(* 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[ 3177835, 53543] NotebookOptionsPosition[ 3155217, 53051] NotebookOutlinePosition[ 3172050, 53357] CellTagsIndexPosition[ 3172007, 53354] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Tema 7 : \nProfundizando en las capacidades gr\[AAcute]ficas de ", StyleBox["Mathematica", FontSlant->"Italic"], " " }], "Title", CellChangeTimes->{ 3.4278162014102983`*^9, {3.459060235953125*^9, 3.459060236453125*^9}}, TextAlignment->Center, TextJustification->0], Cell[CellGroupData[{ Cell["\<\ Representaci\[OAcute]n de curvas en coordenadas polares. El comando PolarPlot\ \>", "Section 1", CellChangeTimes->{{3.459060255515625*^9, 3.45906027796875*^9}, 3.4590609063125*^9}, TextAlignment->Left, TextJustification->1], Cell[TextData[{ "El comando PolarPlot permite representar curvas dadas en coordenadas \ polares. La sintaxis es la siguiente:\n\t", StyleBox["PolarPlot[r, {\[Theta],\[Theta]min,\[Theta]max}]\n", FontWeight->"Bold"], "donde r es funci\[OAcute]n de \[Theta]. El resultado ser\[AAcute] la gr\ \[AAcute]fica de la curva dada en polares como r=r(\[Theta]). Por ejemplo, la \ curva cuya ecuaci\[OAcute]n en coordenadas polares es : r = cos(\[Theta]) con \ \[Theta]\[Element][0,", "\[Pi]", "], es una circunferencia." }], "Text", CellChangeTimes->{{3.427903434824884*^9, 3.427903464835497*^9}, { 3.42790367674584*^9, 3.4279038064038258`*^9}, {3.427904074153186*^9, 3.427904125509314*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PolarPlot", "[", RowBox[{ RowBox[{"Cos", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "Pi"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.427903810953141*^9, 3.427903858191586*^9}}], Cell[BoxData[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw123c81e/7OHBRJBmlUJpURqGsNLgUpYxkpEjZ8pZNQ2RkS9nKSFS2bEK4 7ZHt2M45r2NvJ9n79/o8fo+vf3g+jtfrcY/ruu7r/uOcNrRWN6GloaFxoKOh +d/v///zF/7vr0scEczbO1TwpP8jHxqiCmwdjyRXcb/DblsGhuiB+9e7b+Zw +2cEV4/9fAY0JPM+Cm7vA9KsbiHWEDOANFpxx/1n3+X72x52Y8qTRbjf0k92 Nf18BfbHOaPicF/g5GFninOCQnTG1AO3W/HNTzdDXOHaoLOKIW5ObSnJK5Xu 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Cell["\<\ En este caso se representan dos curva, la circunferencia de centro el origen \ y radio 1, r = 1 y otra curva m\[AAcute]s compleja. 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"Output", CellChangeTimes->{3.459061176984375*^9, 3.469795278078125*^9, 3.4697954121875*^9}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Representaci\[OAcute]n de curvas de nivel \ \>", "Section 1", CellChangeTimes->{{3.459060307703125*^9, 3.459060309328125*^9}, { 3.45906118334375*^9, 3.45906118765625*^9}}], Cell[TextData[{ "Las curvas de nivel de una funci\[OAcute]n de dos variables f(x,y), son \ curvas en el plano xy que satisfacen la ecuaci\[OAcute]n:\nf(x,y) = C siendo \ C una constante. ", StyleBox["Mathematica", FontSlant->"Italic"], " representa varias curvas de nivel de la funci\[OAcute]n f(x,y) en el rect\ \[AAcute]ngulo a\[LessEqual]x\[LessEqual]b , c\[LessEqual]y\[LessEqual]d , \ mediante el comando :\n\t", StyleBox["ContourPlot[f`[x,y],{x,a,b},{y,c,d}].", FontWeight->"Bold"], "\nEste comando tambi\[EAcute]n se puede utilizar para representar una curva \ dada en forma \[IAcute]mplicita:\n\t", StyleBox["ContourPlot[f`[x,y]==C,{x,a,b},{y,c,d}].", FontWeight->"Bold"], "\nObtener informaci\[OAcute]n sobre el comando ContourPlot y sus posibles \ opciones." }], "Text", CellChangeTimes->{{3.42571456559375*^9, 3.425714566296875*^9}, { 3.42736895219573*^9, 3.4273689566467*^9}, {3.428127938578125*^9, 3.428127992203125*^9}}, TextAlignment->Left, TextJustification->1], Cell[CellGroupData[{ Cell[TextData[{ "Ejemplo 3\nRepresentar las curvas de nivel de g(x,y) = xseny+ysenx en la \ regi\[OAcute]n [0,5\[Pi]] x [0,5\[Pi]]. \nRepresentar la curva de ecuaci\ \[OAcute]n : ", 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Del mismo modo con el comando GraphicsGrid se pueden \ representar varias gr\[AAcute]ficas agrupadas en varias filas, es decir, como \ una matriz de gr\[AAcute]ficas en un \[UAcute]nico objeto gr\[AAcute]fico.\ \>", "Text", CellChangeTimes->{{3.425714090546875*^9, 3.4257141003125*^9}, { 3.42812782184375*^9, 3.4281279024375*^9}}, TextAlignment->Left, TextJustification->1], Cell[TextData[{ "Si los gr\[AAcute]ficos que se quiere representar est\[AAcute]n almacenados \ en las variables ", Cell[BoxData[ FormBox[ SubscriptBox["g", "1"], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ SubscriptBox["g", "2"], TraditionalForm]]], ", .., la sintaxis del comando GraphicsRow es:\n\t", Cell[BoxData[ FormBox[ RowBox[{"GraphicsRow", "[", RowBox[{"{", SubscriptBox["g", "1"]}]}], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ SubscriptBox["g", "2"], TraditionalForm]]], ",..}]\nEn el caso del comando GraphicsGrid el argumento es la matriz en la \ que est\[AAcute]n almacenados los gr\[AAcute]ficos. Puede ser interesante la \ utilizaci\[OAcute]n del comando Partition que, a partir de una lista \ sencilla, nos permite generar la matriz." }], "Text", CellChangeTimes->{{3.459061273890625*^9, 3.459061312734375*^9}, { 3.45906139296875*^9, 3.45906143115625*^9}, {3.45906147071875*^9, 3.459061585265625*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "Ejemplo 7\nRepresentar primero por separado y despu\[EAcute]s en dos filas \ de dos gr\[AAcute]ficos cada una las siguientes curvas:\na) r= sen(5 \ \[Theta]/4) , 0 \[LessEqual]\[Theta] \[LessEqual]8\[Pi] ;\nb) r= \[Theta] \ sin \[Theta] , -9\[Pi] \[LessEqual] \[Theta] \[LessEqual] 9\[Pi];\nc) La \ curva de ecuaci\[OAcute]n :\n\tr = ", Cell[BoxData[ SuperscriptBox["e", "sin\[Theta]"]]], " - sin5 \[Theta] + ", Cell[BoxData[ RowBox[{ SuperscriptBox["sen", "6"], RowBox[{"(", " ", RowBox[{"\[Theta]", " ", "/", "9"}], ")"}]}]]], ", 0 \[LessEqual] \[Theta] \[LessEqual]12\[Pi];\nd) r=sin\[Theta] + ", Cell[BoxData[ RowBox[{ SuperscriptBox["cos", "3"], RowBox[{"(", RowBox[{"3", RowBox[{"\[Theta]", " ", "/", "2"}]}], ")"}]}]]], ", 0\[LessEqual] \[Theta] \[LessEqual]4\[Pi]." }], "Subsection", CellChangeTimes->{{3.459061359625*^9, 3.459061384984375*^9}, { 3.459061597546875*^9, 3.459061619875*^9}, {3.45906169028125*^9, 3.45906169203125*^9}, {3.459061766203125*^9, 3.459061772046875*^9}, { 3.45906192171875*^9, 3.459061963765625*^9}, {3.4590620134375*^9, 3.459062021328125*^9}, {3.45906213903125*^9, 3.459062184796875*^9}, { 3.459063960890625*^9, 3.45906396134375*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"r", "[", "\[Theta]_", "]"}], "=", RowBox[{"Sin", "[", FractionBox[ RowBox[{"5", " ", "\[Theta]"}], "4"], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.459061623875*^9, 3.459061630171875*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pp1", "=", RowBox[{"PolarPlot", "[", RowBox[{ RowBox[{"r", "[", "\[Theta]", "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", RowBox[{"8", " ", "\[Pi]"}]}], "}"}], ",", RowBox[{"AspectRatio", 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Para ello se utilizan \ los comandos BarChart y PieChart.\nPara utilizar el comando Barchart es \ necesario cargar previamente el paquete : BarCharts. Esto se hace tecleando : \ Needs[\"BarCharts`\"]. 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