(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 66655, 1527] NotebookOptionsPosition[ 47596, 1149] NotebookOutlinePosition[ 64332, 1449] CellTagsIndexPosition[ 64289, 1446] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Tema 10:\nAplicaciones interactivas con ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Title", CellChangeTimes->{{3.468238973078125*^9, 3.46823898640625*^9}, 3.4682446963125*^9, {3.471671709875*^9, 3.471671728328125*^9}}, TextAlignment->Center], Cell["\<\ El comando Manipulate permite realizar aplicaciones interactivas mediante los \ comandos que ya se han estudiado en los temas anteriores. En muchas ocasiones \ es interesante obtener resultados de problemas en los que los valores de \ ciertos par\[AAcute]metros puedan ir cambiando. Este tipo de aplicaciones \ podr\[IAcute]an realizarse mediante una instricci\[OAcute]n de tipo Table, o \ Do, sin embargo , esto implica distintas salidas , o guardar en un vector los \ resultados para los diferentes valores del contador que se utiliza. El \ comando Manipulate, mediante barras de desplazamiento y otros tipos de \ controles, puede ir cambiando el valor de los par\[AAcute]metros de cualquier \ problema devolviendo instantaneamente el nuevo resultado. Veamos un ejemplo: Se desea conocer el valor de la funci\[OAcute]n Sin[x] en cualquier punto de \ un intervalo entre x=0 y x=\[Pi].\ \>", "Text", CellChangeTimes->{{3.468326171375*^9, 3.46832646325*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", RowBox[{"Sin", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.46823940265625*^9, 3.468239419546875*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 0., Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`x$$], 0, Pi}}, Typeset`size$$ = {84., {3., 11.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`x$1088$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$1088$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> {$CellContext`x$$, Sin[$CellContext`x$$]}, "Specifications" :> {{$CellContext`x$$, 0, Pi}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{378., {71., 78.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.468239420453125*^9}] }, Open ]], Cell[TextData[{ "Tal como se puede apreciar cambiando la posici\[OAcute]n de la barra de \ desplazamiento se pueden obtener los valores de la abscisa y la ordenada de \ la funci\[OAcute]n en cualquier punto del intervalo. El comando Table, \ solamente nos permitir\[IAcute]a conocer los valores en ciertos puntos, \ dependiendo del tama\[NTilde]o de paso que pongamos en el contador.\nOtro de \ los aspectos importantes de este comando es que en la parte correspondiente a \ las sentencias a ejecutar, se puede incorporar cualquier comando de ", StyleBox["Mathematica", FontSlant->"Italic"], " y por lo tanto nos permitir\[AAcute] realizar aplicaciones interactivas de \ muy diversos tipos. Uno de los aspectos mas interesantes es la aplicaci\ \[OAcute]n en la presentqaci\[OAcute]n de gr\[AAcute]ficos.\nEn el siguiente \ ejemplo se desea visualizar una funci\[OAcute]n sinusouidal amortiguada , y \ se desea analizar como afecta el coeficiente de amortiguamiento a dicha \ sinusoide. Por tanto se representa la funci\[OAcute]n ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "*", SuperscriptBox["\[ExponentialE]", RowBox[{"-", "\[Alpha]x"}]]}], TraditionalForm]], FormatType->"TraditionalForm"], " haciendo que el par\[AAcute]metro ", "\[Alpha] pueda ir variando." }], "Text", CellChangeTimes->{{3.468326472453125*^9, 3.4683265621875*^9}, { 3.468326598859375*^9, 3.468326825546875*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "*", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[Alpha]"}], "*", "x"}]]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"10", " ", "\[Pi]"}]}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4682394366875*^9, 3.46823951065625*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`\[Alpha]$$ = 0.09, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`\[Alpha]$$], 0, 1}}, Typeset`size$$ = { 540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`\[Alpha]$2868$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Alpha]$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`\[Alpha]$$, $CellContext`\[Alpha]$2868$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[Sin[$CellContext`x] E^((-$CellContext`\[Alpha]$$) $CellContext`x), {$CellContext`x, 0, 10 Pi}, PlotRange -> {-1, 1}], "Specifications" :> {{$CellContext`\[Alpha]$$, 0, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{605., {229., 236.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.46823948821875*^9, 3.4682395109375*^9}}] }, Open ]], Cell["\<\ La barra de desplazamiento tiene un simbolo + en la parte final que despliega \ una serie de botones que permiten realizar una animaci\[OAcute]n autom\ \[AAcute]tica de la aplicaci\[OAcute]n. Adem\[AAcute]s aparece una ventana en \ que se puede ver el valor exacto que toma el pr\[AAcute]metro en cad \ instante. Dentro de esa misma ventana se puede escribir el valor que se \ desee, con lo que se pueden estudiar situaciones particulares de forma nuy \ sencilla.\ \>", "Text", CellChangeTimes->{{3.468326870078125*^9, 3.468326996625*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`\[Alpha]$$ = 0.6, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`\[Alpha]$$], 0, 1}}, Typeset`size$$ = { 540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`\[Alpha]$2868$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Alpha]$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`\[Alpha]$$, $CellContext`\[Alpha]$2868$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[Sin[$CellContext`x] E^((-$CellContext`\[Alpha]$$) $CellContext`x), {$CellContext`x, 0, 10 Pi}, PlotRange -> {-1, 1}], "Specifications" :> {{$CellContext`\[Alpha]$$, 0, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{605., {248., 255.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Input"], Cell["\<\ Pueden utilizarse varios controles simultaneamente para manejar distintos par\ \[AAcute]metros en una misma demostraci\[OAcute]n. En el siguente \ gr\[AAcute]fico se presenta una sinusoide amortiguada en la que se va \ cambiando la frecuencia, con lo que hay dos par\[AAcute]metros: \[Alpha] que \ controla el amortiguamiento y n que controla la frecuencia de la \ se\[NTilde]al. variando cada uno de llos se puede ver como cambia la funci\ \[OAcute]n de salida.\ \>", "Text", CellChangeTimes->{{3.46832717140625*^9, 3.468327331671875*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"n", "*", "x"}], "]"}], "*", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[Alpha]"}], "*", "x"}]]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"10", " ", "\[Pi]"}]}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4682394366875*^9, 3.46823951065625*^9}, { 3.4682395906875*^9, 3.468239605375*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 3.41, $CellContext`\[Alpha]$$ = 0.042, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`\[Alpha]$$], 0, 1}, { Hold[$CellContext`n$$], 1, 5}}, Typeset`size$$ = {540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`\[Alpha]$5709$$ = 0, $CellContext`n$5710$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 1, $CellContext`\[Alpha]$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`\[Alpha]$$, $CellContext`\[Alpha]$5709$$, 0], Hold[$CellContext`n$$, $CellContext`n$5710$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[Sin[$CellContext`n$$ $CellContext`x] E^((-$CellContext`\[Alpha]$$) $CellContext`x), {$CellContext`x, 0, 10 Pi}, PlotRange -> {-1, 1}], "Specifications" :> {{$CellContext`\[Alpha]$$, 0, 1}, {$CellContext`n$$, 1, 5}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{605., {250., 257.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.4682396064375*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Tama\[NTilde]o de paso", "Section", CellChangeTimes->{{3.46832735946875*^9, 3.46832736196875*^9}}], Cell["\<\ En los ejemplos que hemos visto hasta el momento la variaci\[OAcute]n de los \ par\[AAcute]metros del comando Manipulate era continua , sin embargo en \ muchas ocasiones se desea obtener el resultado solo para ciertos valores, por \ lo que se debe indicar un conjunto discreto de valores en los que se quiere \ que se eval\[UAcute]en los par\[AAcute]metros, al estilo del comando Table. Este aspecto se presenta en el siguiente ejemplo. Se desea obtener el valor \ del factorial de un n\[UAcute]mero entero entre el cero y el 30. Para \ realizar esta operaci\[OAcute]n se debe indicar en el contador n que el \ incremento se realiza de uno en uno, de la misma manera que se hac\[IAcute]a \ en el comando Table.\ \>", "Text", CellChangeTimes->{{3.468327396609375*^9, 3.46832758190625*^9}, { 3.468327620734375*^9, 3.468327719296875*^9}, {3.46832816725*^9, 3.468328180125*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"n", "!"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "30", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.468239656484375*^9, 3.4682396786875*^9}, { 3.468327585125*^9, 3.46832760371875*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 11, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 30, 1}}, Typeset`size$$ = {95., {0., 11.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4821$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4821$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Factorial[$CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 30, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{378., {71., 78.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.468239679421875*^9, 3.46832758571875*^9, 3.468327844265625*^9}] }, Open ]], Cell["\<\ Si se desea introducir alg\[UAcute]n texto en la soluci\[OAcute]n puede \ hacerse de distintas maneras. Por ejemplo introduciendo texto en una fila \ mediante le comando Row.\ \>", "Text", CellChangeTimes->{{3.46832776428125*^9, 3.468327829390625*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", RowBox[{"\"\\"", ",", "n", ",", "\"\< es:\>\"", ",", RowBox[{"n", "!"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "30", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.468239757078125*^9, 3.468239871390625*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 17, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 30, 1}}, Typeset`size$$ = {420., {1., 12.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$8874$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$8874$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Row[{"El factorial de ", $CellContext`n$$, " es:", Factorial[$CellContext`n$$]}], "Specifications" :> {{$CellContext`n$$, 0, 30, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{485., {71., 78.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.46823979559375*^9, 3.46823987409375*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Tipos de controladores", "Section", CellChangeTimes->{{3.468239994921875*^9, 3.468239998484375*^9}}], Cell[TextData[{ "Dependiendo de las caracter\[IAcute]sticas y de las variaciones que vaya a \ tener el par\[AAcute]metro que se utilice, ", StyleBox["Mathematica", FontSlant->"Italic"], " utiliza el tipo de controlador mas adecuado. Para un caso en el que el par\ \[AAcute]metro va a variar como en un comando de tipo Table, el controlador \ mas indicado ser\[IAcute]a una barra de desplazamiento, tal y como hemos \ visto en los ejemplos anteriores. Sin embargo si se considera un peque\ \[NTilde]o listado de valores separados, ", StyleBox["Mathematica", FontSlant->"Italic"], " utiliza una fila de botones." }], "Text", CellChangeTimes->{{3.468328845515625*^9, 3.4683290140625*^9}, { 3.46832973565625*^9, 3.468329777765625*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"n1", " ", "x"}], "]"}], "+", RowBox[{"Sin", "[", RowBox[{"n2", " ", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "xmax"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "2"}]}], "]"}], ",", RowBox[{"{", RowBox[{"n1", ",", "1", ",", "20"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "1", ",", "20"}], "}"}], ",", RowBox[{"{", RowBox[{"xmax", ",", RowBox[{"{", RowBox[{"\[Pi]", ",", RowBox[{"2", "\[Pi]"}], ",", RowBox[{"3", "\[Pi]"}], ",", RowBox[{"4", "\[Pi]"}]}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.468242677703125*^9, 3.468242716078125*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n1$$ = 4.300000000000001, $CellContext`n2$$ = 12.66, $CellContext`xmax$$ = 2 Pi, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n1$$], 1, 20}, { Hold[$CellContext`n2$$], 1, 20}, { Hold[$CellContext`xmax$$], {Pi, 2 Pi, 3 Pi, 4 Pi}}}, Typeset`size$$ = { 540., {167., 177.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n1$25835$$ = 0, $CellContext`n2$25836$$ = 0, $CellContext`xmax$25837$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n1$$ = 1, $CellContext`n2$$ = 1, $CellContext`xmax$$ = Pi}, "ControllerVariables" :> { Hold[$CellContext`n1$$, $CellContext`n1$25835$$, 0], Hold[$CellContext`n2$$, $CellContext`n2$25836$$, 0], Hold[$CellContext`xmax$$, $CellContext`xmax$25837$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[Sin[$CellContext`n1$$ $CellContext`x] + Sin[$CellContext`n2$$ $CellContext`x], {$CellContext`x, 0, $CellContext`xmax$$}, PlotRange -> 2], "Specifications" :> {{$CellContext`n1$$, 1, 20}, {$CellContext`n2$$, 1, 20}, {$CellContext`xmax$$, {Pi, 2 Pi, 3 Pi, 4 Pi}}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{605., {270., 277.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.468242643984375*^9, 3.468242716515625*^9}] }, Open ]], Cell["\<\ Si el listado de valores separados que se desea utilizar es mayor, entonces \ Mathematica cambia la fila de botones por un pop up men\[UAcute] en el que se \ puede seleccinar caulquiera de los valores deseados.\ \>", "Text", CellChangeTimes->{{3.468329786375*^9, 3.468329857234375*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"n1", " ", "x"}], "]"}], "+", RowBox[{"Sin", "[", RowBox[{"n2", " ", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "xmax"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "2"}]}], "]"}], ",", RowBox[{"{", RowBox[{"n1", ",", "1", ",", "20"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "1", ",", "20"}], "}"}], ",", RowBox[{"{", RowBox[{"xmax", ",", RowBox[{"{", RowBox[{"\[Pi]", ",", RowBox[{"2", "\[Pi]"}], ",", RowBox[{"3", "\[Pi]"}], ",", RowBox[{"4", "\[Pi]"}], ",", RowBox[{"5", "\[Pi]"}], ",", RowBox[{"6", "\[Pi]"}], ",", RowBox[{"7", "\[Pi]"}]}], 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En el siguiente ejemplo se utiliza el checkbox para determinar \ si se desea representar adem\[AAcute]s de la sinusoide amortiguada los \ valores de los extremos m\[AAcute]ximo y m\[IAcute]nimo que puede tomar la \ funci\[OAcute]n dependiendo del valor del amortiguamiento..\ \>", "Text", CellChangeTimes->{{3.46833133653125*^9, 3.46833149353125*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"If", "[", RowBox[{"contorno", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"n", "*", "x"}], "]"}], "*", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[Alpha]"}], "*", "x"}]]}], ",", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[Alpha]"}], "*", "x"}]], ",", RowBox[{"-", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[Alpha]"}], "*", "x"}]]}]}], "}"}], ",", RowBox[{ RowBox[{"Sin", "[", RowBox[{"n", "*", "x"}], "]"}], "*", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[Alpha]"}], "*", "x"}]]}]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"10", " ", "\[Pi]"}]}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"contorno", ",", RowBox[{"{", RowBox[{"True", ",", "False"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4682394366875*^9, 3.46823951065625*^9}, { 3.4682395906875*^9, 3.468239605375*^9}, {3.468243299046875*^9, 3.4682434006875*^9}, 3.468243432296875*^9}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`contorno$$ = True, $CellContext`n$$ = 2.2, $CellContext`\[Alpha]$$ = 0.068, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`\[Alpha]$$], 0, 1}, { Hold[$CellContext`n$$], 1, 5}, { Hold[$CellContext`contorno$$], {True, False}}}, Typeset`size$$ = { 540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`\[Alpha]$37735$$ = 0, $CellContext`n$37736$$ = 0, $CellContext`contorno$37737$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`contorno$$ = True, $CellContext`n$$ = 1, $CellContext`\[Alpha]$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`\[Alpha]$$, $CellContext`\[Alpha]$37735$$, 0], Hold[$CellContext`n$$, $CellContext`n$37736$$, 0], Hold[$CellContext`contorno$$, $CellContext`contorno$37737$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[ If[$CellContext`contorno$$, { Sin[$CellContext`n$$ $CellContext`x] E^((-$CellContext`\[Alpha]$$) $CellContext`x), E^((-$CellContext`\[Alpha]$$) $CellContext`x), - E^((-$CellContext`\[Alpha]$$) $CellContext`x)}, Sin[$CellContext`n$$ $CellContext`x] E^((-$CellContext`\[Alpha]$$) $CellContext`x)], {$CellContext`x, 0, 10 Pi}, PlotRange -> {-1, 1}], "Specifications" :> {{$CellContext`\[Alpha]$$, 0, 1}, {$CellContext`n$$, 1, 5}, {$CellContext`contorno$$, {True, False}}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{605., {264., 271.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.468243322578125*^9, 3.468243402828125*^9, 3.46824343296875*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Controladores en dos dimensiones", "Section", CellChangeTimes->{{3.468243516234375*^9, 3.46824352171875*^9}}], Cell["\<\ Existe tambi\[EAcute]n un controlador en dos dimensiones que permite utilizar \ el raton en para posicionar dos valores simultaneamente. Se puede utilizar \ tanto num\[EAcute]ricamente como gr\[AAcute]ficamente. Si se desea representar un vector de dimensi\[OAcute]n dos, mediante este \ controlador, puede realizarse tal como se representa en el siguiente ejemplo.\ \>", "Text", CellChangeTimes->{{3.46833182215625*^9, 3.46833200246875*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", RowBox[{"\"\\"", ",", "pt"}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"pt", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", RowBox[{"-", "4"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.468332015390625*^9, 3.468332120515625*^9}, 3.46833217665625*^9}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`pt$$ = {-2.3750000000000018`, \ -2.3750000000000018`}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`pt$$], {-4, -4}, {4, 4}}}, 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StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.4683320243125*^9, 3.46833212103125*^9}, 3.468332177078125*^9}, ImageSize->{142, 165}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}] }, Open ]], Cell["\<\ Tambi\[EAcute]n se puede utilizar para realizar representaciones \ gr\[AAcute]ficas, posicionando el valor del punto en un gr\[AAcute]fico.\ \>", "Text", CellChangeTimes->{{3.46833213615625*^9, 3.468332162640625*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", RowBox[{"PointSize", "[", "0.1", "]"}], ",", RowBox[{"Point", "[", "punto", "]"}]}], "}"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", "1.2"}]}], "]"}], ",", RowBox[{"{", RowBox[{"punto", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]], "Input", 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Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Graphics[{Red, PointSize[0.1], Point[$CellContext`punto$$]}, Axes -> True, PlotRange -> 1.2], "Specifications" :> {{$CellContext`punto$$, {-1, -1}, {1, 1}}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{605., {374., 381.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.46824355084375*^9, 3.4682435640625*^9}, { 3.468243603296875*^9, 3.46824364503125*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Utilizaci\[OAcute]n de puntos", "Section", CellChangeTimes->{{3.468243794046875*^9, 3.468243798640625*^9}}], Cell[TextData[{ "Se pueden introducir en una demostraci\[OAcute]n puntos interactivos que \ pueden moverse a lo largo de todo el gr\[AAcute]fico, con lo que las \ aplicaciones de este tiopo de comandos se amplian para poder realizar un \ mayor n\[UAcute]mero de ejmplos.La nomenclatura de este controlador dentro \ del comando manipulate es la siguiente, {nombre,punto,Locator). En primer \ lugar se indica el nombre de la variable (un punto), a continuaci\[OAcute]n \ la posici\[OAcute]n inicial de dicho punto y por \[UAcute]ltimo Locator este \ es el nomnre clave que advierte a ", StyleBox["Mathematica", FontSlant->"Italic"], " que la variable que se acaba de definir es un punto interactivo.\nEn el \ siguiente ejemplo se han utilzado tres puntos de este tipo para que ", StyleBox["Mathematica", FontSlant->"Italic"], " calcule el polinomio interpolador que pasa por los tres." }], "Text", CellChangeTimes->{{3.468332316328125*^9, 3.4683326566875*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"InterpolatingPolynomial", "[", RowBox[{ RowBox[{"{", RowBox[{"pt1", ",", "pt2", ",", "pt3"}], "}"}], ",", "x"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "2"}], ",", "3"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt1", ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], ",", "Locator"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt2", ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", "Locator"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt3", ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}]}], "}"}], ",", "Locator"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.468243812796875*^9, 3.468243906765625*^9}, { 3.468243982109375*^9, 3.468244009078125*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`pt1$$ = {-0.9550000000000001, 0.35999999999999943`}, $CellContext`pt2$$ = { 0.6000000000000001, -2.8400000000000007`}, $CellContext`pt3$$ = { 2.3850000000000002`, -2.0199999999999996`}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`pt1$$], {0, 0}}, Automatic}, {{ Hold[$CellContext`pt2$$], {1, -1}}, Automatic}, {{ Hold[$CellContext`pt3$$], {2, 1}}, Automatic}}, Typeset`size$$ = { 540., {162., 172.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`pt1$$ = {0, 0}, $CellContext`pt2$$ = { 1, -1}, $CellContext`pt3$$ = {2, 1}}, "ControllerVariables" :> {}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[ Evaluate[ InterpolatingPolynomial[{$CellContext`pt1$$, $CellContext`pt2$$, \ $CellContext`pt3$$}, $CellContext`x]], {$CellContext`x, -2, 3}], "Specifications" :> {{{$CellContext`pt1$$, {0, 0}}, Automatic, ControlType -> Locator}, {{$CellContext`pt2$$, {1, -1}}, Automatic, ControlType -> Locator}, {{$CellContext`pt3$$, {2, 1}}, Automatic, ControlType -> Locator}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{614., {210., 217.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.468243913125*^9, {3.46824398284375*^9, 3.468244009421875*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Varias salidas simultaneas", "Section", CellChangeTimes->{{3.46824410078125*^9, 3.468244109453125*^9}, 3.4683326729375*^9}], Cell[TextData[{ "La potencia del comando Manipulate se aprecia cuando en un mismo proyecto \ de demostraci\[OAcute]n se presentan los resultados correspondientes al \ prorblema de diversas maneras, en ventanas distintas pero simultaneamente. \ Esto es posible debido a la gran potencia de ", StyleBox["Mathematica", FontSlant->"Italic"], ". Si se van realizando todos los c\[AAcute]lculos previos a la presentaci\ \[OAcute]n de las salidas dentro del propio comando Manipulate, en un \ Bloque, o separando las sentencias con ; se pueden hacer presentaciones en \ las que finalmente mediante columnas, o gr\[AAcute]ficos simultaneos u otras \ tecnicas, el comando Manipulate devuelva diversos valores.\nEn el siguiente \ ejemplo se presentan simultaneamente tres resultado en una columna. En la \ primera fila las posiciones de cuatro puntos interactivos que se pueden mover \ dentro del gr\[AAcute]fico. A continuaci\[OAcute]n el polinomio interpolador \ que pasa por los cuatro puntos anteiores y finalmente un grafico en el que se \ ve simultaneamente los puntos y el polinomio." }], "Text", CellChangeTimes->{{3.46833288978125*^9, 3.46833323809375*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{ RowBox[{"pol", "=", RowBox[{"Evaluate", "[", RowBox[{"InterpolatingPolynomial", "[", RowBox[{ RowBox[{"{", RowBox[{"pt1", ",", "pt2", ",", "pt3", ",", "pt4"}], "}"}], ",", "x"}], "]"}], "]"}]}], ";", RowBox[{"Column", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"pt1", ",", "pt2", ",", "pt3", ",", "pt4"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Row", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"pol", "//", "Expand"}]}], "}"}], "]"}], ",", RowBox[{"Plot", "[", RowBox[{"pol", ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "2"}], ",", "3"}], "}"}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"400", ",", "250"}], "}"}]}]}], "]"}]}], "}"}], ",", "Center", ",", RowBox[{"Frame", "\[Rule]", "All"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt1", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}], ",", "Locator"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt2", ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", "Locator"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt3", ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", "Locator"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt4", ",", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}]}], "}"}], ",", "Locator"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.468243812796875*^9, 3.468243906765625*^9}, { 3.468243982109375*^9, 3.468244009078125*^9}, {3.468244133421875*^9, 3.468244349796875*^9}, {3.4682445391875*^9, 3.46824457271875*^9}, { 3.468244604296875*^9, 3.468244664296875*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`pt1$$ = {-1.42, -0.5999999999999943}, \ $CellContext`pt2$$ = {-0.6000000000000001, -15.599999999999994`}, \ $CellContext`pt3$$ = {0.5049999999999999, 2.1799999999999997`}, $CellContext`pt4$$ = {1.98, 4.04}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`pt1$$], {-1, 0}}, Automatic}, {{ Hold[$CellContext`pt2$$], {0, -1}}, Automatic}, {{ Hold[$CellContext`pt3$$], {1, 1}}, Automatic}, {{ Hold[$CellContext`pt4$$], {2, 3}}, Automatic}}, Typeset`size$$ = { 704., {229.5, 236.5}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`pt1$$ = {-1, 0}, $CellContext`pt2$$ = { 0, -1}, $CellContext`pt3$$ = {1, 1}, $CellContext`pt4$$ = {2, 3}}, "ControllerVariables" :> {}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`pol = Evaluate[ InterpolatingPolynomial[{$CellContext`pt1$$, $CellContext`pt2$$, \ $CellContext`pt3$$, $CellContext`pt4$$}, $CellContext`x]]; Column[{ Row[{"puntos:", {$CellContext`pt1$$, $CellContext`pt2$$, \ $CellContext`pt3$$, $CellContext`pt4$$}}], Row[{"polinomio:", Expand[$CellContext`pol]}], Plot[$CellContext`pol, {$CellContext`x, -2, 3}, ImageSize -> {400, 250}]}, Center, Frame -> All]), "Specifications" :> {{{$CellContext`pt1$$, {-1, 0}}, Automatic, ControlType -> Locator}, {{$CellContext`pt2$$, {0, -1}}, Automatic, ControlType -> Locator}, {{$CellContext`pt3$$, {1, 1}}, Automatic, ControlType -> Locator}, {{$CellContext`pt4$$, {2, 3}}, Automatic, ControlType -> Locator}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{778., {277., 284.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.468244161296875*^9, {3.468244228546875*^9, 3.46824425996875*^9}, 3.468244318015625*^9, 3.468244351296875*^9, {3.46824454909375*^9, 3.46824457296875*^9}, 3.46824460928125*^9, {3.468244656421875*^9, 3.46824466509375*^9}}] }, Open ]], Cell[TextData[{ "la demostracion anterior es solo un ejemplo sencillo de las inmensas \ posibilidades que proporciona el comando Manipulate de ", StyleBox["Mathematica", FontSlant->"Italic"], ". Para obtener una visi\[OAcute]n mas amplia del mismo es recomendable \ acudir a la ayuda del programa y al tutorial espec\[IAcute]fico que hay para \ este comando.\nTambien resulta muy \[UAcute]til para comprobar las \ capacidades de este comando explorar la p\[AAcute]gina web \ http://demonstrations.wolfram.com/ . En la misma existe mas de 5000 \ demostraciones de diversos conceptos de todos los \[AAcute]mbitos de las \ ciencias en las que se ha aplicado el comando Manipulate." }], "Text", CellChangeTimes->{{3.468333243421875*^9, 3.468333385984375*^9}, { 3.468333489546875*^9, 3.46833354296875*^9}}] }, Open ]] }, Open ]] }, WindowToolbars->"EditBar", WindowSize->{1672, 933}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], FEPrivate`Join[{ Cell[ BoxData[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztXXdYFNfaz3O/f+79vudek3vTLKBIEaQpTRC7BgtqLCTWGxNjYsFookE0 NoxRY6oFuyIiWJCO9N4WWHrZpSy7VKkiBo2iy+5+Z/fsHg4zO7NLUZJ4fs/I Mztz5j3v+87u+zvnPe+Meuu3L1v/P6+99poJ+Gf+t9dek+8LBwiBIHvu/Byd ManLXMoSE+ExkQoZX+8W641rHWPUaDZZav+BZOoa6ZRVkhkftXrdrC3lg60h JuGh667nVjNkJjbd4ywfjhzbcP7iQFUiICAgIHiVkHfVO0dHL0tnDFd/XNGH q/g3bgrz84VFRVmnznAMrGRjDCSjxz6xmCFx3iFZtl/ickC6ZK/U6YtnS7Y/ 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