104}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[gv, gvp];\)\)], "Input", CellLabel->"In[14]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[14]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\omWIf@?o0?l0UooIfMT000oofMWI00?o0000omWIfOoIfMT08?oI fMT3o`3o043ofMWI1Ol0000=omWIf@?o0?l0U_oIfMT000oofMWI00?o0000omWIfOoIfMT07ooIfMT3 o`3o04?ofMWI1Ol0000omWIf@003ooIfMT0 0ol0003ofMWIomWIf@0GomWIf@?o0?l0G_oIfMT4o`0000;ofMWI0ol0o`2=omWIf@003ooIfMT2o`00 01OofMWI0ol0o`1PomWIf@Go000000CofMWIo`3o0?l0o`3o0?l0S?oIfMT000oofMWI00?o0000omWI fOoIfMT05_oIfMT2o`3o06?ofMWI1?l000001?oIfMWo0?l0o`3o0?l0o`2;omWIf@003ooIfMT00ol0 003ofMWIomWIf@0EomWIf@?o0?l0IOoIfMT4o`0000;o0?l0RooIfMT000oofMWI00?o0000omWIfOoI fMT05?oIfMT3o`3o06OofMWI0ol00003o`3o08[ofMWI000?omWIf@03o`000?oIfMWofMWI01?ofMWI 0ol0o`1ZomWIf@;o00000ol0o`29omWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI 00?o0000omWIfOoIfMT04_oIfMT3o`3o06cofMWI0_l00003o`3o08SofMWI0002omWIf@03o`000?oI fMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@0BomWIf@;o0?l0 KooIfMT01?l0003o0?l0o`3o0?l0o`27omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`00 0?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT04OoIfMT3o`3o073ofMWI00?o0000o`3o0?l0 o`000_l00025omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWIo`0000Co fMWI0ol0000@omWIf@?o0?l0L_oIfMT3o`3o00;o0000Q?oIfMT000;ofMWI00?o0000omWIfOoIfMT0 0_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI00oofMWI0ol0o`1domWIf@?o 0?l00ol00022omWIf@0000?ofMWIo`000?l000001?oIfMT01?l0003ofMWIomWIfOl00004omWIf@03 o`000?oIfMWofMWI00oofMWI0_l0o`1fomWIf@?o0?l00ol00021omWIf@000_oIfMT00ol0003ofMWI omWIf@03omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@0>omWIf@?o0?l0MooIfMT2o`3o0003omWI fOl0003o000000;o0000OooIfMT000oofMWI00?o0000omWIfOoIfMT03OoIfMT3o`3o07SofMWI0ol0 o`000ooIfMWo0000o`000002o`0007kofMWI000?omWIf@03o`000?oIfMWofMWI00cofMWI0ol0o`1j omWIf@?o0?l00_oIfMT4o`0007cofMWI000?omWIf@03o`000?oIfMWofMWI00cofMWI0_l0o`1lomWI f@?o0?l00_oIfMT4o`0007_ofMWI000?omWIf@03o`000?oIfMWofMWI00_ofMWI0ol0o`1momWIf@?o 0?l00ooIfMT4o`0007WofMWI000?omWIf@;o00002ooIfMT3o`3o07oofMWI0_l0o`04omWIf@Co0000 N?oIfMT000oofMWI00?o0000omWIfOoIfMT02_oIfMT2o`3o083ofMWI0ol0o`05omWIf@Co0000M_oI fMT000oofMWI00?o0000omWIfOoIfMT02OoIfMT3o`3o087ofMWI0ol0o`05omWIf@Co0000MOoIfMT0 00oofMWI00?o0000omWIfOoIfMT02?oIfMT3o`3o08?ofMWI0ol0o`06omWIf@Co0000LooIfMT000oo fMWI00?o0000omWIfOoIfMT01ooIfMT3o`3o08GofMWI0_l0o`07omWIf@Co0000L_oIfMT000oofMWI 00?o0000omWIfOoIfMT01ooIfMT2o`3o08KofMWI0ol0o`08omWIf@?o0000LOoIfMT000oofMWI00?o 0000omWIfOoIfMT01_oIfMT3o`3o08OofMWI0ol0o`08omWIf@Co0000KooIfMT000oofMWI00?o0000 omWIfOoIfMT01OoIfMT3o`3o08WofMWI0ol0o`08omWIf@Co0000K_oIfMT000oofMWI00?o0000omWI fOoIfMT01?oIfMT3o`3o08_ofMWI0_l0o`0:omWIf@Co0000K?oIfMT000oofMWI0_l00004omWIf@?o 0?l0S?oIfMT3o`3o00[ofMWI1?l0001[omWIf@003ooIfMT00ol0003ofMWIomWIf@02omWIf@?o0?l0 S_oIfMT3o`3o00_ofMWI0ol0001ZomWIf@003ooIfMT01?l0003ofMWIomWIfOoIfMT3o`3o093ofMWI 0_l0o`0omWIf@?o0000HooIfMT000kofMWI0ol0o`2IomWIf@?o0?l03_oIfMT3o`0005Wo fMWI0_l0o`07omWIf@003_oIfMT2o`3o09_ofMWI0ol0o`0>omWIf@?o0000F?oIfMT2o`3o00OofMWI 000?omWIf@03o`000?oIfMWofMWI09[ofMWI0ol0o`0>omWIf@?o0000E_oIfMT3o`3o00OofMWI000? omWIf@03o`000?oIfMWofMWI09_ofMWI0ol0o`0>omWIf@Co0000DooIfMT3o`3o00SofMWI000?omWI f@03o`000?oIfMWofMWI09cofMWI0ol0o`0>omWIf@Co0000DOoIfMT3o`3o00WofMWI000?omWIf@03 o`000?oIfMWofMWI09gofMWI0_l0o`0@omWIf@?o0000CooIfMT3o`3o00[ofMWI000?omWIf@03o`00 0?oIfMWofMWI09gofMWI0ol0o`0@omWIf@Co0000C?oIfMT3o`3o00_ofMWI000?omWIf@03o`000?oI fMWofMWI09kofMWI0ol0o`0@omWIf@Co0000B_oIfMT3o`3o00cofMWI000?omWIf@;o0000X?oIfMT3 o`3o017ofMWI0ol00019omWIf@;o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0X?oIfMT3o`3o 017ofMWI1?l00016omWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoIfMT3o`3o017o fMWI1?l00014omWIf@?o0?l03_oIfMT000oofMWI00?o0000omWIfOoIfMT0X_oIfMT3o`3o01;ofMWI 0ol00012omWIf@?o0?l03ooIfMT000oofMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o01;ofMWI1?l0 000oomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o01;ofMWI1?l0000m omWIf@?o0?l04OoIfMT000Go00000ooIfMT2o`0000GofMWI00?o0000omWIfOoIfMT0YOoIfMT3o`3o 01?ofMWI0ol0000komWIf@?o0?l04_oIfMT00005omWIfOl0003ofMWIomWIfOl000000_oIfMT01?l0 003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:KofMWI0ol0o`0ComWIf@?o0000>OoIfMT3 o`3o01?ofMWI0002omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT3 o`000:OofMWI0ol0o`0ComWIf@?o0000=ooIfMT3o`3o01CofMWI0003omWIf@05o`000?oIfMWofMWI omWIfOl000000_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`0C omWIf@?o0000=OoIfMT3o`3o01GofMWI00001Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000 omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@2YomWIf@?o0?l04ooIfMT3o`0003?ofMWI0ol0 o`0FomWIf@0000Go0000omWIfOoIfMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI 00?o0000omWIfOoIfMT0Z_oIfMT3o`3o01?ofMWI0ol0000aomWIf@?o0?l05ooIfMT00004omWIfOl0 003o0000o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI0:_ofMWI0ol0o`0ComWIf@?o0000 ;ooIfMT3o`3o01SofMWI000?omWIf@03o`000?oIfMWofMWI0:cofMWI1?l0o`0BomWIf@?o0000;OoI fMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI1?l0o`0BomWIf@?o0000:ooIfMT3 o`3o01[ofMWI000?omWIf@03o`000?oIfMWofMWI0:oofMWI0ol0o`0BomWIf@?o0000:OoIfMT3o`3o 01_ofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0BomWIf@?o00009_oIfMT4o`3o01co fMWI000?omWIf@;o0000/_oIfMT3o`3o01;ofMWI0ol0000TomWIf@Co0?l07OoIfMT000oofMWI00?o 0000omWIfOoIfMT0/_oIfMT4o`3o017ofMWI0ol0000RomWIf@?o0?l07ooIfMT000oofMWI00?o0000 omWIfOoIfMT0/ooIfMT4o`3o017ofMWI0ol0000OomWIf@Co0?l08?oIfMT000oofMWI00?o0000omWI fOoIfMT0]OoIfMT3o`3o017ofMWI0ol0000MomWIf@Co0?l08OoIfMT000oofMWI00?o0000omWIfOoI fMT0]_oIfMT3o`3o017ofMWI0ol0000JomWIf@Co0?l08ooIfMT000oofMWI00?o0000omWIfOoIfMT0 ]ooIfMT4o`3o013ofMWI0ol0000HomWIf@Co0?l09?oIfMT000oofMWI00?o0000omWIfOoIfMT0^?oI fMT4o`3o013ofMWI0ol0000FomWIf@?o0?l09_oIfMT000oofMWI00?o0000omWIfOoIfMT0^_oIfMT4 o`3o00oofMWI0ol0000ComWIf@Co0?l09ooIfMT000oofMWI0_l0002lomWIf@Co0?l03ooIfMT2o`00 017ofMWI1Ol0o`0XomWIf@003ooIfMT00ol0003ofMWIomWIf@2momWIf@Co0?l03OoIfMT3o`0000ko fMWI1Ol0o`0ZomWIf@003ooIfMT00ol0003ofMWIomWIf@2nomWIf@Ko0?l02ooIfMT3o`0000_ofMWI 1Ol0o`0/omWIf@003ooIfMT00ol0003ofMWIomWIf@30omWIf@Oo0?l02OoIfMT3o`0000SofMWI1Ol0 o`0^omWIf@003ooIfMT00ol0003ofMWIomWIf@33omWIf@Oo0?l01ooIfMT3o`0000CofMWI1_l0o`0` omWIf@003ooIfMT00ol0003ofMWIomWIf@36omWIf@[o0?l000?ofMWIo`3o0?l0o`002Ol0o`0bomWI f@003ooIfMT00ol0003ofMWIomWIf@39omWIfA3o0?l0=OoIfMT000oofMWI00?o0000omWIfOoIfMT0 c_oIfMT5o`3o0004omWIfOl0003o0000o`0003OofMWI000?omWIf@;o0000e_oIfMT3o`0003KofMWI 000?omWIf@03o`000?oIfMWofMWI0=KofMWI0ol0000eomWIf@003ooIfMT00ol0003ofMWIomWIf@3G omWIf@?o0000=?oIfMT000oofMWI00?o0000omWIfOoIfMT0f?oIfMT3o`0003?ofMWI000?omWIf@03 o`000?oIfMWofMWI0=WofMWI0ol0000bomWIf@003ooIfMT00ol0003ofMWIomWIf@3JomWIf@?o0000 3ofMWI0ol0000[omWIf@003ooIfMT00ol0003ofMWIomWIf@3Q omWIf@?o0000:_oIfMT000oofMWI00?o0000omWIfOoIfMT0h_oIfMT3o`0002WofMWI00001?oIfMWo 0000o`000?l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@3SomWIf@?o0000:?oIfMT00005 o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWo fMWI0>CofMWI0_l0000XomWIf@001?oIfMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWo fMWI00;ofMWI00?o0000omWIfOoIfMT0i?oIfMT3o`0002OofMWI0002omWIf@;o00000ooIfMT01?l0 003ofMWIomWIfOl00004omWIf@?o0000iOoIfMT3o`0002KofMWI0004omWIf@04o`000?oIfMWofMWI o`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWIomWIf@3VomWIf@?o00009OoIfMT0 0005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oI fMWofMWI0>OofMWI0ol0000TomWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI00?o 0000omWIfOoIfMT0j?oIfMT3o`0002?ofMWI000?omWIf@03o`000?oIfMWofMWI0>WofMWI0ol0000R omWIf@003ooIfMT00ol0003ofMWIomWIf@3ZomWIf@?o00008OoIfMT000oofMWI00?o0000omWIfOoI fMT0jooIfMT3o`00023ofMWI000?omWIf@03o`000?oIfMWofMWI0>cofMWI0ol0000OomWIf@003ooI fMT2o`000>kofMWI0ol0000NomWIf@003ooIfMT00ol0003ofMWIomWIf@3^omWIf@?o00007OoIfMT0 00oofMWI00?o0000omWIfOoIfMT0kooIfMT3o`0001cofMWI000?omWIf@03o`000?oIfMWofMWI0?3o fMWI0_l0000LomWIf@003ooIfMT00ol0003ofMWIomWIf@3`omWIf@?o00006ooIfMT000oofMWI00?o 0000omWIfOoIfMT0lOoIfMT3o`0001[ofMWI000?omWIf@03o`000?oIfMWofMWI0?;ofMWI0ol0000I omWIf@003ooIfMT00ol0003ofMWIomWIf@3comWIf@?o00006?oIfMT000oofMWI0_l0003eomWIf@?o 00005ooIfMT000oofMWI00?o0000omWIfOoIfMT0mOoIfMT3o`0001KofMWI000?omWIf@03o`000?oI fMWofMWI0?KofMWI0ol0000EomWIf@003ooIfMT00ol0003ofMWIomWIf@3gomWIf@?o00005?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0n?oIfMT3o`0001?ofMWI000?omWIf@03o`000?oIfMWofMWI0?Wo fMWI0ol0000BomWIf@003ooIfMT00ol0003ofMWIomWIf@3jomWIf@?o00004OoIfMT000oofMWI00?o 0000omWIfOoIfMT0nooIfMT2o`00017ofMWI000?omWIf@03o`000?oIfMWofMWI0?_ofMWI0ol0000@ omWIf@003ooIfMT2o`000?gofMWI0ol0000?omWIf@003ooIfMT00ol0003ofMWIomWIf@3momWIf@?o 00003_oIfMT000oofMWI00?o0000omWIfOoIfMT0o_oIfMT2o`0000kofMWI000?omWIf@03o`000?oI fMWofMWI0?kofMWI0ol0000=omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@?o00003?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0oooIfMT1omWIf@?o00002ooIfMT000oofMWI00?o0000omWIfOoI fMT0oooIfMT2omWIf@?o00002_oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT3omWIf@;o0000 2_oIfMT000oofMWI0_l0003oomWIf@CofMWI0ol00009omWIf@003ooIfMT00ol0003ofMWIomWIf@3o omWIf@CofMWI0ol00008omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@GofMWI0ol00007omWI f@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@KofMWI0_l00007omWIf@003ooIfMT00ol0003ofMWI omWIf@3oomWIf@oofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000 omWIfOoIfMT0oooIfMT?omWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.12112, \ 0.0237193, 0.241311}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c.- ", FontColor->RGBColor[1, 0, 0]], "Calcular ", "la norma de la funci\[OAcute]n error." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(e[x_] := v[x] - vp\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ne = Sqrt[pe[e[x], e[x]]] // N\)], "Input", CellLabel->"In[16]:=", FontSize->14], Cell[BoxData[ \(18.00250212986795`\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[17]:=", FontSize->14] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{0, 1024}, {0, 698}}, WindowSize->{748, 557}, WindowMargins->{{32, Automatic}, {Automatic, 35}}, StyleDefinitions -> "ArticleModern.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 228, 5, 90, "Title"], Cell[CellGroupData[{ Cell[2029, 62, 140, 2, 76, "SectionFirst"], Cell[2172, 66, 306, 8, 42, "Text"], Cell[2481, 76, 1315, 39, 91, "Text"], Cell[3799, 117, 293, 7, 42, "Text"], Cell[4095, 126, 193, 6, 43, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4325, 137, 342, 9, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[4692, 150, 930, 33, 153, "Subsubsection"], Cell[5625, 185, 62, 0, 24, "Text"], Cell[5690, 187, 130, 3, 43, "Input"], Cell[5823, 192, 112, 3, 43, "Input"], Cell[CellGroupData[{ Cell[5960, 199, 87, 3, 43, "Input"], Cell[6050, 204, 95, 2, 44, "Output"] }, Open ]], Cell[6160, 209, 215, 7, 26, "Text"], Cell[CellGroupData[{ Cell[6400, 220, 112, 3, 43, "Input"], Cell[6515, 225, 95, 2, 44, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[6659, 233, 280, 9, 62, "Subsubsection"], Cell[6942, 244, 320, 6, 40, "Text"], Cell[7265, 252, 3225, 95, 63, "Text"], Cell[10493, 349, 411, 10, 42, "Text"], Cell[CellGroupData[{ Cell[10929, 363, 87, 3, 43, "Input"], Cell[11019, 368, 77, 2, 42, "Output"] }, Open ]], Cell[11111, 373, 961, 26, 74, "Text"], Cell[CellGroupData[{ Cell[12097, 403, 88, 3, 43, "Input"], Cell[12188, 408, 96, 2, 42, "Output"] }, Open ]], Cell[12299, 413, 238, 7, 26, "Text"], Cell[CellGroupData[{ Cell[12562, 424, 87, 3, 43, "Input"], Cell[12652, 429, 130, 3, 42, "Output"] }, Open ]], Cell[12797, 435, 258, 5, 40, "Text"], Cell[13058, 442, 2511, 68, 120, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[15606, 515, 216, 8, 44, "Subsubsection"], Cell[15825, 525, 813, 23, 94, "Text"], Cell[16641, 550, 119, 3, 43, "Input"], Cell[CellGroupData[{ Cell[16785, 557, 103, 3, 43, "Input"], Cell[16891, 562, 101, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17029, 569, 87, 3, 43, "Input"], Cell[17119, 574, 400, 12, 84, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17556, 591, 114, 3, 43, "Input"], Cell[17673, 596, 397, 12, 84, "Output"] }, Open ]], Cell[18085, 611, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[18421, 624, 97, 3, 43, "Input"], Cell[18521, 629, 63, 2, 42, "Output"] }, Open ]], Cell[18599, 634, 2956, 85, 203, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[21592, 724, 496, 16, 45, "Subsubsection"], Cell[22091, 742, 226, 5, 24, "Text"], Cell[CellGroupData[{ Cell[22342, 751, 263, 7, 64, "Input"], Cell[22608, 760, 485, 10, 70, "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[23142, 776, 273, 9, 28, "Subsubsection"], Cell[23418, 787, 74, 0, 24, "Text"], Cell[CellGroupData[{ Cell[23517, 791, 97, 3, 43, "Input"], Cell[23617, 796, 64, 2, 70, "Output"] }, Open ]], Cell[23696, 801, 113, 3, 24, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[23846, 809, 439, 14, 47, "Subsubsection"], Cell[CellGroupData[{ Cell[24310, 827, 142, 4, 43, "Input"], Cell[24455, 833, 63, 2, 70, "Output"] }, Open ]], Cell[24533, 838, 102, 3, 43, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[24684, 847, 189, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[24898, 854, 882, 29, 153, "Subsubsection"], Cell[CellGroupData[{ Cell[25805, 887, 235, 5, 61, "Input"], Cell[26043, 894, 114, 2, 70, "Output"] }, Open ]], Cell[26172, 899, 3225, 95, 63, "Text"], Cell[29400, 996, 3310, 92, 139, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[32747, 1093, 352, 10, 46, "Subsubsection"], Cell[33102, 1105, 182, 4, 40, "Text"], Cell[33287, 1111, 252, 6, 61, "Input"], Cell[CellGroupData[{ Cell[33564, 1121, 144, 4, 43, "Input"], Cell[33711, 1127, 62, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33810, 1134, 121, 3, 43, "Input"], Cell[33934, 1139, 60, 2, 70, "Output"] }, Open ]], Cell[34009, 1144, 101, 3, 43, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[34159, 1153, 257, 5, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[34441, 1162, 854, 32, 117, "Subsubsection"], Cell[35298, 1196, 116, 3, 24, "Text"], Cell[35417, 1201, 115, 3, 43, "Input"], Cell[CellGroupData[{ Cell[35557, 1208, 114, 3, 43, "Input"], Cell[35674, 1213, 114, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35825, 1220, 118, 3, 43, "Input"], Cell[35946, 1225, 393, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36376, 1242, 113, 3, 43, "Input"], Cell[36492, 1247, 399, 12, 70, "Output"] }, Open ]], Cell[36906, 1262, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[37242, 1275, 96, 3, 43, "Input"], Cell[37341, 1280, 62, 2, 70, "Output"] }, Open ]], Cell[37418, 1285, 4546, 137, 63, "Text"], Cell[41967, 1424, 3635, 104, 101, "Text"], Cell[45605, 1530, 3061, 89, 203, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[48703, 1624, 267, 9, 28, "Subsubsection"], Cell[48973, 1635, 705, 22, 62, "Text"], Cell[49681, 1659, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[49814, 1666, 101, 3, 43, "Input"], Cell[49918, 1671, 173, 4, 70, "Output"] }, Open ]], Cell[50106, 1678, 219, 6, 26, "Text"], Cell[CellGroupData[{ Cell[50350, 1688, 125, 3, 43, "Input"], Cell[50478, 1693, 62, 2, 70, "Output"] }, Open ]], Cell[50555, 1698, 283, 9, 44, "Text"], Cell[CellGroupData[{ Cell[50863, 1711, 94, 3, 43, "Input"], Cell[50960, 1716, 62, 2, 70, "Output"] }, Open ]], Cell[51037, 1721, 3120, 89, 283, "Text"], Cell[54160, 1812, 102, 3, 43, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[54311, 1821, 244, 5, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[54580, 1830, 635, 21, 95, "Subsubsection"], Cell[55218, 1853, 153, 4, 43, "Input"], Cell[CellGroupData[{ Cell[55396, 1861, 175, 5, 43, "Input"], Cell[55574, 1868, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[55683, 1876, 326, 10, 62, "Subsubsection"], Cell[56012, 1888, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[56145, 1895, 103, 3, 43, "Input"], Cell[56251, 1900, 232, 4, 116, "Output"] }, Open ]], Cell[56498, 1907, 536, 15, 44, "Text"], Cell[CellGroupData[{ Cell[57059, 1926, 128, 3, 43, "Input"], Cell[57190, 1931, 88, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[57315, 1938, 176, 5, 43, "Input"], Cell[57494, 1945, 133, 3, 57, "Output"] }, Open ]], Cell[57642, 1951, 101, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[57792, 1960, 298, 5, 122, "SectionFirst"], Cell[CellGroupData[{ Cell[58115, 1969, 1746, 54, 181, "Subsubsection"], Cell[59864, 2025, 74, 1, 24, "Text"], Cell[59941, 2028, 278, 5, 26, "Text"], Cell[60222, 2035, 528, 18, 26, "Text"], Cell[60753, 2055, 131, 4, 24, "Text"], Cell[60887, 2061, 117, 3, 43, "Input"], Cell[61007, 2066, 197, 4, 79, "Input"], Cell[61207, 2072, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[61340, 2079, 123, 3, 43, "Input"], Cell[61466, 2084, 111, 2, 61, "Output"] }, Open ]], Cell[61592, 2089, 295, 7, 42, "Text"], Cell[CellGroupData[{ Cell[61912, 2100, 181, 5, 43, "Input"], Cell[62096, 2107, 62, 2, 42, "Output"] }, Open ]], Cell[62173, 2112, 23, 0, 24, "Text"], Cell[CellGroupData[{ Cell[62221, 2116, 127, 3, 43, "Input"], Cell[62351, 2121, 91, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[62479, 2128, 87, 3, 43, "Input"], Cell[62569, 2133, 393, 12, 84, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[63011, 2151, 652, 19, 81, "Subsubsection"], Cell[63666, 2172, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[63785, 2179, 172, 5, 43, "Input"], Cell[63960, 2186, 118, 3, 60, "Output"] }, Open ]], Cell[64093, 2192, 330, 10, 42, "Text"], Cell[CellGroupData[{ Cell[64448, 2206, 583, 16, 61, "Input"], Cell[65034, 2224, 21946, 573, 194, 5142, 360, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[86995, 2800, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[87322, 2812, 164, 5, 43, "Input"], Cell[87489, 2819, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[103021, 3244, 199, 6, 61, "Input"], Cell[103223, 3252, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[122146, 3780, 92, 3, 43, "Input"], Cell[122241, 3785, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[142605, 4342, 272, 10, 44, "Subsubsection"], Cell[142880, 4354, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[142997, 4361, 104, 3, 43, "Input"], Cell[143104, 4366, 77, 2, 42, "Output"] }, Open ]], Cell[143196, 4371, 102, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[143347, 4380, 194, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[143566, 4387, 2001, 62, 251, "Subsubsection"], Cell[145570, 4451, 1404, 50, 110, "Text"], Cell[146977, 4503, 620, 23, 26, "Text"], Cell[147600, 4528, 403, 14, 26, "Text"], Cell[148006, 4544, 2523, 80, 62, "Text"], Cell[150532, 4626, 131, 4, 24, "Text"], Cell[150666, 4632, 378, 8, 97, "Input"], Cell[151047, 4642, 100, 3, 24, "Text"], Cell[CellGroupData[{ Cell[151172, 4649, 342, 9, 79, "Input"], Cell[151517, 4660, 17566, 412, 194, 3292, 231, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[169098, 5075, 181, 4, 24, "Text"], Cell[CellGroupData[{ Cell[169304, 5083, 146, 4, 43, "Input"], Cell[169453, 5089, 106, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[169596, 5096, 104, 3, 43, "Input"], Cell[169703, 5101, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[169817, 5108, 98, 3, 43, "Input"], Cell[169918, 5113, 386, 6, 27, "Message"], Cell[170307, 5121, 84, 2, 42, "Output"] }, Open ]], Cell[170406, 5126, 41, 0, 24, "Text"], Cell[170450, 5128, 144, 4, 43, "Input"], Cell[CellGroupData[{ Cell[170619, 5136, 156, 4, 61, "Input"], Cell[170778, 5142, 459, 10, 40, "Print"] }, Open ]], Cell[171252, 5155, 97, 3, 24, "Text"], Cell[CellGroupData[{ Cell[171374, 5162, 197, 6, 43, "Input"], Cell[171574, 5170, 21760, 521, 194, 4200, 299, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[193371, 5696, 91, 3, 43, "Input"], Cell[193465, 5701, 22239, 533, 194, 4327, 307, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[215719, 6237, 106, 3, 24, "Text"], Cell[215828, 6242, 109, 3, 43, "Input"], Cell[CellGroupData[{ Cell[215962, 6249, 239, 5, 79, "Input"], Cell[216204, 6256, 214, 4, 68, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[216455, 6265, 122, 3, 43, "Input"], Cell[216580, 6270, 187, 4, 42, "Output"] }, Open ]], Cell[216782, 6277, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[217109, 6289, 271, 6, 61, "Input"], Cell[217383, 6297, 156, 4, 42, "Output"] }, Open ]], Cell[217554, 6304, 35, 0, 24, "Text"], Cell[217592, 6306, 259, 7, 43, "Input"], Cell[CellGroupData[{ Cell[217876, 6317, 63, 2, 42, "Input"], Cell[217942, 6321, 152, 3, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[218131, 6329, 103, 2, 42, "Input"], Cell[218237, 6333, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[218351, 6340, 199, 6, 43, "Input"], Cell[218553, 6348, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[237476, 6876, 92, 3, 43, "Input"], Cell[237571, 6881, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[257935, 7438, 272, 10, 44, "Subsubsection"], Cell[258210, 7450, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[258327, 7457, 104, 3, 43, "Input"], Cell[258434, 7462, 77, 2, 42, "Output"] }, Open ]], Cell[258526, 7467, 102, 3, 43, "Input"] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) fMT00ooIfMT01Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000omWIfOoIfMWo00000_oI fMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWofMWI00;ofMWI00?o0000omWIfOl0o`00 0_l0o`3jomWIf@0000Oo0000omWIfOoIfMWofMWIo`000?oIfMWo000000?ofMWI00Co0000omWIfOoI fMWo00000_oIfMT01?l0003ofMWIomWIfOl00002omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o 0000omWIfOoIfMT00_oIfMT01?l0003o0?l0o`3o0?l0o`3komWIf@0000Oo0000omWIfOoIfMWofMWI o`000?oIfMWo000000?ofMWI00Co0000omWIfOoIfMWo00000_oIfMT01?l0003ofMWIomWIfOl00002 omWIf@04o`000?oIfMWofMWIo`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT3o`3o0?cofMWI0000 1?oIfMWo0000o`000?l00003omWIf@?o00001?oIfMT2o`0000CofMWI0_l00004omWIf@;o00001?oI fMT3o`3o0?gofMWI000PomWIf@;o0?l0o_oIfMT0027ofMWI0_l0003momWIf@008OoIfMT00ol0003o fMWIomWIf@3lomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWI f@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00oooIfMTQomWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-8.73034, 7382.5, 0.262564, \ 90.2821}}] }, Open ]], Cell["\", "Text"], Cell[BoxData[ \("In[17]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[{ \(\(a1 = \(Transpose[A]\)[\([1]\)];\)\), "\[IndentingNewLine]", \(\(a2 = \(Transpose[A]\)[\([2]\)];\)\), "\[IndentingNewLine]", \(o = GramSchmidt[{a1, a2}]\)}], "Input", CellLabel->"In[18]:=", FontSize->14], Cell[BoxData[ \({{1\/\@6, 1\/\@6, 1\/\@6, 1\/\@6, 1\/\@6, 1\/\@6}, {\(-\@\(5\/14\)\), \(-\(3\/\@70\)\), \(-\(1\/\@70\)\), 1\/\@70, 3\/\@70, \@\(5\/14\)}}\)], "Output", CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(bp = Sum[Projection[b, o[\([i]\)]], {i, 2}] // N\)], "Input", CellLabel->"In[21]:=", FontSize->14], Cell[BoxData[ \({9.862382354414756`, 9.713489018094522`, 9.56459568177429`, 9.415702345454058`, 9.266809009133825`, 9.117915672813591`}\)], "Output",\ CellLabel->"Out[21]="] }, Open ]], Cell[TextData[{ "Aunque nos puede resultar m\[AAcute]s c\[OAcute]modo dibujrlas por \ separado con colores distintos y utilizar posteriormente la funci\[OAcute]n \ ", StyleBox["Show", FontFamily->"Courier", FontWeight->"Bold"], " para mostrar las dos gr\[AAcute]ficas juntas:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(sistema = Table[l\[Alpha]*a1[\([i]\)] + \[Beta]*a2[\([i]\)] \[Equal] bp[\([i]\)], {i, Length[a1]}];\)\), "\[IndentingNewLine]", \(Solve[sistema, {l\[Alpha], \[Beta]}]\)}], "Input", CellLabel->"In[26]:=", FontSize->14], Cell[BoxData[ \({{l\[Alpha] \[Rule] 10.011275690734989`, \[Beta] \[Rule] \ \(-0.01488933363202328`\)}}\)], "Output", CellLabel->"Out[27]="] }, Open ]], Cell["La curva pedida es:", "Text"], Cell[BoxData[ \(\(ng[ t_] := \((Exp[ l\[Alpha]] /. {\(%27[\([1]\)]\)[\([1]\)]})\)*\((Exp[\[Beta]* t])\) /. {\[Beta] \[Rule] \(%27[\([1]\)]\)[\([2]\)]};\)\)], \ "Input", CellLabel->"In[42]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ng[t]\)], "Input", CellLabel->"In[43]:="], Cell[BoxData[ \(22276.23492450123`\ \[ExponentialE]\^\(t\ \((\[Beta] \[Rule] \ \(-0.01488933363202328`\))\)\)\)], "Output", CellLabel->"Out[43]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Exp[l\[Alpha]] /. {\(%27[\([1]\)]\)[\([1]\)]}\)], "Input", CellLabel->"In[37]:="], Cell[BoxData[ \(22276.23492450123`\)], "Output", CellLabel->"Out[37]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(gvp = Plot[vp, {x, 0, 2 Pi}, PlotStyle \[Rule] {RGBColor[0, 1, 0], Thickness[0.01]}];\)\)], "Input", CellLabel->"In[13]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[13]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\?oIfMT3o`3o0:?ofMWI000?omWIf@03o`000?oIfMWo fMWI02gofMWI0ol0o`0iomWIf@?o0?l0X_oIfMT000oofMWI00?o0000omWIfOoIfMT0;?oIfMT3o`3o 03_ofMWI0ol0o`2QomWIf@003ooIfMT00ol0003ofMWIomWIf@0[omWIf@?o0?l0?OoIfMT2o`3o0:7o fMWI000?omWIf@03o`000?oIfMWofMWI02_ofMWI0_l0o`0nomWIf@?o0?l0X?oIfMT000oofMWI0_l0 000[omWIf@?o0?l0?ooIfMT3o`3o09oofMWI000?omWIf@03o`000?oIfMWofMWI02WofMWI0ol0o`11 omWIf@;o0?l0WooIfMT000oofMWI00?o0000omWIfOoIfMT0:?oIfMT3o`3o04;ofMWI0ol0o`2NomWI f@003ooIfMT00ol0003ofMWIomWIf@0XomWIf@;o0?l0A?oIfMT3o`3o09gofMWI000?omWIf@03o`00 0?oIfMWofMWI02OofMWI0ol0o`15omWIf@;o0?l0WOoIfMT000oofMWI00?o0000omWIfOoIfMT09_oI fMT3o`3o04KofMWI0ol0o`2LomWIf@003ooIfMT2o`0002OofMWI0_l0o`18omWIf@?o0?l0VooIfMT0 00oofMWI00?o0000omWIfOoIfMT09OoIfMT3o`3o04WofMWI0_l0o`2KomWIf@003ooIfMT00ol0003o fMWIomWIf@0TomWIf@?o0?l0B_oIfMT3o`3o09[ofMWI000?omWIf@03o`000?oIfMWofMWI02CofMWI 0_l0o`1omWIf@?o0?l0V?oIfMT000[ofMWI00?o0000omWIfOoIfMT00_oIfMT0 0ol0003ofMWIomWIf@0RomWIf@;o0?l0D?oIfMT2o`3o09SofMWI000:omWIf@03o`000?oIfMWofMWI 00;ofMWI0ol0000QomWIf@?o0?l0D?oIfMT3o`3o09OofMWI0006omWIf@Co00001OoIfMT00ol0003o fMWIomWIf@0QomWIf@;o0?l0D_oIfMT3o`3o09KofMWI0006omWIf@03o`000?oIfMWofMWI00KofMWI 00?o0000omWIfOoIfMT08?oIfMT3o`3o05?ofMWI0_l0o`2FomWIf@001_oIfMT5o`0000CofMWI00?o 0000omWIfOoIfMT07ooIfMT3o`3o05CofMWI0ol0o`2EomWIf@003ooIfMT00ol0003ofMWIomWIf@0O omWIf@;o0?l0E_oIfMT2o`3o09GofMWI000?omWIf@03o`000?oIfMWofMWI01kofMWI0ol0o`1FomWI f@?o0?l0U?oIfMT000oofMWI0_l0000NomWIf@?o0?l0F?oIfMT3o`3o09?ofMWI000?omWIf@03o`00 0?oIfMWofMWI01gofMWI0_l0o`1JomWIf@;o0?l0TooIfMT000oofMWI00?o0000omWIfOoIfMT07?oI fMT3o`3o05[ofMWI0ol0o`2BomWIf@003ooIfMT00ol0003ofMWIomWIf@0LomWIf@;o0?l0G?oIfMT2 o`3o09;ofMWI000?omWIf@03o`000?oIfMWofMWI01_ofMWI0ol0o`1LomWIf@?o0?l0TOoIfMT000oo fMWI00?o0000omWIfOoIfMT06ooIfMT2o`3o05kofMWI0ol0o`2@omWIf@003ooIfMT2o`0001_ofMWI 0ol0o`1OomWIf@;o0?l0T?oIfMT000oofMWI00?o0000omWIfOoIfMT06OoIfMT3o`3o063ofMWI0ol0 o`2?omWIf@003ooIfMT00ol0003ofMWIomWIf@0IomWIf@;o0?l0H_oIfMT2o`3o08oofMWI000?omWI f@03o`000?oIfMWofMWI01SofMWI0ol0o`1RomWIf@?o0?l0S_oIfMT000oofMWI00?o0000omWIfOoI fMT06?oIfMT2o`3o06CofMWI0_l0o`2>omWIf@003ooIfMT00ol0003ofMWIomWIf@0GomWIf@?o0?l0 I?oIfMT3o`3o08gofMWI000?omWIf@;o00006?oIfMT2o`3o06KofMWI0ol0o`2omWIf@?o0?l0N?oIfMT000oofMWI 00?o0000omWIfOoIfMT00_oIfMT3o`3o08oofMWI0_l0o`1homWIf@0000CofMWIo`000?l0003o0000 0ooIfMT3o`0000GofMWI00Co0000omWIfOoIfMWofMWI0ol0o`2@omWIf@?o0?l0MooIfMT000;ofMWI 00Go0000omWIfOoIfMWofMWIo`000003omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoI fMWofMWI0_l0o`2BomWIf@;o0?l0MooIfMT000;ofMWI00?o0000omWIfOoIfMT01OoIfMT00ol0003o fMWIomWIf@02omWIf@03o`000?oIfMWofMWI00?o0?l0T_oIfMT3o`3o07KofMWI0002omWIf@03o`00 0?oIfMWofMWI00GofMWI00?o0000omWIfOoIfMT00_oIfMT3o`0000;o0?l0U?oIfMT2o`3o07KofMWI 0002omWIf@04o`000?oIfMWofMWIomWIf@Co00001OoIfMT00ol0003ofMWIo`3o0002o`3o09CofMWI 0ol0o`1eomWIf@0000?ofMWIo`000?l000000ooIfMT00ol0003ofMWIomWIf@06omWIf@04o`000?oI fMWo0?l0o`3o09KofMWI0_l0o`1eomWIf@000_oIfMT01?l0003ofMWIomWIfOoIfMT5o`0000CofMWI 00Co0000o`3o0?l0o`3o0?l0U_oIfMT3o`3o07CofMWI000?omWIf@03o`000?l0o`3o0?l009SofMWI 0_l0o`1domWIf@003ooIfMT3o`3o09SofMWI0ol0o`1comWIf@003ooIfMT2o`3o09[ofMWI0ol0o`1b omWIf@003_oIfMT3o`3o09_ofMWI0_l0o`1YomWIf@;o0?l01ooIfMT000kofMWI0_l0o`2LomWIf@?o 0?l0J?oIfMT2o`3o00OofMWI000?omWIf@03o`000?oIfMWofMWI09_ofMWI0_l0o`1WomWIf@?o0?l0 1ooIfMT000oofMWI00?o0000omWIfOoIfMT0VooIfMT3o`3o06KofMWI0_l0o`08omWIf@003ooIfMT0 0ol0003ofMWIomWIf@2LomWIf@?o0?l0I?oIfMT3o`3o00SofMWI000?omWIf@;o0000W_oIfMT2o`3o 06?ofMWI0ol0o`09omWIf@003ooIfMT00ol0003ofMWIomWIf@2MomWIf@?o0?l0H_oIfMT2o`3o00[o fMWI000?omWIf@03o`000?oIfMWofMWI09kofMWI0_l0o`1QomWIf@?o0?l02_oIfMT000oofMWI00?o 0000omWIfOoIfMT0W_oIfMT3o`3o063ofMWI0_l0o`0;omWIf@003ooIfMT00ol0003ofMWIomWIf@2O omWIf@;o0?l0GooIfMT3o`3o00_ofMWI000?omWIf@03o`000?oIfMWofMWI09oofMWI0ol0o`1MomWI f@?o0?l03?oIfMT000oofMWI0_l0002QomWIf@?o0?l0G?oIfMT2o`3o00gofMWI000?omWIf@03o`00 0?oIfMWofMWI0:7ofMWI0_l0o`1KomWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoI fMT3o`3o05[ofMWI0_l0o`0>omWIf@003ooIfMT00ol0003ofMWIomWIf@2RomWIf@;o0?l0FOoIfMT3 o`3o00kofMWI000?omWIf@03o`000?oIfMWofMWI0:;ofMWI0ol0o`1HomWIf@;o0?l03ooIfMT000oo fMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o05KofMWI0ol0o`0?omWIf@003ooIfMT2o`000:GofMWI 0_l0o`1EomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o05CofMWI0_l0 o`0AomWIf@003ooIfMT00ol0003ofMWIomWIf@2UomWIf@;o0?l0DooIfMT3o`3o017ofMWI000?omWI f@03o`000?oIfMWofMWI0:GofMWI0ol0o`1BomWIf@;o0?l04_oIfMT000Go00000ooIfMT2o`0000Go fMWI00?o0000omWIfOoIfMT0Y_oIfMT3o`3o053ofMWI0ol0o`0BomWIf@0000GofMWIo`000?oIfMWo fMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT0YooIfMT2o`3o 04oofMWI0ol0o`0ComWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWIo`00 00CofMWI00?o0000omWIfOoIfMT0YooIfMT3o`3o04kofMWI0_l0o`0DomWIf@000ooIfMT01Ol0003o fMWIomWIfOoIfMWo000000;ofMWI00?o0000omWIfOoIfMT00_oIfMT3o`000:SofMWI0_l0o`1=omWI f@?o0?l05?oIfMT00005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004 omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`1;omWIf@?o0?l05OoIfMT00005o`000?oIfMWofMWI omWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:WofMWI0ol0 o`1:omWIf@;o0?l05_oIfMT00004omWIfOl0003o0000o`0000CofMWI0_l00005omWIf@03o`000?oI fMWofMWI0:[ofMWI0_l0o`19omWIf@?o0?l05_oIfMT000oofMWI00?o0000omWIfOoIfMT0Z_oIfMT3 o`3o04OofMWI0ol0o`0GomWIf@003ooIfMT00ol0003ofMWIomWIf@2[omWIf@;o0?l0A_oIfMT3o`3o 01SofMWI000?omWIf@;o0000[?oIfMT3o`3o04GofMWI0_l0o`0IomWIf@003ooIfMT00ol0003ofMWI omWIf@2/omWIf@?o0?l0@ooIfMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI0_l0 o`12omWIf@?o0?l06_oIfMT000oofMWI00?o0000omWIfOoIfMT0[OoIfMT3o`3o047ofMWI0_l0o`0K omWIf@003ooIfMT00ol0003ofMWIomWIf@2^omWIf@?o0?l0?ooIfMT3o`3o01_ofMWI000?omWIf@03 o`000?oIfMWofMWI0:oofMWI0ol0o`0momWIf@?o0?l07?oIfMT000oofMWI0_l0002aomWIf@;o0?l0 ?OoIfMT2o`3o01gofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0komWIf@?o0?l07OoI fMT000oofMWI00?o0000omWIfOoIfMT0/OoIfMT3o`3o03WofMWI0ol0o`0NomWIf@003ooIfMT00ol0 003ofMWIomWIf@2bomWIf@?o0?l0=ooIfMT3o`3o01oofMWI000?omWIf@03o`000?oIfMWofMWI0;?o fMWI0_l0o`0fomWIf@?o0?l08?oIfMT000oofMWI00?o0000omWIfOoIfMT0/ooIfMT3o`3o03CofMWI 0ol0o`0QomWIf@003ooIfMT2o`000;GofMWI0ol0o`0bomWIf@?o0?l08_oIfMT000oofMWI00?o0000 omWIfOoIfMT0]OoIfMT3o`3o033ofMWI0ol0o`0SomWIf@003ooIfMT00ol0003ofMWIomWIf@2fomWI f@?o0?l0;_oIfMT3o`3o02CofMWI000?omWIf@03o`000?oIfMWofMWI0;OofMWI1?l0o`0[omWIf@?o 0?l09OoIfMT000oofMWI00?o0000omWIfOoIfMT0^?oIfMT4o`3o02WofMWI0ol0o`0VomWIf@003ooI fMT00ol0003ofMWIomWIf@2jomWIf@?o0?l09_oIfMT4o`3o02OofMWI000?omWIf@03o`000?oIfMWo fMWI0;_ofMWI0ol0o`0TomWIf@Co0?l0:?oIfMT000oofMWI0_l0002momWIf@?o0?l08_oIfMT3o`3o 02[ofMWI000?omWIf@03o`000?oIfMWofMWI0;gofMWI1?l0o`0OomWIf@?o0?l0:ooIfMT000oofMWI 00?o0000omWIfOoIfMT0__oIfMT5o`3o01cofMWI0ol0o`0/omWIf@001Ol00002omWIf@?o00001OoI fMT00ol0003ofMWIomWIf@30omWIf@Co0?l06OoIfMT4o`3o02gofMWI00001ooIfMWo0000omWIfOoI fMWo0000omWIfOl000000ooIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0OoIfMT000oofMWI00?o0000omWIfOoIfMT0oooI fMT?omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@oofMWI000?omWIf@;o0000oooIfMT@omWI f@00oooIfMTQomWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -2.25451, \ 0.0237193, 0.161104}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[gv, gvp];\)\)], "Input", CellLabel->"In[14]:=", FontSize->14], Cell[GraphicsData["PostScript", "\"], "Graphics", CellLabel->"From In[14]:=", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\omWIf@?o0?l0UooIfMT000oofMWI00?o0000omWIfOoIfMT08?oI fMT3o`3o043ofMWI1Ol0000=omWIf@?o0?l0U_oIfMT000oofMWI00?o0000omWIfOoIfMT07ooIfMT3 o`3o04?ofMWI1Ol0000omWIf@003ooIfMT0 0ol0003ofMWIomWIf@0GomWIf@?o0?l0G_oIfMT4o`0000;ofMWI0ol0o`2=omWIf@003ooIfMT2o`00 01OofMWI0ol0o`1PomWIf@Go000000CofMWIo`3o0?l0o`3o0?l0S?oIfMT000oofMWI00?o0000omWI fOoIfMT05_oIfMT2o`3o06?ofMWI1?l000001?oIfMWo0?l0o`3o0?l0o`2;omWIf@003ooIfMT00ol0 003ofMWIomWIf@0EomWIf@?o0?l0IOoIfMT4o`0000;o0?l0RooIfMT000oofMWI00?o0000omWIfOoI fMT05?oIfMT3o`3o06OofMWI0ol00003o`3o08[ofMWI000?omWIf@03o`000?oIfMWofMWI01?ofMWI 0ol0o`1ZomWIf@;o00000ol0o`29omWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI 00?o0000omWIfOoIfMT04_oIfMT3o`3o06cofMWI0_l00003o`3o08SofMWI0002omWIf@03o`000?oI fMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@0BomWIf@;o0?l0 KooIfMT01?l0003o0?l0o`3o0?l0o`27omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`00 0?oIfMWofMWIo`0000CofMWI00?o0000omWIfOoIfMT04OoIfMT3o`3o073ofMWI00?o0000o`3o0?l0 o`000_l00025omWIf@000_oIfMT00ol0003ofMWIomWIf@02omWIf@04o`000?oIfMWofMWIo`0000Co fMWI0ol0000@omWIf@?o0?l0L_oIfMT3o`3o00;o0000Q?oIfMT000;ofMWI00?o0000omWIfOoIfMT0 0_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI00oofMWI0ol0o`1domWIf@?o 0?l00ol00022omWIf@0000?ofMWIo`000?l000001?oIfMT01?l0003ofMWIomWIfOl00004omWIf@03 o`000?oIfMWofMWI00oofMWI0_l0o`1fomWIf@?o0?l00ol00021omWIf@000_oIfMT00ol0003ofMWI omWIf@03omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@0>omWIf@?o0?l0MooIfMT2o`3o0003omWI fOl0003o000000;o0000OooIfMT000oofMWI00?o0000omWIfOoIfMT03OoIfMT3o`3o07SofMWI0ol0 o`000ooIfMWo0000o`000002o`0007kofMWI000?omWIf@03o`000?oIfMWofMWI00cofMWI0ol0o`1j omWIf@?o0?l00_oIfMT4o`0007cofMWI000?omWIf@03o`000?oIfMWofMWI00cofMWI0_l0o`1lomWI f@?o0?l00_oIfMT4o`0007_ofMWI000?omWIf@03o`000?oIfMWofMWI00_ofMWI0ol0o`1momWIf@?o 0?l00ooIfMT4o`0007WofMWI000?omWIf@;o00002ooIfMT3o`3o07oofMWI0_l0o`04omWIf@Co0000 N?oIfMT000oofMWI00?o0000omWIfOoIfMT02_oIfMT2o`3o083ofMWI0ol0o`05omWIf@Co0000M_oI fMT000oofMWI00?o0000omWIfOoIfMT02OoIfMT3o`3o087ofMWI0ol0o`05omWIf@Co0000MOoIfMT0 00oofMWI00?o0000omWIfOoIfMT02?oIfMT3o`3o08?ofMWI0ol0o`06omWIf@Co0000LooIfMT000oo fMWI00?o0000omWIfOoIfMT01ooIfMT3o`3o08GofMWI0_l0o`07omWIf@Co0000L_oIfMT000oofMWI 00?o0000omWIfOoIfMT01ooIfMT2o`3o08KofMWI0ol0o`08omWIf@?o0000LOoIfMT000oofMWI00?o 0000omWIfOoIfMT01_oIfMT3o`3o08OofMWI0ol0o`08omWIf@Co0000KooIfMT000oofMWI00?o0000 omWIfOoIfMT01OoIfMT3o`3o08WofMWI0ol0o`08omWIf@Co0000K_oIfMT000oofMWI00?o0000omWI fOoIfMT01?oIfMT3o`3o08_ofMWI0_l0o`0:omWIf@Co0000K?oIfMT000oofMWI0_l00004omWIf@?o 0?l0S?oIfMT3o`3o00[ofMWI1?l0001[omWIf@003ooIfMT00ol0003ofMWIomWIf@02omWIf@?o0?l0 S_oIfMT3o`3o00_ofMWI0ol0001ZomWIf@003ooIfMT01?l0003ofMWIomWIfOoIfMT3o`3o093ofMWI 0_l0o`0omWIf@?o0000HooIfMT000kofMWI0ol0o`2IomWIf@?o0?l03_oIfMT3o`0005Wo fMWI0_l0o`07omWIf@003_oIfMT2o`3o09_ofMWI0ol0o`0>omWIf@?o0000F?oIfMT2o`3o00OofMWI 000?omWIf@03o`000?oIfMWofMWI09[ofMWI0ol0o`0>omWIf@?o0000E_oIfMT3o`3o00OofMWI000? omWIf@03o`000?oIfMWofMWI09_ofMWI0ol0o`0>omWIf@Co0000DooIfMT3o`3o00SofMWI000?omWI f@03o`000?oIfMWofMWI09cofMWI0ol0o`0>omWIf@Co0000DOoIfMT3o`3o00WofMWI000?omWIf@03 o`000?oIfMWofMWI09gofMWI0_l0o`0@omWIf@?o0000CooIfMT3o`3o00[ofMWI000?omWIf@03o`00 0?oIfMWofMWI09gofMWI0ol0o`0@omWIf@Co0000C?oIfMT3o`3o00_ofMWI000?omWIf@03o`000?oI fMWofMWI09kofMWI0ol0o`0@omWIf@Co0000B_oIfMT3o`3o00cofMWI000?omWIf@;o0000X?oIfMT3 o`3o017ofMWI0ol00019omWIf@;o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0X?oIfMT3o`3o 017ofMWI1?l00016omWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoIfMT3o`3o017o fMWI1?l00014omWIf@?o0?l03_oIfMT000oofMWI00?o0000omWIfOoIfMT0X_oIfMT3o`3o01;ofMWI 0ol00012omWIf@?o0?l03ooIfMT000oofMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o01;ofMWI1?l0 000oomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o01;ofMWI1?l0000m omWIf@?o0?l04OoIfMT000Go00000ooIfMT2o`0000GofMWI00?o0000omWIfOoIfMT0YOoIfMT3o`3o 01?ofMWI0ol0000komWIf@?o0?l04_oIfMT00005omWIfOl0003ofMWIomWIfOl000000_oIfMT01?l0 003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:KofMWI0ol0o`0ComWIf@?o0000>OoIfMT3 o`3o01?ofMWI0002omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT3 o`000:OofMWI0ol0o`0ComWIf@?o0000=ooIfMT3o`3o01CofMWI0003omWIf@05o`000?oIfMWofMWI omWIfOl000000_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`0C omWIf@?o0000=OoIfMT3o`3o01GofMWI00001Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000 omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@2YomWIf@?o0?l04ooIfMT3o`0003?ofMWI0ol0 o`0FomWIf@0000Go0000omWIfOoIfMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI 00?o0000omWIfOoIfMT0Z_oIfMT3o`3o01?ofMWI0ol0000aomWIf@?o0?l05ooIfMT00004omWIfOl0 003o0000o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI0:_ofMWI0ol0o`0ComWIf@?o0000 ;ooIfMT3o`3o01SofMWI000?omWIf@03o`000?oIfMWofMWI0:cofMWI1?l0o`0BomWIf@?o0000;OoI fMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI1?l0o`0BomWIf@?o0000:ooIfMT3 o`3o01[ofMWI000?omWIf@03o`000?oIfMWofMWI0:oofMWI0ol0o`0BomWIf@?o0000:OoIfMT3o`3o 01_ofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0BomWIf@?o00009_oIfMT4o`3o01co fMWI000?omWIf@;o0000/_oIfMT3o`3o01;ofMWI0ol0000TomWIf@Co0?l07OoIfMT000oofMWI00?o 0000omWIfOoIfMT0/_oIfMT4o`3o017ofMWI0ol0000RomWIf@?o0?l07ooIfMT000oofMWI00?o0000 omWIfOoIfMT0/ooIfMT4o`3o017ofMWI0ol0000OomWIf@Co0?l08?oIfMT000oofMWI00?o0000omWI fOoIfMT0]OoIfMT3o`3o017ofMWI0ol0000MomWIf@Co0?l08OoIfMT000oofMWI00?o0000omWIfOoI fMT0]_oIfMT3o`3o017ofMWI0ol0000JomWIf@Co0?l08ooIfMT000oofMWI00?o0000omWIfOoIfMT0 ]ooIfMT4o`3o013ofMWI0ol0000HomWIf@Co0?l09?oIfMT000oofMWI00?o0000omWIfOoIfMT0^?oI fMT4o`3o013ofMWI0ol0000FomWIf@?o0?l09_oIfMT000oofMWI00?o0000omWIfOoIfMT0^_oIfMT4 o`3o00oofMWI0ol0000ComWIf@Co0?l09ooIfMT000oofMWI0_l0002lomWIf@Co0?l03ooIfMT2o`00 017ofMWI1Ol0o`0XomWIf@003ooIfMT00ol0003ofMWIomWIf@2momWIf@Co0?l03OoIfMT3o`0000ko fMWI1Ol0o`0ZomWIf@003ooIfMT00ol0003ofMWIomWIf@2nomWIf@Ko0?l02ooIfMT3o`0000_ofMWI 1Ol0o`0/omWIf@003ooIfMT00ol0003ofMWIomWIf@30omWIf@Oo0?l02OoIfMT3o`0000SofMWI1Ol0 o`0^omWIf@003ooIfMT00ol0003ofMWIomWIf@33omWIf@Oo0?l01ooIfMT3o`0000CofMWI1_l0o`0` omWIf@003ooIfMT00ol0003ofMWIomWIf@36omWIf@[o0?l000?ofMWIo`3o0?l0o`002Ol0o`0bomWI f@003ooIfMT00ol0003ofMWIomWIf@39omWIfA3o0?l0=OoIfMT000oofMWI00?o0000omWIfOoIfMT0 c_oIfMT5o`3o0004omWIfOl0003o0000o`0003OofMWI000?omWIf@;o0000e_oIfMT3o`0003KofMWI 000?omWIf@03o`000?oIfMWofMWI0=KofMWI0ol0000eomWIf@003ooIfMT00ol0003ofMWIomWIf@3G omWIf@?o0000=?oIfMT000oofMWI00?o0000omWIfOoIfMT0f?oIfMT3o`0003?ofMWI000?omWIf@03 o`000?oIfMWofMWI0=WofMWI0ol0000bomWIf@003ooIfMT00ol0003ofMWIomWIf@3JomWIf@?o0000 3ofMWI0ol0000[omWIf@003ooIfMT00ol0003ofMWIomWIf@3Q omWIf@?o0000:_oIfMT000oofMWI00?o0000omWIfOoIfMT0h_oIfMT3o`0002WofMWI00001?oIfMWo 0000o`000?l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@3SomWIf@?o0000:?oIfMT00005 o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWo fMWI0>CofMWI0_l0000XomWIf@001?oIfMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWo fMWI00;ofMWI00?o0000omWIfOoIfMT0i?oIfMT3o`0002OofMWI0002omWIf@;o00000ooIfMT01?l0 003ofMWIomWIfOl00004omWIf@?o0000iOoIfMT3o`0002KofMWI0004omWIf@04o`000?oIfMWofMWI o`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWIomWIf@3VomWIf@?o00009OoIfMT0 0005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oI fMWofMWI0>OofMWI0ol0000TomWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI00?o 0000omWIfOoIfMT0j?oIfMT3o`0002?ofMWI000?omWIf@03o`000?oIfMWofMWI0>WofMWI0ol0000R omWIf@003ooIfMT00ol0003ofMWIomWIf@3ZomWIf@?o00008OoIfMT000oofMWI00?o0000omWIfOoI fMT0jooIfMT3o`00023ofMWI000?omWIf@03o`000?oIfMWofMWI0>cofMWI0ol0000OomWIf@003ooI fMT2o`000>kofMWI0ol0000NomWIf@003ooIfMT00ol0003ofMWIomWIf@3^omWIf@?o00007OoIfMT0 00oofMWI00?o0000omWIfOoIfMT0kooIfMT3o`0001cofMWI000?omWIf@03o`000?oIfMWofMWI0?3o fMWI0_l0000LomWIf@003ooIfMT00ol0003ofMWIomWIf@3`omWIf@?o00006ooIfMT000oofMWI00?o 0000omWIfOoIfMT0lOoIfMT3o`0001[ofMWI000?omWIf@03o`000?oIfMWofMWI0?;ofMWI0ol0000I omWIf@003ooIfMT00ol0003ofMWIomWIf@3comWIf@?o00006?oIfMT000oofMWI0_l0003eomWIf@?o 00005ooIfMT000oofMWI00?o0000omWIfOoIfMT0mOoIfMT3o`0001KofMWI000?omWIf@03o`000?oI fMWofMWI0?KofMWI0ol0000EomWIf@003ooIfMT00ol0003ofMWIomWIf@3gomWIf@?o00005?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0n?oIfMT3o`0001?ofMWI000?omWIf@03o`000?oIfMWofMWI0?Wo fMWI0ol0000BomWIf@003ooIfMT00ol0003ofMWIomWIf@3jomWIf@?o00004OoIfMT000oofMWI00?o 0000omWIfOoIfMT0nooIfMT2o`00017ofMWI000?omWIf@03o`000?oIfMWofMWI0?_ofMWI0ol0000@ omWIf@003ooIfMT2o`000?gofMWI0ol0000?omWIf@003ooIfMT00ol0003ofMWIomWIf@3momWIf@?o 00003_oIfMT000oofMWI00?o0000omWIfOoIfMT0o_oIfMT2o`0000kofMWI000?omWIf@03o`000?oI fMWofMWI0?kofMWI0ol0000=omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@?o00003?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0oooIfMT1omWIf@?o00002ooIfMT000oofMWI00?o0000omWIfOoI fMT0oooIfMT2omWIf@?o00002_oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT3omWIf@;o0000 2_oIfMT000oofMWI0_l0003oomWIf@CofMWI0ol00009omWIf@003ooIfMT00ol0003ofMWIomWIf@3o omWIf@CofMWI0ol00008omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@GofMWI0ol00007omWI f@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@KofMWI0_l00007omWIf@003ooIfMT00ol0003ofMWI omWIf@3oomWIf@oofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000 omWIfOoIfMT0oooIfMT?omWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.12112, \ 0.0237193, 0.241311}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c.- ", FontColor->RGBColor[1, 0, 0]], "Calcular ", "la norma de la funci\[OAcute]n error." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(e[x_] := v[x] - vp\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ne = Sqrt[pe[e[x], e[x]]] // N\)], "Input", CellLabel->"In[16]:=", FontSize->14], Cell[BoxData[ \(18.00250212986795`\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[17]:=", FontSize->14] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{0, 1024}, {0, 698}}, WindowSize->{748, 557}, WindowMargins->{{32, Automatic}, {Automatic, 35}}, StyleDefinitions -> "ArticleModern.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 228, 5, 90, "Title"], Cell[CellGroupData[{ Cell[2029, 62, 140, 2, 76, "SectionFirst"], Cell[2172, 66, 306, 8, 42, "Text"], Cell[2481, 76, 1315, 39, 91, "Text"], Cell[3799, 117, 293, 7, 42, "Text"], Cell[4095, 126, 193, 6, 43, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4325, 137, 342, 9, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[4692, 150, 930, 33, 153, "Subsubsection"], Cell[5625, 185, 62, 0, 24, "Text"], Cell[5690, 187, 130, 3, 43, "Input"], Cell[5823, 192, 112, 3, 43, "Input"], Cell[CellGroupData[{ Cell[5960, 199, 87, 3, 43, "Input"], Cell[6050, 204, 95, 2, 44, "Output"] }, Open ]], Cell[6160, 209, 215, 7, 26, "Text"], Cell[CellGroupData[{ Cell[6400, 220, 112, 3, 43, "Input"], Cell[6515, 225, 95, 2, 44, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[6659, 233, 280, 9, 62, "Subsubsection"], Cell[6942, 244, 320, 6, 40, "Text"], Cell[7265, 252, 3225, 95, 63, "Text"], Cell[10493, 349, 411, 10, 42, "Text"], Cell[CellGroupData[{ Cell[10929, 363, 87, 3, 43, "Input"], Cell[11019, 368, 77, 2, 42, "Output"] }, Open ]], Cell[11111, 373, 961, 26, 74, "Text"], Cell[CellGroupData[{ Cell[12097, 403, 88, 3, 43, "Input"], Cell[12188, 408, 96, 2, 42, "Output"] }, Open ]], Cell[12299, 413, 238, 7, 26, "Text"], Cell[CellGroupData[{ Cell[12562, 424, 87, 3, 43, "Input"], Cell[12652, 429, 130, 3, 42, "Output"] }, Open ]], Cell[12797, 435, 258, 5, 40, "Text"], Cell[13058, 442, 2511, 68, 120, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[15606, 515, 216, 8, 44, "Subsubsection"], Cell[15825, 525, 813, 23, 94, "Text"], Cell[16641, 550, 119, 3, 43, "Input"], Cell[CellGroupData[{ Cell[16785, 557, 103, 3, 43, "Input"], Cell[16891, 562, 101, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17029, 569, 87, 3, 43, "Input"], Cell[17119, 574, 400, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17556, 591, 114, 3, 43, "Input"], Cell[17673, 596, 397, 12, 70, "Output"] }, Open ]], Cell[18085, 611, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[18421, 624, 97, 3, 43, "Input"], Cell[18521, 629, 63, 2, 70, "Output"] }, Open ]], Cell[18599, 634, 2956, 85, 203, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[21592, 724, 496, 16, 29, "Subsubsection"], Cell[22091, 742, 226, 5, 24, "Text"], Cell[CellGroupData[{ Cell[22342, 751, 263, 7, 64, "Input"], Cell[22608, 760, 485, 10, 70, "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[23142, 776, 273, 9, 28, "Subsubsection"], Cell[23418, 787, 74, 0, 24, "Text"], Cell[CellGroupData[{ Cell[23517, 791, 97, 3, 43, "Input"], Cell[23617, 796, 64, 2, 70, "Output"] }, Open ]], Cell[23696, 801, 113, 3, 24, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[23846, 809, 439, 14, 47, "Subsubsection"], Cell[CellGroupData[{ Cell[24310, 827, 142, 4, 43, "Input"], Cell[24455, 833, 63, 2, 70, "Output"] }, Open ]], Cell[24533, 838, 102, 3, 43, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[24684, 847, 189, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[24898, 854, 882, 29, 153, "Subsubsection"], Cell[CellGroupData[{ Cell[25805, 887, 235, 5, 61, "Input"], Cell[26043, 894, 114, 2, 42, "Output"] }, Open ]], Cell[26172, 899, 3225, 95, 63, "Text"], Cell[29400, 996, 3310, 92, 139, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[32747, 1093, 352, 10, 62, "Subsubsection"], Cell[33102, 1105, 182, 4, 40, "Text"], Cell[33287, 1111, 252, 6, 61, "Input"], Cell[CellGroupData[{ Cell[33564, 1121, 144, 4, 43, "Input"], Cell[33711, 1127, 62, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33810, 1134, 121, 3, 43, "Input"], Cell[33934, 1139, 60, 2, 42, "Output"] }, Open ]], Cell[34009, 1144, 101, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[34159, 1153, 257, 5, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[34441, 1162, 1552, 56, 81, "Subsubsection"], Cell[35996, 1220, 606, 19, 62, "Text"], Cell[36605, 1241, 113, 3, 43, "Input"], Cell[36721, 1246, 145, 4, 61, "Input"], Cell[36869, 1252, 664, 17, 58, "Text"], Cell[37536, 1271, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[37669, 1278, 123, 3, 43, "Input"], Cell[37795, 1283, 131, 3, 47, "Output"] }, Open ]], Cell[37941, 1289, 710, 23, 44, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[38688, 1317, 485, 17, 62, "Subsubsection"], Cell[39176, 1336, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[39295, 1343, 172, 5, 43, "Input"], Cell[39470, 1350, 299, 5, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39806, 1360, 88, 3, 43, "Input"], Cell[39897, 1365, 167, 3, 44, "Output"] }, Open ]], Cell[40079, 1371, 137, 3, 24, "Text"], Cell[CellGroupData[{ Cell[40241, 1378, 578, 16, 61, "Input"], Cell[40822, 1396, 17220, 439, 194, 3919, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[58079, 1840, 159, 5, 43, "Input"], Cell[58241, 1847, 16273, 405, 194, 3482, 241, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[74551, 2257, 195, 6, 43, "Input"], Cell[74749, 2265, 15908, 397, 194, 3376, 236, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[90694, 2667, 92, 3, 43, "Input"], Cell[90789, 2672, 17174, 437, 194, 3888, 268, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[108012, 3115, 259, 9, 44, "Subsubsection"], Cell[108274, 3126, 85, 1, 24, "Text"], Cell[108362, 3129, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[108479, 3136, 104, 3, 43, "Input"], Cell[108586, 3141, 81, 2, 42, "Output"] }, Open ]], Cell[108682, 3146, 102, 3, 43, "Input"], Cell[108787, 3151, 466, 15, 44, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[109302, 3172, 264, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[109591, 3181, 1810, 64, 98, "Subsubsection"], Cell[111404, 3247, 153, 4, 43, "Input"], Cell[CellGroupData[{ Cell[111582, 3255, 175, 5, 43, "Input"], Cell[111760, 3262, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[111869, 3270, 326, 10, 62, "Subsubsection"], Cell[112198, 3282, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[112331, 3289, 103, 3, 43, "Input"], Cell[112437, 3294, 232, 4, 68, "Output"] }, Open ]], Cell[112684, 3301, 536, 15, 44, "Text"], Cell[CellGroupData[{ Cell[113245, 3320, 128, 3, 43, "Input"], Cell[113376, 3325, 88, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[113501, 3332, 176, 5, 43, "Input"], Cell[113680, 3339, 133, 3, 57, "Output"] }, Open ]], Cell[113828, 3345, 101, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[113978, 3354, 298, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[114301, 3363, 1746, 54, 181, "Subsubsection"], Cell[116050, 3419, 74, 1, 24, "Text"], Cell[116127, 3422, 278, 5, 26, "Text"], Cell[116408, 3429, 528, 18, 26, "Text"], Cell[116939, 3449, 131, 4, 24, "Text"], Cell[117073, 3455, 117, 3, 43, "Input"], Cell[117193, 3460, 197, 4, 79, "Input"], Cell[117393, 3466, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[117526, 3473, 123, 3, 43, "Input"], Cell[117652, 3478, 111, 2, 61, "Output"] }, Open ]], Cell[117778, 3483, 295, 7, 42, "Text"], Cell[CellGroupData[{ Cell[118098, 3494, 181, 5, 43, "Input"], Cell[118282, 3501, 62, 2, 42, "Output"] }, Open ]], Cell[118359, 3506, 23, 0, 24, "Text"], Cell[CellGroupData[{ Cell[118407, 3510, 127, 3, 43, "Input"], Cell[118537, 3515, 91, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[118665, 3522, 87, 3, 43, "Input"], Cell[118755, 3527, 393, 12, 84, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[119197, 3545, 652, 19, 81, "Subsubsection"], Cell[119852, 3566, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[119971, 3573, 172, 5, 43, "Input"], Cell[120146, 3580, 118, 3, 60, "Output"] }, Open ]], Cell[120279, 3586, 330, 10, 42, "Text"], Cell[CellGroupData[{ Cell[120634, 3600, 583, 16, 61, "Input"], Cell[121220, 3618, 21946, 573, 194, 5142, 360, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[143181, 4194, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[143508, 4206, 164, 5, 43, "Input"], Cell[143675, 4213, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[159207, 4638, 199, 6, 43, "Input"], Cell[159409, 4646, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[178332, 5174, 92, 3, 43, "Input"], Cell[178427, 5179, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[198791, 5736, 272, 10, 44, "Subsubsection"], Cell[199066, 5748, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[199183, 5755, 104, 3, 43, "Input"], Cell[199290, 5760, 77, 2, 42, "Output"] }, Open ]], Cell[199382, 5765, 102, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[199533, 5774, 194, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[199752, 5781, 2001, 62, 251, "Subsubsection"], Cell[201756, 5845, 1404, 50, 92, "Text"], Cell[203163, 5897, 620, 23, 26, "Text"], Cell[203786, 5922, 403, 14, 26, "Text"], Cell[204192, 5938, 2523, 80, 62, "Text"], Cell[206718, 6020, 131, 4, 24, "Text"], Cell[206852, 6026, 378, 8, 97, "Input"], Cell[207233, 6036, 100, 3, 24, "Text"], Cell[CellGroupData[{ Cell[207358, 6043, 342, 9, 79, "Input"], Cell[207703, 6054, 17566, 412, 194, 3292, 231, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[225284, 6469, 181, 4, 24, "Text"], Cell[CellGroupData[{ Cell[225490, 6477, 146, 4, 43, "Input"], Cell[225639, 6483, 106, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[225782, 6490, 104, 3, 43, "Input"], Cell[225889, 6495, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[226003, 6502, 98, 3, 43, "Input"], Cell[226104, 6507, 386, 6, 27, "Message"], Cell[226493, 6515, 84, 2, 42, "Output"] }, Open ]], Cell[226592, 6520, 41, 0, 24, "Text"], Cell[226636, 6522, 144, 4, 43, "Input"], Cell[CellGroupData[{ Cell[226805, 6530, 156, 4, 61, "Input"], Cell[226964, 6536, 459, 10, 40, "Print"] }, Open ]], Cell[227438, 6549, 97, 3, 24, "Text"], Cell[CellGroupData[{ Cell[227560, 6556, 197, 6, 43, "Input"], Cell[227760, 6564, 21760, 521, 194, 4200, 299, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[249557, 7090, 91, 3, 43, "Input"], Cell[249651, 7095, 22239, 533, 194, 4327, 307, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[271905, 7631, 106, 3, 24, "Text"], Cell[272014, 7636, 109, 3, 43, "Input"], Cell[CellGroupData[{ Cell[272148, 7643, 239, 5, 79, "Input"], Cell[272390, 7650, 214, 4, 68, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[272641, 7659, 122, 3, 43, "Input"], Cell[272766, 7664, 187, 4, 42, "Output"] }, Open ]], Cell[272968, 7671, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[273295, 7683, 271, 6, 61, "Input"], Cell[273569, 7691, 156, 4, 42, "Output"] }, Open ]], Cell[273740, 7698, 35, 0, 24, "Text"], Cell[273778, 7700, 259, 7, 43, "Input"], Cell[CellGroupData[{ Cell[274062, 7711, 63, 2, 42, "Input"], Cell[274128, 7715, 152, 3, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[274317, 7723, 103, 2, 42, "Input"], Cell[274423, 7727, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[274537, 7734, 199, 6, 43, "Input"], Cell[274739, 7742, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[293662, 8270, 92, 3, 43, "Input"], Cell[293757, 8275, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[314121, 8832, 272, 10, 44, "Subsubsection"], Cell[314396, 8844, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[314513, 8851, 104, 3, 43, "Input"], Cell[314620, 8856, 77, 2, 42, "Output"] }, Open ]], Cell[314712, 8861, 102, 3, 43, "Input"] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) I0>WofMWI0ol0000R omWIf@003ooIfMT00ol0003ofMWIomWIf@3ZomWIf@?o00008OoIfMT000oofMWI00?o0000omWIfOoI fMT0jooIfMT3o`00023ofMWI000?omWIf@03o`000?oIfMWofMWI0>cofMWI0ol0000OomWIf@003ooI fMT2o`000>kofMWI0ol0000NomWIf@003ooIfMT00ol0003ofMWIomWIf@3^omWIf@?o00007OoIfMT0 00oofMWI00?o0000omWIfOoIfMT0kooIfMT3o`0001cofMWI000?omWIf@03o`000?oIfMWofMWI0?3o fMWI0_l0000LomWIf@003ooIfMT00ol0003ofMWIomWIf@3`omWIf@?o00006ooIfMT000oofMWI00?o 0000omWIfOoIfMT0lOoIfMT3o`0001[ofMWI000?omWIf@03o`000?oIfMWofMWI0?;ofMWI0ol0000I omWIf@003ooIfMT00ol0003ofMWIomWIf@3comWIf@?o00006?oIfMT000oofMWI0_l0003eomWIf@?o 00005ooIfMT000oofMWI00?o0000omWIfOoIfMT0mOoIfMT3o`0001KofMWI000?omWIf@03o`000?oI fMWofMWI0?KofMWI0ol0000EomWIf@003ooIfMT00ol0003ofMWIomWIf@3gomWIf@?o00005?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0n?oIfMT3o`0001?ofMWI000?omWIf@03o`000?oIfMWofMWI0?Wo fMWI0ol0000BomWIf@003ooIfMT00ol0003ofMWIomWIf@3jomWIf@?o00004OoIfMT000oofMWI00?o 0000omWIfOoIfMT0nooIfMT2o`00017ofMWI000?omWIf@03o`000?oIfMWofMWI0?_ofMWI0ol0000@ omWIf@003ooIfMT2o`000?gofMWI0ol0000?omWIf@003ooIfMT00ol0003ofMWIomWIf@3momWIf@?o 00003_oIfMT000oofMWI00?o0000omWIfOoIfMT0o_oIfMT2o`0000kofMWI000?omWIf@03o`000?oI fMWofMWI0?kofMWI0ol0000=omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@?o00003?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0oooIfMT1omWIf@?o00002ooIfMT000oofMWI00?o0000omWIfOoI fMT0oooIfMT2omWIf@?o00002_oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT3omWIf@;o0000 2_oIfMT000oofMWI0_l0003oomWIf@CofMWI0ol00009omWIf@003ooIfMT00ol0003ofMWIomWIf@3o omWIf@CofMWI0ol00008omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@GofMWI0ol00007omWI f@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@KofMWI0_l00007omWIf@003ooIfMT00ol0003ofMWI omWIf@3oomWIf@oofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000 omWIfOoIfMT0oooIfMT?omWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.12112, \ 0.0237193, 0.241311}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c.- ", FontColor->RGBColor[1, 0, 0]], "Calcular ", "la norma de la funci\[OAcute]n error." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(e[x_] := v[x] - vp\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ne = Sqrt[pe[e[x], e[x]]] // N\)], "Input", CellLabel->"In[16]:=", FontSize->14], Cell[BoxData[ \(18.00250212986795`\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[17]:=", FontSize->14] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{0, 1024}, {0, 698}}, WindowSize->{748, 557}, WindowMargins->{{32, Automatic}, {Automatic, 35}}, StyleDefinitions -> "ArticleModern.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 228, 5, 90, "Title"], Cell[CellGroupData[{ Cell[2029, 62, 140, 2, 76, "SectionFirst"], Cell[2172, 66, 306, 8, 42, "Text"], Cell[2481, 76, 1315, 39, 91, "Text"], Cell[3799, 117, 293, 7, 42, "Text"], Cell[4095, 126, 193, 6, 43, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4325, 137, 342, 9, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[4692, 150, 930, 33, 153, "Subsubsection"], Cell[5625, 185, 62, 0, 24, "Text"], Cell[5690, 187, 130, 3, 43, "Input"], Cell[5823, 192, 112, 3, 43, "Input"], Cell[CellGroupData[{ Cell[5960, 199, 87, 3, 43, "Input"], Cell[6050, 204, 95, 2, 44, "Output"] }, Open ]], Cell[6160, 209, 215, 7, 26, "Text"], Cell[CellGroupData[{ Cell[6400, 220, 112, 3, 43, "Input"], Cell[6515, 225, 95, 2, 44, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[6659, 233, 280, 9, 62, "Subsubsection"], Cell[6942, 244, 320, 6, 40, "Text"], Cell[7265, 252, 3225, 95, 63, "Text"], Cell[10493, 349, 411, 10, 42, "Text"], Cell[CellGroupData[{ Cell[10929, 363, 87, 3, 43, "Input"], Cell[11019, 368, 77, 2, 42, "Output"] }, Open ]], Cell[11111, 373, 961, 26, 74, "Text"], Cell[CellGroupData[{ Cell[12097, 403, 88, 3, 43, "Input"], Cell[12188, 408, 96, 2, 42, "Output"] }, Open ]], Cell[12299, 413, 238, 7, 26, "Text"], Cell[CellGroupData[{ Cell[12562, 424, 87, 3, 43, "Input"], Cell[12652, 429, 130, 3, 42, "Output"] }, Open ]], Cell[12797, 435, 258, 5, 40, "Text"], Cell[13058, 442, 2511, 68, 120, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[15606, 515, 216, 8, 44, "Subsubsection"], Cell[15825, 525, 813, 23, 94, "Text"], Cell[16641, 550, 119, 3, 43, "Input"], Cell[CellGroupData[{ Cell[16785, 557, 103, 3, 43, "Input"], Cell[16891, 562, 101, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17029, 569, 87, 3, 43, "Input"], Cell[17119, 574, 400, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17556, 591, 114, 3, 43, "Input"], Cell[17673, 596, 397, 12, 70, "Output"] }, Open ]], Cell[18085, 611, 311, 9, 44, "Text"], Cell[CellGroupData[{ Cell[18421, 624, 97, 3, 43, "Input"], Cell[18521, 629, 63, 2, 70, "Output"] }, Open ]], Cell[18599, 634, 2956, 85, 203, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[21592, 724, 496, 16, 29, "Subsubsection"], Cell[22091, 742, 226, 5, 24, "Text"], Cell[CellGroupData[{ Cell[22342, 751, 263, 7, 64, "Input"], Cell[22608, 760, 485, 10, 70, "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[23142, 776, 273, 9, 28, "Subsubsection"], Cell[23418, 787, 74, 0, 24, "Text"], Cell[CellGroupData[{ Cell[23517, 791, 97, 3, 43, "Input"], Cell[23617, 796, 64, 2, 70, "Output"] }, Open ]], Cell[23696, 801, 113, 3, 24, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[23846, 809, 439, 14, 47, "Subsubsection"], Cell[CellGroupData[{ Cell[24310, 827, 142, 4, 43, "Input"], Cell[24455, 833, 63, 2, 70, "Output"] }, Open ]], Cell[24533, 838, 102, 3, 43, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[24684, 847, 189, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[24898, 854, 882, 29, 153, "Subsubsection"], Cell[CellGroupData[{ Cell[25805, 887, 235, 5, 61, "Input"], Cell[26043, 894, 114, 2, 42, "Output"] }, Open ]], Cell[26172, 899, 3225, 95, 63, "Text"], Cell[29400, 996, 3310, 92, 139, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[32747, 1093, 352, 10, 62, "Subsubsection"], Cell[33102, 1105, 182, 4, 40, "Text"], Cell[33287, 1111, 252, 6, 61, "Input"], Cell[CellGroupData[{ Cell[33564, 1121, 121, 3, 43, "Input"], Cell[33688, 1126, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[33797, 1134, 656, 24, 44, "Subsubsection"], Cell[CellGroupData[{ Cell[34478, 1162, 196, 5, 43, "Input"], Cell[34677, 1169, 62, 2, 45, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[34788, 1177, 774, 23, 65, "Subsubsection"], Cell[35565, 1202, 151, 4, 43, "Input"], Cell[CellGroupData[{ Cell[35741, 1210, 124, 3, 43, "Input"], Cell[35868, 1215, 114, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36019, 1222, 86, 3, 43, "Input"], Cell[36108, 1227, 442, 13, 100, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[36599, 1246, 461, 16, 28, "Subsubsection"], Cell[37063, 1264, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[37196, 1271, 339, 8, 61, "Input"], Cell[37538, 1281, 129, 3, 57, "Output"] }, Open ]], Cell[37682, 1287, 243, 7, 25, "Text"], Cell[CellGroupData[{ Cell[37950, 1298, 266, 9, 43, "Input"], Cell[38219, 1309, 110, 2, 42, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[38378, 1317, 462, 16, 28, "Subsubsection"], Cell[CellGroupData[{ Cell[38865, 1337, 94, 3, 43, "Input"], Cell[38962, 1342, 183, 4, 68, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[39194, 1352, 513, 18, 28, "Subsubsection"], Cell[39710, 1372, 95, 3, 43, "Input"], Cell[CellGroupData[{ Cell[39830, 1379, 118, 3, 43, "Input"], Cell[39951, 1384, 89, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[40077, 1391, 143, 4, 43, "Input"], Cell[40223, 1397, 63, 2, 42, "Output"] }, Open ]], Cell[40301, 1402, 299, 7, 41, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[40637, 1414, 771, 25, 46, "Subsubsection"], Cell[41411, 1441, 981, 30, 62, "Text"], Cell[CellGroupData[{ Cell[42417, 1475, 148, 4, 43, "Input"], Cell[42568, 1481, 251, 5, 27, "Message"], Cell[42822, 1488, 172, 3, 66, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[43031, 1496, 215, 5, 61, "Input"], Cell[43249, 1503, 973, 29, 80, "Print"] }, Open ]], Cell[44237, 1535, 102, 3, 43, "Input"], Cell[44342, 1540, 5042, 177, 128, "Text"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[49433, 1723, 303, 6, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[49761, 1733, 1552, 56, 81, "Subsubsection"], Cell[51316, 1791, 606, 19, 62, "Text"], Cell[51925, 1812, 113, 3, 43, "Input"], Cell[52041, 1817, 145, 4, 61, "Input"], Cell[52189, 1823, 664, 17, 58, "Text"], Cell[52856, 1842, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[52989, 1849, 123, 3, 43, "Input"], Cell[53115, 1854, 131, 3, 47, "Output"] }, Open ]], Cell[53261, 1860, 710, 23, 44, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[54008, 1888, 485, 17, 62, "Subsubsection"], Cell[54496, 1907, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[54615, 1914, 172, 5, 43, "Input"], Cell[54790, 1921, 299, 5, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[55126, 1931, 88, 3, 43, "Input"], Cell[55217, 1936, 167, 3, 44, "Output"] }, Open ]], Cell[55399, 1942, 137, 3, 24, "Text"], Cell[CellGroupData[{ Cell[55561, 1949, 578, 16, 61, "Input"], Cell[56142, 1967, 17220, 439, 194, 3919, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[73399, 2411, 159, 5, 43, "Input"], Cell[73561, 2418, 16273, 405, 194, 3482, 241, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[89871, 2828, 195, 6, 43, "Input"], Cell[90069, 2836, 15908, 397, 194, 3376, 236, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[106014, 3238, 92, 3, 43, "Input"], Cell[106109, 3243, 17174, 437, 194, 3888, 268, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[123332, 3686, 259, 9, 44, "Subsubsection"], Cell[123594, 3697, 85, 1, 24, "Text"], Cell[123682, 3700, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[123799, 3707, 104, 3, 43, "Input"], Cell[123906, 3712, 81, 2, 42, "Output"] }, Open ]], Cell[124002, 3717, 102, 3, 43, "Input"], Cell[124107, 3722, 466, 15, 44, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[124622, 3743, 264, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[124911, 3752, 1810, 64, 98, "Subsubsection"], Cell[126724, 3818, 153, 4, 43, "Input"], Cell[CellGroupData[{ Cell[126902, 3826, 175, 5, 43, "Input"], Cell[127080, 3833, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[127189, 3841, 326, 10, 62, "Subsubsection"], Cell[127518, 3853, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[127651, 3860, 103, 3, 43, "Input"], Cell[127757, 3865, 232, 4, 68, "Output"] }, Open ]], Cell[128004, 3872, 536, 15, 44, "Text"], Cell[CellGroupData[{ Cell[128565, 3891, 128, 3, 43, "Input"], Cell[128696, 3896, 88, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[128821, 3903, 176, 5, 43, "Input"], Cell[129000, 3910, 133, 3, 57, "Output"] }, Open ]], Cell[129148, 3916, 101, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[129298, 3925, 298, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[129621, 3934, 1746, 54, 181, "Subsubsection"], Cell[131370, 3990, 74, 1, 24, "Text"], Cell[131447, 3993, 278, 5, 26, "Text"], Cell[131728, 4000, 528, 18, 26, "Text"], Cell[132259, 4020, 131, 4, 24, "Text"], Cell[132393, 4026, 117, 3, 43, "Input"], Cell[132513, 4031, 197, 4, 79, "Input"], Cell[132713, 4037, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[132846, 4044, 123, 3, 43, "Input"], Cell[132972, 4049, 111, 2, 61, "Output"] }, Open ]], Cell[133098, 4054, 295, 7, 42, "Text"], Cell[CellGroupData[{ Cell[133418, 4065, 181, 5, 43, "Input"], Cell[133602, 4072, 62, 2, 42, "Output"] }, Open ]], Cell[133679, 4077, 23, 0, 24, "Text"], Cell[CellGroupData[{ Cell[133727, 4081, 127, 3, 43, "Input"], Cell[133857, 4086, 91, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[133985, 4093, 87, 3, 43, "Input"], Cell[134075, 4098, 393, 12, 84, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[134517, 4116, 652, 19, 81, "Subsubsection"], Cell[135172, 4137, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[135291, 4144, 172, 5, 43, "Input"], Cell[135466, 4151, 118, 3, 60, "Output"] }, Open ]], Cell[135599, 4157, 330, 10, 42, "Text"], Cell[CellGroupData[{ Cell[135954, 4171, 583, 16, 61, "Input"], Cell[136540, 4189, 21946, 573, 194, 5142, 360, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[158501, 4765, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[158828, 4777, 164, 5, 43, "Input"], Cell[158995, 4784, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[174527, 5209, 199, 6, 43, "Input"], Cell[174729, 5217, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[193652, 5745, 92, 3, 43, "Input"], Cell[193747, 5750, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[214111, 6307, 272, 10, 44, "Subsubsection"], Cell[214386, 6319, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[214503, 6326, 104, 3, 43, "Input"], Cell[214610, 6331, 77, 2, 42, "Output"] }, Open ]], Cell[214702, 6336, 102, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[214853, 6345, 194, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[215072, 6352, 2001, 62, 251, "Subsubsection"], Cell[217076, 6416, 1404, 50, 92, "Text"], Cell[218483, 6468, 620, 23, 26, "Text"], Cell[219106, 6493, 403, 14, 26, "Text"], Cell[219512, 6509, 2523, 80, 62, "Text"], Cell[222038, 6591, 131, 4, 24, "Text"], Cell[222172, 6597, 378, 8, 97, "Input"], Cell[222553, 6607, 100, 3, 24, "Text"], Cell[CellGroupData[{ Cell[222678, 6614, 342, 9, 79, "Input"], Cell[223023, 6625, 17566, 412, 194, 3292, 231, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[240604, 7040, 181, 4, 24, "Text"], Cell[CellGroupData[{ Cell[240810, 7048, 146, 4, 43, "Input"], Cell[240959, 7054, 106, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[241102, 7061, 104, 3, 43, "Input"], Cell[241209, 7066, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[241323, 7073, 98, 3, 43, "Input"], Cell[241424, 7078, 386, 6, 27, "Message"], Cell[241813, 7086, 84, 2, 42, "Output"] }, Open ]], Cell[241912, 7091, 41, 0, 24, "Text"], Cell[241956, 7093, 144, 4, 43, "Input"], Cell[CellGroupData[{ Cell[242125, 7101, 156, 4, 61, "Input"], Cell[242284, 7107, 459, 10, 40, "Print"] }, Open ]], Cell[242758, 7120, 97, 3, 24, "Text"], Cell[CellGroupData[{ Cell[242880, 7127, 197, 6, 43, "Input"], Cell[243080, 7135, 21760, 521, 194, 4200, 299, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[264877, 7661, 91, 3, 43, "Input"], Cell[264971, 7666, 22239, 533, 194, 4327, 307, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[287225, 8202, 106, 3, 24, "Text"], Cell[287334, 8207, 109, 3, 43, "Input"], Cell[CellGroupData[{ Cell[287468, 8214, 239, 5, 79, "Input"], Cell[287710, 8221, 214, 4, 68, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[287961, 8230, 122, 3, 43, "Input"], Cell[288086, 8235, 187, 4, 42, "Output"] }, Open ]], Cell[288288, 8242, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[288615, 8254, 271, 6, 61, "Input"], Cell[288889, 8262, 156, 4, 42, "Output"] }, Open ]], Cell[289060, 8269, 35, 0, 24, "Text"], Cell[289098, 8271, 259, 7, 43, "Input"], Cell[CellGroupData[{ Cell[289382, 8282, 63, 2, 42, "Input"], Cell[289448, 8286, 152, 3, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[289637, 8294, 103, 2, 42, "Input"], Cell[289743, 8298, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[289857, 8305, 199, 6, 43, "Input"], Cell[290059, 8313, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[308982, 8841, 92, 3, 43, "Input"], Cell[309077, 8846, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[329441, 9403, 272, 10, 44, "Subsubsection"], Cell[329716, 9415, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[329833, 9422, 104, 3, 43, "Input"], Cell[329940, 9427, 77, 2, 42, "Output"] }, Open ]], Cell[330032, 9432, 102, 3, 43, "Input"] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) t"] }, Open ]], Cell[328951, 9436, 102, 3, 43, "Input"] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) { Cell[115060, 3505, 104, 3, 43, "Input"], Cell[115167, 3510, 81, 2, 42, "Output"] }, Open ]], Cell[115263, 3515, 102, 3, 43, "Input"], Cell[115368, 3520, 466, 15, 44, "Text"], Cell[115837, 3537, 658, 18, 62, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[116544, 3561, 240, 4, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[116809, 3569, 1810, 64, 98, "Subsubsection"], Cell[118622, 3635, 153, 4, 43, "Input"], Cell[CellGroupData[{ Cell[118800, 3643, 175, 5, 43, "Input"], Cell[118978, 3650, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[119087, 3658, 326, 10, 62, "Subsubsection"], Cell[119416, 3670, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[119549, 3677, 103, 3, 43, "Input"], Cell[119655, 3682, 232, 4, 68, "Output"] }, Open ]], Cell[119902, 3689, 536, 15, 44, "Text"], Cell[CellGroupData[{ Cell[120463, 3708, 128, 3, 43, "Input"], Cell[120594, 3713, 88, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[120719, 3720, 176, 5, 43, "Input"], Cell[120898, 3727, 133, 3, 57, "Output"] }, Open ]], Cell[121046, 3733, 101, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[121196, 3742, 298, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[121519, 3751, 1746, 54, 181, "Subsubsection"], Cell[123268, 3807, 74, 1, 24, "Text"], Cell[123345, 3810, 278, 5, 26, "Text"], Cell[123626, 3817, 528, 18, 26, "Text"], Cell[124157, 3837, 131, 4, 24, "Text"], Cell[124291, 3843, 117, 3, 43, "Input"], Cell[124411, 3848, 197, 4, 79, "Input"], Cell[124611, 3854, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[124744, 3861, 123, 3, 43, "Input"], Cell[124870, 3866, 111, 2, 61, "Output"] }, Open ]], Cell[124996, 3871, 295, 7, 42, "Text"], Cell[CellGroupData[{ Cell[125316, 3882, 181, 5, 43, "Input"], Cell[125500, 3889, 62, 2, 42, "Output"] }, Open ]], Cell[125577, 3894, 23, 0, 24, "Text"], Cell[CellGroupData[{ Cell[125625, 3898, 127, 3, 43, "Input"], Cell[125755, 3903, 91, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[125883, 3910, 87, 3, 43, "Input"], Cell[125973, 3915, 393, 12, 84, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[126415, 3933, 652, 19, 81, "Subsubsection"], Cell[127070, 3954, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[127189, 3961, 172, 5, 43, "Input"], Cell[127364, 3968, 118, 3, 60, "Output"] }, Open ]], Cell[127497, 3974, 330, 10, 42, "Text"], Cell[CellGroupData[{ Cell[127852, 3988, 583, 16, 61, "Input"], Cell[128438, 4006, 21946, 573, 194, 5142, 360, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[150399, 4582, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[150726, 4594, 164, 5, 43, "Input"], Cell[150893, 4601, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[166425, 5026, 199, 6, 43, "Input"], Cell[166627, 5034, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[185550, 5562, 92, 3, 43, "Input"], Cell[185645, 5567, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[206009, 6124, 272, 10, 44, "Subsubsection"], Cell[206284, 6136, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[206401, 6143, 104, 3, 43, "Input"], Cell[206508, 6148, 77, 2, 42, "Output"] }, Open ]], Cell[206600, 6153, 102, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[206751, 6162, 194, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[206970, 6169, 2001, 62, 251, "Subsubsection"], Cell[208974, 6233, 1404, 50, 92, "Text"], Cell[210381, 6285, 620, 23, 26, "Text"], Cell[211004, 6310, 403, 14, 26, "Text"], Cell[211410, 6326, 2523, 80, 62, "Text"], Cell[213936, 6408, 131, 4, 24, "Text"], Cell[214070, 6414, 378, 8, 97, "Input"], Cell[214451, 6424, 100, 3, 24, "Text"], Cell[CellGroupData[{ Cell[214576, 6431, 342, 9, 79, "Input"], Cell[214921, 6442, 17566, 412, 194, 3292, 231, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[232502, 6857, 181, 4, 24, "Text"], Cell[CellGroupData[{ Cell[232708, 6865, 146, 4, 43, "Input"], Cell[232857, 6871, 106, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[233000, 6878, 104, 3, 43, "Input"], Cell[233107, 6883, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[233221, 6890, 98, 3, 43, "Input"], Cell[233322, 6895, 386, 6, 27, "Message"], Cell[233711, 6903, 84, 2, 42, "Output"] }, Open ]], Cell[233810, 6908, 41, 0, 24, "Text"], Cell[233854, 6910, 144, 4, 43, "Input"], Cell[CellGroupData[{ Cell[234023, 6918, 156, 4, 61, "Input"], Cell[234182, 6924, 459, 10, 40, "Print"] }, Open ]], Cell[234656, 6937, 97, 3, 24, "Text"], Cell[CellGroupData[{ Cell[234778, 6944, 197, 6, 43, "Input"], Cell[234978, 6952, 21760, 521, 194, 4200, 299, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[256775, 7478, 91, 3, 43, "Input"], Cell[256869, 7483, 22239, 533, 194, 4327, 307, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[279123, 8019, 106, 3, 24, "Text"], Cell[279232, 8024, 109, 3, 43, "Input"], Cell[CellGroupData[{ Cell[279366, 8031, 239, 5, 79, "Input"], Cell[279608, 8038, 214, 4, 68, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[279859, 8047, 122, 3, 43, "Input"], Cell[279984, 8052, 187, 4, 42, "Output"] }, Open ]], Cell[280186, 8059, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[280513, 8071, 164, 5, 43, "Input"], Cell[280680, 8078, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[296212, 8503, 199, 6, 43, "Input"], Cell[296414, 8511, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[315337, 9039, 92, 3, 43, "Input"], Cell[315432, 9044, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[335796, 9601, 272, 10, 44, "Subsubsection"], Cell[336071, 9613, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[336188, 9620, 104, 3, 43, "Input"], Cell[336295, 9625, 77, 2, 42, "Output"] }, Open ]], Cell[336387, 9630, 102, 3, 43, "Input"] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) 0KooIfMT000oofMWI00?o0000 omWIfOoIfMT01OoIfMT3o`3o08WofMWI0ol0o`08omWIf@Co0000K_oIfMT000oofMWI00?o0000omWI fOoIfMT01?oIfMT3o`3o08_ofMWI0_l0o`0:omWIf@Co0000K?oIfMT000oofMWI0_l00004omWIf@?o 0?l0S?oIfMT3o`3o00[ofMWI1?l0001[omWIf@003ooIfMT00ol0003ofMWIomWIf@02omWIf@?o0?l0 S_oIfMT3o`3o00_ofMWI0ol0001ZomWIf@003ooIfMT01?l0003ofMWIomWIfOoIfMT3o`3o093ofMWI 0_l0o`0omWIf@?o0000HooIfMT000kofMWI0ol0o`2IomWIf@?o0?l03_oIfMT3o`0005Wo fMWI0_l0o`07omWIf@003_oIfMT2o`3o09_ofMWI0ol0o`0>omWIf@?o0000F?oIfMT2o`3o00OofMWI 000?omWIf@03o`000?oIfMWofMWI09[ofMWI0ol0o`0>omWIf@?o0000E_oIfMT3o`3o00OofMWI000? omWIf@03o`000?oIfMWofMWI09_ofMWI0ol0o`0>omWIf@Co0000DooIfMT3o`3o00SofMWI000?omWI f@03o`000?oIfMWofMWI09cofMWI0ol0o`0>omWIf@Co0000DOoIfMT3o`3o00WofMWI000?omWIf@03 o`000?oIfMWofMWI09gofMWI0_l0o`0@omWIf@?o0000CooIfMT3o`3o00[ofMWI000?omWIf@03o`00 0?oIfMWofMWI09gofMWI0ol0o`0@omWIf@Co0000C?oIfMT3o`3o00_ofMWI000?omWIf@03o`000?oI fMWofMWI09kofMWI0ol0o`0@omWIf@Co0000B_oIfMT3o`3o00cofMWI000?omWIf@;o0000X?oIfMT3 o`3o017ofMWI0ol00019omWIf@;o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0X?oIfMT3o`3o 017ofMWI1?l00016omWIf@?o0?l03OoIfMT000oofMWI00?o0000omWIfOoIfMT0XOoIfMT3o`3o017o fMWI1?l00014omWIf@?o0?l03_oIfMT000oofMWI00?o0000omWIfOoIfMT0X_oIfMT3o`3o01;ofMWI 0ol00012omWIf@?o0?l03ooIfMT000oofMWI00?o0000omWIfOoIfMT0XooIfMT3o`3o01;ofMWI1?l0 000oomWIf@?o0?l04?oIfMT000oofMWI00?o0000omWIfOoIfMT0Y?oIfMT3o`3o01;ofMWI1?l0000m omWIf@?o0?l04OoIfMT000Go00000ooIfMT2o`0000GofMWI00?o0000omWIfOoIfMT0YOoIfMT3o`3o 01?ofMWI0ol0000komWIf@?o0?l04_oIfMT00005omWIfOl0003ofMWIomWIfOl000000_oIfMT01?l0 003ofMWIomWIfOl00004omWIf@03o`000?oIfMWofMWI0:KofMWI0ol0o`0ComWIf@?o0000>OoIfMT3 o`3o01?ofMWI0002omWIf@03o`000?oIfMWofMWI00;ofMWI00Co0000omWIfOoIfMWo00001?oIfMT3 o`000:OofMWI0ol0o`0ComWIf@?o0000=ooIfMT3o`3o01CofMWI0003omWIf@05o`000?oIfMWofMWI omWIfOl000000_oIfMT00ol0003ofMWIomWIf@02omWIf@03o`000?oIfMWofMWI0:SofMWI0ol0o`0C omWIf@?o0000=OoIfMT3o`3o01GofMWI00001Ol0003ofMWIomWIfOoIfMWo000000;ofMWI00Co0000 omWIfOoIfMWo00001?oIfMT00ol0003ofMWIomWIf@2YomWIf@?o0?l04ooIfMT3o`0003?ofMWI0ol0 o`0FomWIf@0000Go0000omWIfOoIfMWofMWIo`000002omWIf@04o`000?oIfMWofMWIo`0000CofMWI 00?o0000omWIfOoIfMT0Z_oIfMT3o`3o01?ofMWI0ol0000aomWIf@?o0?l05ooIfMT00004omWIfOl0 003o0000o`0000CofMWI0_l00005omWIf@03o`000?oIfMWofMWI0:_ofMWI0ol0o`0ComWIf@?o0000 ;ooIfMT3o`3o01SofMWI000?omWIf@03o`000?oIfMWofMWI0:cofMWI1?l0o`0BomWIf@?o0000;OoI fMT3o`3o01WofMWI000?omWIf@03o`000?oIfMWofMWI0:gofMWI1?l0o`0BomWIf@?o0000:ooIfMT3 o`3o01[ofMWI000?omWIf@03o`000?oIfMWofMWI0:oofMWI0ol0o`0BomWIf@?o0000:OoIfMT3o`3o 01_ofMWI000?omWIf@03o`000?oIfMWofMWI0;3ofMWI0ol0o`0BomWIf@?o00009_oIfMT4o`3o01co fMWI000?omWIf@;o0000/_oIfMT3o`3o01;ofMWI0ol0000TomWIf@Co0?l07OoIfMT000oofMWI00?o 0000omWIfOoIfMT0/_oIfMT4o`3o017ofMWI0ol0000RomWIf@?o0?l07ooIfMT000oofMWI00?o0000 omWIfOoIfMT0/ooIfMT4o`3o017ofMWI0ol0000OomWIf@Co0?l08?oIfMT000oofMWI00?o0000omWI fOoIfMT0]OoIfMT3o`3o017ofMWI0ol0000MomWIf@Co0?l08OoIfMT000oofMWI00?o0000omWIfOoI fMT0]_oIfMT3o`3o017ofMWI0ol0000JomWIf@Co0?l08ooIfMT000oofMWI00?o0000omWIfOoIfMT0 ]ooIfMT4o`3o013ofMWI0ol0000HomWIf@Co0?l09?oIfMT000oofMWI00?o0000omWIfOoIfMT0^?oI fMT4o`3o013ofMWI0ol0000FomWIf@?o0?l09_oIfMT000oofMWI00?o0000omWIfOoIfMT0^_oIfMT4 o`3o00oofMWI0ol0000ComWIf@Co0?l09ooIfMT000oofMWI0_l0002lomWIf@Co0?l03ooIfMT2o`00 017ofMWI1Ol0o`0XomWIf@003ooIfMT00ol0003ofMWIomWIf@2momWIf@Co0?l03OoIfMT3o`0000ko fMWI1Ol0o`0ZomWIf@003ooIfMT00ol0003ofMWIomWIf@2nomWIf@Ko0?l02ooIfMT3o`0000_ofMWI 1Ol0o`0/omWIf@003ooIfMT00ol0003ofMWIomWIf@30omWIf@Oo0?l02OoIfMT3o`0000SofMWI1Ol0 o`0^omWIf@003ooIfMT00ol0003ofMWIomWIf@33omWIf@Oo0?l01ooIfMT3o`0000CofMWI1_l0o`0` omWIf@003ooIfMT00ol0003ofMWIomWIf@36omWIf@[o0?l000?ofMWIo`3o0?l0o`002Ol0o`0bomWI f@003ooIfMT00ol0003ofMWIomWIf@39omWIfA3o0?l0=OoIfMT000oofMWI00?o0000omWIfOoIfMT0 c_oIfMT5o`3o0004omWIfOl0003o0000o`0003OofMWI000?omWIf@;o0000e_oIfMT3o`0003KofMWI 000?omWIf@03o`000?oIfMWofMWI0=KofMWI0ol0000eomWIf@003ooIfMT00ol0003ofMWIomWIf@3G omWIf@?o0000=?oIfMT000oofMWI00?o0000omWIfOoIfMT0f?oIfMT3o`0003?ofMWI000?omWIf@03 o`000?oIfMWofMWI0=WofMWI0ol0000bomWIf@003ooIfMT00ol0003ofMWIomWIf@3JomWIf@?o0000 3ofMWI0ol0000[omWIf@003ooIfMT00ol0003ofMWIomWIf@3Q omWIf@?o0000:_oIfMT000oofMWI00?o0000omWIfOoIfMT0h_oIfMT3o`0002WofMWI00001?oIfMWo 0000o`000?l00004omWIf@;o00001OoIfMT00ol0003ofMWIomWIf@3SomWIf@?o0000:?oIfMT00005 o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oIfMWo fMWI0>CofMWI0_l0000XomWIf@001?oIfMT01?l0003ofMWIomWIfOl00002omWIf@03o`000?oIfMWo fMWI00;ofMWI00?o0000omWIfOoIfMT0i?oIfMT3o`0002OofMWI0002omWIf@;o00000ooIfMT01?l0 003ofMWIomWIfOl00004omWIf@?o0000iOoIfMT3o`0002KofMWI0004omWIf@04o`000?oIfMWofMWI o`0000;ofMWI00?o0000omWIfOoIfMT00_oIfMT00ol0003ofMWIomWIf@3VomWIf@?o00009OoIfMT0 0005o`000?oIfMWofMWIomWIfOl000000_oIfMT01?l0003ofMWIomWIfOl00004omWIf@03o`000?oI fMWofMWI0>OofMWI0ol0000TomWIf@0000CofMWIo`000?l0003o00001?oIfMT2o`0000GofMWI00?o 0000omWIfOoIfMT0j?oIfMT3o`0002?ofMWI000?omWIf@03o`000?oIfMWofMWI0>WofMWI0ol0000R omWIf@003ooIfMT00ol0003ofMWIomWIf@3ZomWIf@?o00008OoIfMT000oofMWI00?o0000omWIfOoI fMT0jooIfMT3o`00023ofMWI000?omWIf@03o`000?oIfMWofMWI0>cofMWI0ol0000OomWIf@003ooI fMT2o`000>kofMWI0ol0000NomWIf@003ooIfMT00ol0003ofMWIomWIf@3^omWIf@?o00007OoIfMT0 00oofMWI00?o0000omWIfOoIfMT0kooIfMT3o`0001cofMWI000?omWIf@03o`000?oIfMWofMWI0?3o fMWI0_l0000LomWIf@003ooIfMT00ol0003ofMWIomWIf@3`omWIf@?o00006ooIfMT000oofMWI00?o 0000omWIfOoIfMT0lOoIfMT3o`0001[ofMWI000?omWIf@03o`000?oIfMWofMWI0?;ofMWI0ol0000I omWIf@003ooIfMT00ol0003ofMWIomWIf@3comWIf@?o00006?oIfMT000oofMWI0_l0003eomWIf@?o 00005ooIfMT000oofMWI00?o0000omWIfOoIfMT0mOoIfMT3o`0001KofMWI000?omWIf@03o`000?oI fMWofMWI0?KofMWI0ol0000EomWIf@003ooIfMT00ol0003ofMWIomWIf@3gomWIf@?o00005?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0n?oIfMT3o`0001?ofMWI000?omWIf@03o`000?oIfMWofMWI0?Wo fMWI0ol0000BomWIf@003ooIfMT00ol0003ofMWIomWIf@3jomWIf@?o00004OoIfMT000oofMWI00?o 0000omWIfOoIfMT0nooIfMT2o`00017ofMWI000?omWIf@03o`000?oIfMWofMWI0?_ofMWI0ol0000@ omWIf@003ooIfMT2o`000?gofMWI0ol0000?omWIf@003ooIfMT00ol0003ofMWIomWIf@3momWIf@?o 00003_oIfMT000oofMWI00?o0000omWIfOoIfMT0o_oIfMT2o`0000kofMWI000?omWIf@03o`000?oI fMWofMWI0?kofMWI0ol0000=omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@?o00003?oIfMT0 00oofMWI00?o0000omWIfOoIfMT0oooIfMT1omWIf@?o00002ooIfMT000oofMWI00?o0000omWIfOoI fMT0oooIfMT2omWIf@?o00002_oIfMT000oofMWI00?o0000omWIfOoIfMT0oooIfMT3omWIf@;o0000 2_oIfMT000oofMWI0_l0003oomWIf@CofMWI0ol00009omWIf@003ooIfMT00ol0003ofMWIomWIf@3o omWIf@CofMWI0ol00008omWIf@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@GofMWI0ol00007omWI f@003ooIfMT00ol0003ofMWIomWIf@3oomWIf@KofMWI0_l00007omWIf@003ooIfMT00ol0003ofMWI omWIf@3oomWIf@oofMWI000?omWIf@03o`000?oIfMWofMWI0?oofMWI3ooIfMT000oofMWI00?o0000 omWIfOoIfMT0oooIfMT?omWIf@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.367127, -3.12112, \ 0.0237193, 0.241311}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c.- ", FontColor->RGBColor[1, 0, 0]], "Calcular ", "la norma de la funci\[OAcute]n error." }], "Subsubsection", CellDingbat->None, TextAlignment->AlignmentMarker, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(e[x_] := v[x] - vp\)], "Input", CellLabel->"In[15]:=", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(ne = Sqrt[pe[e[x], e[x]]] // N\)], "Input", CellLabel->"In[16]:=", FontSize->14], Cell[BoxData[ \(18.00250212986795`\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[BoxData[ \(Clear["\", $Line]\)], "Input", CellLabel->"In[17]:=", FontSize->14] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{38, 1280}, {0, 778}}, WindowSize->{810, 633}, WindowMargins->{{Automatic, 206}, {Automatic, 0}}, StyleDefinitions -> "ArticleModern.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 228, 5, 90, "Title"], Cell[CellGroupData[{ Cell[2029, 62, 140, 2, 76, "SectionFirst"], Cell[2172, 66, 1798, 50, 108, "Text"], Cell[CellGroupData[{ Cell[3995, 120, 109, 3, 43, "Input"], Cell[4107, 125, 87, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4231, 132, 108, 3, 43, "Input"], Cell[4342, 137, 529, 8, 41, "Message"] }, Open ]], Cell[4886, 148, 53, 0, 24, "Text"], Cell[4942, 150, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[5059, 157, 87, 3, 43, "Input"], Cell[5149, 162, 103, 2, 61, "Output"] }, Open ]], Cell[5267, 167, 94, 3, 24, "Text"], Cell[CellGroupData[{ Cell[5386, 174, 119, 3, 43, "Input"], Cell[5508, 179, 152, 3, 42, "Output"] }, Open ]], Cell[5675, 185, 926, 19, 108, "Text"], Cell[CellGroupData[{ Cell[6626, 208, 82, 3, 43, "Input"], Cell[6711, 213, 118, 3, 42, "Output"] }, Open ]], Cell[6844, 219, 101, 3, 43, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[6982, 227, 368, 10, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[7375, 241, 1392, 46, 99, "Subsubsection"], Cell[8770, 289, 107, 3, 43, "Input"], Cell[8880, 294, 511, 14, 79, "Input"], Cell[CellGroupData[{ Cell[9416, 312, 81, 3, 43, "Input"], Cell[9500, 317, 59, 2, 42, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[9608, 325, 481, 17, 28, "Subsubsection"], Cell[CellGroupData[{ Cell[10114, 346, 137, 4, 61, "Input"], Cell[10254, 352, 62, 2, 45, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[10365, 360, 656, 24, 28, "Subsubsection"], Cell[CellGroupData[{ Cell[11046, 388, 146, 4, 61, "Input"], Cell[11195, 394, 61, 2, 45, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[11305, 402, 503, 16, 29, "Subsubsection"], Cell[11811, 420, 1851, 47, 136, "Text"], Cell[13665, 469, 115, 3, 43, "Input"], Cell[CellGroupData[{ Cell[13805, 476, 127, 3, 43, "Input"], Cell[13935, 481, 91, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14063, 488, 87, 3, 43, "Input"], Cell[14153, 493, 394, 12, 84, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[14596, 511, 541, 18, 28, "Subsubsection"], Cell[15140, 531, 222, 4, 40, "Text"], Cell[15365, 537, 109, 3, 43, "Input"], Cell[CellGroupData[{ Cell[15499, 544, 113, 3, 43, "Input"], Cell[15615, 549, 97, 2, 42, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[15761, 557, 540, 18, 28, "Subsubsection"], Cell[CellGroupData[{ Cell[16326, 579, 253, 6, 43, "Input"], Cell[16582, 587, 97, 2, 42, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[16728, 595, 430, 14, 46, "Subsubsection"], Cell[17161, 611, 111, 3, 43, "Input"], Cell[CellGroupData[{ Cell[17297, 618, 288, 7, 43, "Input"], Cell[17588, 627, 112, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17737, 634, 119, 3, 43, "Input"], Cell[17859, 639, 168, 4, 86, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[18076, 649, 511, 18, 28, "Subsubsection"], Cell[18590, 669, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[18707, 676, 161, 5, 43, "Input"], Cell[18871, 683, 80, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18988, 690, 161, 5, 43, "Input"], Cell[19152, 697, 273, 5, 125, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19462, 707, 85, 3, 43, "Input"], Cell[19550, 712, 80, 2, 57, "Output"] }, Open ]], Cell[19645, 717, 102, 3, 43, "Input"], Cell[19750, 722, 463, 15, 46, "Text"], Cell[20216, 739, 1612, 57, 48, "Text"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[21877, 802, 370, 10, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[22272, 816, 1249, 41, 118, "Subsubsection"], Cell[23524, 859, 275, 8, 24, "Text"], Cell[CellGroupData[{ Cell[23824, 871, 110, 3, 43, "Input"], Cell[23937, 876, 60, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24034, 883, 114, 3, 43, "Input"], Cell[24151, 888, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[24260, 896, 548, 19, 44, "Subsubsection"], Cell[CellGroupData[{ Cell[24833, 919, 111, 3, 43, "Input"], Cell[24947, 924, 62, 2, 45, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[25058, 932, 656, 24, 44, "Subsubsection"], Cell[CellGroupData[{ Cell[25739, 960, 196, 5, 43, "Input"], Cell[25938, 967, 62, 2, 45, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[26049, 975, 774, 23, 82, "Subsubsection"], Cell[26826, 1000, 151, 4, 43, "Input"], Cell[CellGroupData[{ Cell[27002, 1008, 124, 3, 43, "Input"], Cell[27129, 1013, 114, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27280, 1020, 86, 3, 43, "Input"], Cell[27369, 1025, 442, 13, 100, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[27860, 1044, 461, 16, 44, "Subsubsection"], Cell[28324, 1062, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[28457, 1069, 339, 8, 61, "Input"], Cell[28799, 1079, 129, 3, 57, "Output"] }, Open ]], Cell[28943, 1085, 236, 7, 25, "Text"], Cell[CellGroupData[{ Cell[29204, 1096, 266, 9, 43, "Input"], Cell[29473, 1107, 110, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[29632, 1115, 462, 16, 44, "Subsubsection"], Cell[CellGroupData[{ Cell[30119, 1135, 94, 3, 43, "Input"], Cell[30216, 1140, 183, 4, 68, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[30448, 1150, 513, 18, 44, "Subsubsection"], Cell[30964, 1170, 95, 3, 43, "Input"], Cell[CellGroupData[{ Cell[31084, 1177, 118, 3, 43, "Input"], Cell[31205, 1182, 89, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[31331, 1189, 143, 4, 43, "Input"], Cell[31477, 1195, 63, 2, 42, "Output"] }, Open ]], Cell[31555, 1200, 299, 7, 41, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[31891, 1212, 771, 25, 62, "Subsubsection"], Cell[32665, 1239, 979, 30, 62, "Text"], Cell[CellGroupData[{ Cell[33669, 1273, 148, 4, 43, "Input"], Cell[33820, 1279, 251, 5, 27, "Message"], Cell[34074, 1286, 172, 3, 66, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34283, 1294, 215, 5, 61, "Input"], Cell[34501, 1301, 973, 29, 80, "Print"] }, Open ]], Cell[35489, 1333, 102, 3, 43, "Input"], Cell[35594, 1338, 5042, 177, 128, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[40685, 1521, 279, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[40989, 1530, 1552, 56, 81, "Subsubsection"], Cell[42544, 1588, 639, 20, 46, "Text"], Cell[43186, 1610, 113, 3, 43, "Input"], Cell[43302, 1615, 145, 4, 43, "Input"], Cell[43450, 1621, 664, 17, 58, "Text"], Cell[44117, 1640, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[44250, 1647, 123, 3, 43, "Input"], Cell[44376, 1652, 131, 3, 47, "Output"] }, Open ]], Cell[44522, 1658, 710, 23, 44, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[45269, 1686, 485, 17, 44, "Subsubsection"], Cell[45757, 1705, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[45876, 1712, 172, 5, 43, "Input"], Cell[46051, 1719, 299, 5, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[46387, 1729, 88, 3, 43, "Input"], Cell[46478, 1734, 167, 3, 44, "Output"] }, Open ]], Cell[46660, 1740, 137, 3, 24, "Text"], Cell[CellGroupData[{ Cell[46822, 1747, 578, 16, 61, "Input"], Cell[47403, 1765, 17220, 439, 194, 3919, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[64660, 2209, 159, 5, 43, "Input"], Cell[64822, 2216, 16273, 405, 194, 3482, 241, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[81132, 2626, 195, 6, 43, "Input"], Cell[81330, 2634, 15908, 397, 194, 3376, 236, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[97275, 3036, 92, 3, 43, "Input"], Cell[97370, 3041, 17174, 437, 194, 3888, 268, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[114593, 3484, 259, 9, 44, "Subsubsection"], Cell[114855, 3495, 85, 1, 24, "Text"], Cell[114943, 3498, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[115060, 3505, 104, 3, 43, "Input"], Cell[115167, 3510, 81, 2, 42, "Output"] }, Open ]], Cell[115263, 3515, 102, 3, 43, "Input"], Cell[115368, 3520, 466, 15, 44, "Text"], Cell[115837, 3537, 658, 18, 62, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[116544, 3561, 240, 4, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[116809, 3569, 1810, 64, 98, "Subsubsection"], Cell[118622, 3635, 153, 4, 43, "Input"], Cell[CellGroupData[{ Cell[118800, 3643, 175, 5, 43, "Input"], Cell[118978, 3650, 60, 2, 42, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[119087, 3658, 326, 10, 62, "Subsubsection"], Cell[119416, 3670, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[119549, 3677, 103, 3, 43, "Input"], Cell[119655, 3682, 232, 4, 68, "Output"] }, Open ]], Cell[119902, 3689, 536, 15, 44, "Text"], Cell[CellGroupData[{ Cell[120463, 3708, 128, 3, 43, "Input"], Cell[120594, 3713, 88, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[120719, 3720, 176, 5, 43, "Input"], Cell[120898, 3727, 133, 3, 57, "Output"] }, Open ]], Cell[121046, 3733, 101, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[121196, 3742, 298, 5, 99, "SectionFirst"], Cell[CellGroupData[{ Cell[121519, 3751, 1746, 54, 181, "Subsubsection"], Cell[123268, 3807, 74, 1, 24, "Text"], Cell[123345, 3810, 278, 5, 26, "Text"], Cell[123626, 3817, 528, 18, 26, "Text"], Cell[124157, 3837, 131, 4, 24, "Text"], Cell[124291, 3843, 117, 3, 43, "Input"], Cell[124411, 3848, 197, 4, 79, "Input"], Cell[124611, 3854, 108, 3, 43, "Input"], Cell[CellGroupData[{ Cell[124744, 3861, 123, 3, 43, "Input"], Cell[124870, 3866, 111, 2, 61, "Output"] }, Open ]], Cell[124996, 3871, 295, 7, 42, "Text"], Cell[CellGroupData[{ Cell[125316, 3882, 181, 5, 43, "Input"], Cell[125500, 3889, 62, 2, 42, "Output"] }, Open ]], Cell[125577, 3894, 23, 0, 24, "Text"], Cell[CellGroupData[{ Cell[125625, 3898, 127, 3, 43, "Input"], Cell[125755, 3903, 91, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[125883, 3910, 87, 3, 43, "Input"], Cell[125973, 3915, 393, 12, 84, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[126415, 3933, 652, 19, 81, "Subsubsection"], Cell[127070, 3954, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[127189, 3961, 172, 5, 43, "Input"], Cell[127364, 3968, 118, 3, 60, "Output"] }, Open ]], Cell[127497, 3974, 330, 10, 42, "Text"], Cell[CellGroupData[{ Cell[127852, 3988, 583, 16, 61, "Input"], Cell[128438, 4006, 21946, 573, 194, 5142, 360, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[150399, 4582, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[150726, 4594, 164, 5, 43, "Input"], Cell[150893, 4601, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[166425, 5026, 199, 6, 43, "Input"], Cell[166627, 5034, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[185550, 5562, 92, 3, 43, "Input"], Cell[185645, 5567, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[206009, 6124, 272, 10, 44, "Subsubsection"], Cell[206284, 6136, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[206401, 6143, 104, 3, 43, "Input"], Cell[206508, 6148, 77, 2, 42, "Output"] }, Open ]], Cell[206600, 6153, 102, 3, 43, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[206751, 6162, 194, 3, 76, "SectionFirst"], Cell[CellGroupData[{ Cell[206970, 6169, 2001, 62, 251, "Subsubsection"], Cell[208974, 6233, 1404, 50, 92, "Text"], Cell[210381, 6285, 620, 23, 26, "Text"], Cell[211004, 6310, 403, 14, 26, "Text"], Cell[211410, 6326, 2523, 80, 62, "Text"], Cell[213936, 6408, 131, 4, 24, "Text"], Cell[214070, 6414, 378, 8, 97, "Input"], Cell[214451, 6424, 100, 3, 24, "Text"], Cell[CellGroupData[{ Cell[214576, 6431, 342, 9, 79, "Input"], Cell[214921, 6442, 17566, 412, 194, 3292, 231, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[232502, 6857, 181, 4, 24, "Text"], Cell[CellGroupData[{ Cell[232708, 6865, 146, 4, 43, "Input"], Cell[232857, 6871, 106, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[233000, 6878, 104, 3, 43, "Input"], Cell[233107, 6883, 77, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[233221, 6890, 98, 3, 43, "Input"], Cell[233322, 6895, 386, 6, 27, "Message"], Cell[233711, 6903, 84, 2, 42, "Output"] }, Open ]], Cell[233810, 6908, 41, 0, 24, "Text"], Cell[233854, 6910, 144, 4, 43, "Input"], Cell[CellGroupData[{ Cell[234023, 6918, 156, 4, 61, "Input"], Cell[234182, 6924, 459, 10, 40, "Print"] }, Open ]], Cell[234656, 6937, 97, 3, 24, "Text"], Cell[CellGroupData[{ Cell[234778, 6944, 197, 6, 43, "Input"], Cell[234978, 6952, 21760, 521, 194, 4200, 299, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[256775, 7478, 91, 3, 43, "Input"], Cell[256869, 7483, 22239, 533, 194, 4327, 307, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[279157, 8022, 652, 19, 81, "Subsubsection"], Cell[279812, 8043, 94, 3, 43, "Input"], Cell[CellGroupData[{ Cell[279931, 8050, 172, 5, 43, "Input"], Cell[280106, 8057, 118, 3, 60, "Output"] }, Open ]], Cell[280239, 8063, 330, 10, 42, "Text"], Cell[CellGroupData[{ Cell[280594, 8077, 583, 16, 61, "Input"], Cell[281180, 8095, 21946, 573, 194, 5142, 360, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[303141, 8671, 302, 8, 41, "Text"], Cell[CellGroupData[{ Cell[303468, 8683, 164, 5, 43, "Input"], Cell[303635, 8690, 15495, 420, 194, 3771, 270, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[319167, 9115, 199, 6, 43, "Input"], Cell[319369, 9123, 18886, 523, 194, 4905, 345, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[338292, 9651, 92, 3, 43, "Input"], Cell[338387, 9656, 20315, 551, 194, 5111, 358, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[358751, 10213, 272, 10, 44, "Subsubsection"], Cell[359026, 10225, 92, 3, 43, "Input"], Cell[CellGroupData[{ Cell[359143, 10232, 104, 3, 43, "Input"], Cell[359250, 10237, 77, 2, 42, "Output"] }, Open ]], Cell[359342, 10242, 102, 3, 43, "Input"] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)