(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 67630, 1809] NotebookOptionsPosition[ 48020, 1478] NotebookOutlinePosition[ 52323, 1555] CellTagsIndexPosition[ 52244, 1550] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", "FirstSlide", CellTags-> "SlideShowHeader",ExpressionUUID->"ae861ed8-5fa1-4088-84fd-2651cc7b368a"], Cell["Introdu\[CCedilla]\[ATilde]o \[AGrave] F\[IAcute]sica Computacional I \ (2022.2)", "Title", CellChangeTimes->{ 3.559948400406288*^9, {3.699269571766136*^9, 3.699269573578824*^9}, { 3.7099080105038958`*^9, 3.7099080108133383`*^9}, {3.727189496068931*^9, 3.7271894962748613`*^9}, {3.83932299294512*^9, 3.839323000605739*^9}, { 3.8704194394469357`*^9, 3.870419439521731*^9}},ExpressionUUID->"92508663-47f1-4deb-9615-\ d2c271e8e453"], Cell["\<\ Aula 2: manipula\[CCedilla]\[ATilde]o alg\[EAcute]brica; fun\[CCedilla]\ \[OTilde]es definidas pelo usu\[AAcute]rio; gr\[AAcute]ficos simples\ \>", "Subtitle", CellChangeTimes->{{3.699269582406044*^9, 3.699269584285553*^9}, { 3.8393232649484053`*^9, 3.839323284264048*^9}},ExpressionUUID->"14f8f51b-58e9-4033-aea1-\ fd611ac95bb9"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"ee3ea2a1-973b-4e9a-a704-0d8a3c30d1be"], Cell[CellGroupData[{ Cell["Transformando express\[OTilde]es alg\[EAcute]bricas", "Section", CellChangeTimes->{ 3.699269664116198*^9, 3.70454748091461*^9, {3.704547516075143*^9, 3.7045475190812902`*^9}, {3.706294276733098*^9, 3.706294304716371*^9}, { 3.839323324298633*^9, 3.839323331059084*^9}},ExpressionUUID->"7da6da63-6378-4f26-b58d-\ d42a7250afa4"], Cell[TextData[{ "Existem ", ButtonBox["muitas fun\[CCedilla]\[OTilde]es", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/tutorial/\ AlgebraicCalculations.html"], None}, ButtonNote-> "https://reference.wolfram.com/language/tutorial/AlgebraicCalculations.\ html"], " no Mathematica para manipula\[CCedilla]\[ATilde]o de express\[OTilde]es \ alg\[EAcute]bricas. Vamos listar aqui algumas delas, atrav\[EAcute]s de \ exemplos." }], "Text", CellChangeTimes->{{3.6992696952616243`*^9, 3.6992696957779827`*^9}, { 3.704547416597644*^9, 3.704547418388081*^9}, {3.8393233348613234`*^9, 3.839323366214238*^9}, {3.839323576559081*^9, 3.839323576563138*^9}, { 3.870419447381391*^9, 3.870419447607505*^9}},ExpressionUUID->"3b730a40-c305-44bd-95b8-\ df5440115120"], Cell[BoxData[{ RowBox[{ RowBox[{"expr1", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "^", "2"}], " ", "*", RowBox[{"(", RowBox[{ RowBox[{"2", "*", "x"}], "+", "7"}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"5", "*", "x"}], "-", "3"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Expand", "[", "expr1", "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Expande", " ", "todos", " ", "os", " ", "produtos", " ", "e", " ", "pot\[EHat]ncias", " ", "positivas"}], " ", "*)"}]}]}], "Input", CellChangeTimes->{{3.8393233792138987`*^9, 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CellChangeTimes->{{3.699269751716757*^9, 3.699269753436467*^9}, 3.699269850923047*^9, 3.706294357396751*^9, {3.8393238265541153`*^9, 3.839323829860652*^9}},ExpressionUUID->"cfedd870-03fc-4542-ad5a-\ fa159d5053b2"], Cell[TextData[{ "A fun\[CCedilla]\[ATilde]o ", StyleBox[ButtonBox["Simplify", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Simplify.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Simplify.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], " busca simplificar express\[OTilde]es alg\[EAcute]bricas, mas nem sempre \ atua da forma como desejamos, e \[EAcute] preciso recorrer a outras fun\ \[CCedilla]\[OTilde]es ou a op\[CCedilla]\[OTilde]es adicionais." }], "Text", CellChangeTimes->{ 3.6992697457019463`*^9, 3.6992698838436613`*^9, {3.70454744273073*^9, 3.704547443267602*^9}, {3.8393241276946487`*^9, 3.839324197837492*^9}, { 3.8393248302085047`*^9, 3.839324831309167*^9}, {3.8704195697103453`*^9, 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12d66c48d2e1"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"a9293dc0-a2a2-41d7-a17f-f7683ae167d3"], Cell[TextData[{ "A fun\[CCedilla]\[ATilde]o ", StyleBox[ButtonBox["Simplify", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Simplify.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Simplify.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], " aplica diversas transforma\[CCedilla]\[OTilde]es em busca da forma mais \ simples para uma express\[ATilde]o. Ainda mais \ transforma\[CCedilla]\[OTilde]es s\[ATilde]o aplicadas pela fun\[CCedilla]\ \[ATilde]o ", StyleBox[ButtonBox["FullSimplify", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/FullSimplify.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/FullSimplify.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], ", cuja execu\[CCedilla]\[ATilde]o, no entanto, pode demorar bem mais. " }], "Text", CellChangeTimes->{{3.839324772370719*^9, 3.839324875848732*^9}, { 3.870419591927593*^9, 3.8704196150569563`*^9}},ExpressionUUID->"d9dc2b1f-4946-4194-956e-\ e065020159d4"], Cell[BoxData[ RowBox[{"expr6", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "x"}], ")"}], "/", RowBox[{"(", RowBox[{"7", "+", "x"}], ")"}]}], "]"}], "*", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"x", "^", "2"}]}], ")"}], "/", RowBox[{"(", RowBox[{"25", "-", RowBox[{"x", "^", "2"}]}], ")"}]}], "]"}], "*", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"5", "+", "x"}], ")"}], "*", RowBox[{"(", RowBox[{"2", "-", "x"}], ")"}]}], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"4", "-", RowBox[{"x", "^", "2"}]}], "]"}], "*", RowBox[{"Sqrt", "[", RowBox[{"3", "-", RowBox[{"x", "^", "2"}]}], "]"}]}], ")"}]}]}]], "Input", CellChangeTimes->{{3.839324886261983*^9, 3.839324960529715*^9}},ExpressionUUID->"30068dc6-61b3-4db7-8208-\ a0ff890851c9"], Cell[BoxData[ RowBox[{"Simplify", "[", "expr6", "]"}]], "Input", CellChangeTimes->{{3.839324981357628*^9, 3.839324990464635*^9}},ExpressionUUID->"94d06fb9-89ab-409c-987d-\ f41504fee3d2"], Cell[BoxData[ RowBox[{"FullSimplify", "[", "expr6", "]"}]], "Input", CellChangeTimes->{{3.83932499340432*^9, 3.839324998743884*^9}},ExpressionUUID->"22a0ab24-159f-4a09-b0f3-\ 4143fbe52a6a"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"04dc39ac-49b4-4583-b876-d13d47c8024d"], Cell[TextData[{ "Algumas simplifica\[CCedilla]\[OTilde]es podem ser alcan\[CCedilla]adas \ indicando ", StyleBox["suposi\[CCedilla]\[OTilde]es", FontWeight->"Bold"], ", que s\[ATilde]o dadas como segundo argumento da fun\[CCedilla]\[ATilde]o ", StyleBox[ButtonBox["Simplify", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Simplify.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Simplify.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], " (ou de outras fun\[CCedilla]\[OTilde]es de manipula\[CCedilla]\[ATilde]o \ alg\[EAcute]brica)." }], "Text", CellChangeTimes->{{3.839325029861676*^9, 3.8393250686734667`*^9}, { 3.870419625717188*^9, 3.870419625721344*^9}},ExpressionUUID->"7b8928b2-a6f1-4b41-a057-\ 6edb6599b9f4"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"expr7", "=", RowBox[{"Sqrt", "[", RowBox[{"x", "^", "2"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", "expr7", "]"}]}], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839325093486574*^9, 3.839325105743197*^9}, { 3.839325199646644*^9, 3.839325206251816*^9}},ExpressionUUID->"fa0e01a4-7e83-4a71-93f5-\ 71f33d222672"], Cell[BoxData[ RowBox[{ RowBox[{"Simplify", "[", RowBox[{"expr7", ",", RowBox[{"x", ">", "0"}]}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Supondo", " ", "que", " ", "x", " ", "\[EAcute]", " ", "positivo"}], " ", "*)"}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393251114184*^9, 3.8393251247551117`*^9}, { 3.839325170553528*^9, 3.8393252062527847`*^9}, 3.839357261651691*^9},ExpressionUUID->"f98b966b-1281-46a7-b11b-\ 4d049db6cdcd"], Cell[BoxData[ RowBox[{ RowBox[{"Simplify", "[", RowBox[{"expr7", ",", RowBox[{"x", "\[Element]", "Reals"}]}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Supondo", " ", "que", " ", "x", " ", "\[EAcute]", " ", "um", " ", "n\[UAcute]mero", " ", "real"}], " ", "*)"}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839325128847848*^9, 3.8393251705550528`*^9}},ExpressionUUID->"49cb6901-091e-47e4-a157-\ fcc0b5d5646a"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"53cf55d8-a27b-4a57-afc5-7769ff8f849c"], Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{"Log", "[", RowBox[{"x", "^", "r"}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.839325256509141*^9, 3.8393252642110863`*^9}},ExpressionUUID->"84983a64-0d66-4b44-9f45-\ f0777c9c62e3"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{"x", "^", "r"}], "]"}], ",", RowBox[{"x", ">", "0"}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393252710544252`*^9, 3.8393252795004997`*^9}, 3.8393254710046377`*^9},ExpressionUUID->"7bdcd088-5ffa-465a-a107-\ b4217c6e712a"], Cell["\<\ A fun\[CCedilla]\[ATilde]o logaritmo \[EAcute] multivalorada se o argumento \ \[EAcute] complexo, de modo que, para obter a \ simplifica\[CCedilla]\[ATilde]o, temos que garantir que o argumento seja \ real. Para isso, usamos a constru\[CCedilla]\[ATilde]o abaixo: \ \>", "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.83932529184065*^9, 3.839325337717225*^9}, 3.839325471006303*^9},ExpressionUUID->"2a9dc02a-7653-49e5-88ff-\ d427fa868620"], Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{"x", "^", "r"}], "]"}], ",", RowBox[{ RowBox[{"x", ">", "0"}], " ", "&&", " ", RowBox[{"r", "\[Element]", "Reals"}]}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393253411206007`*^9, 3.839325359700364*^9}, 3.8393254710074377`*^9},ExpressionUUID->"37f06f7b-ba61-453c-9a29-\ 32cc7bdbf3f7"], Cell[TextData[{ "Note que combinamos duas suposi\[CCedilla]\[OTilde]es (de que ", StyleBox["x", FontFamily->"Source Code Pro", FontWeight->"Regular"], " \[EAcute] positivo e de que ", StyleBox["r", FontFamily->"Source Code Pro", FontWeight->"Regular"], " pertence ao conjunto dos n\[UAcute]meros reais) usando o ", StyleBox["operador l\[OAcute]gico", FontWeight->"Bold"], " ", StyleBox["&&", FontFamily->"Source Code Pro", FontWeight->"Regular"], " (\[OpenCurlyDoubleQuote]e\[CloseCurlyDoubleQuote]). \[CapitalEAcute] uma \ constru\[CCedilla]\[ATilde]o que lembra bastante a nota\[CCedilla]\[ATilde]o \ matem\[AAcute]tica \[OpenCurlyDoubleQuote]escrita \[AGrave] m\[ATilde]o\ \[CloseCurlyDoubleQuote]." }], "Subitem", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839325369780776*^9, 3.839325471008833*^9}, { 3.839357269638699*^9, 3.8393572697411337`*^9}},ExpressionUUID->"705f8a1d-de27-4848-b5e3-\ 3aa84ba1d8e5"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"9711ac4c-53d8-4ca4-b78f-fa198caf9c15"], Cell[TextData[{ "Fun\[CCedilla]\[OTilde]es intr\[IAcute]nsecas que aceitam suposi\[CCedilla]\ \[OTilde]es, como ", StyleBox[ButtonBox["Simplify", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Simplify.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Simplify.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], ", podem tamb\[EAcute]m ser invocadas como argumento da fun\[CCedilla]\ \[ATilde]o intr\[IAcute]nseca ", StyleBox[ButtonBox["Assuming", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Assuming.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Assuming.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], ", cuja sintaxe \[EAcute] exemplificada abaixo:" }], "Text", CellChangeTimes->{{3.839325683990046*^9, 3.8393257290569344`*^9}, { 3.8393258575447206`*^9, 3.839325867950495*^9}, {3.87041964080049*^9, 3.870419666254673*^9}},ExpressionUUID->"f55b8e52-9d74-4c44-b99b-\ 65f8fce977cc"], Cell[BoxData[ RowBox[{"Assuming", "[", RowBox[{ RowBox[{"x", ">", "0"}], ",", RowBox[{"Simplify", "[", RowBox[{"Sqrt", "[", RowBox[{"x", "^", "2"}], "]"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.839325738985613*^9, 3.839325751524947*^9}},ExpressionUUID->"ec45a7c2-2cd9-456a-a5b1-\ c00b137104ad"], Cell[BoxData[ RowBox[{"Assuming", "[", RowBox[{ RowBox[{ RowBox[{"x", ">", "0"}], " ", "&&", " ", RowBox[{"r", "\[Element]", "Reals"}]}], ",", RowBox[{"Simplify", "[", RowBox[{"Log", "[", RowBox[{"x", "^", "r"}], "]"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.8393257556683064`*^9, 3.83932577889682*^9}},ExpressionUUID->"1822d9ac-0810-4efe-8e7c-\ 4f6d2c109b26"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"f1ea6945-699f-482b-8fd0-06e69f1653cb"], Cell[CellGroupData[{ Cell["Transformando express\[OTilde]es trigonom\[EAcute]tricas", "Subsection", CellChangeTimes->{ 3.6992696669461823`*^9, 3.704547487208755*^9, {3.704547526705332*^9, 3.704547527681479*^9}, 3.706294284132339*^9, {3.706294315644496*^9, 3.706294318355414*^9}, {3.8393259523490953`*^9, 3.839325960032419*^9}},ExpressionUUID->"4d99dca9-28c2-45ee-ae65-\ bfa655d56d4c"], Cell["\<\ Para manipular express\[OTilde]es contendo fun\[CCedilla]\[OTilde]es trigonom\ \[EAcute]tricas, o Mathematica disp\[OTilde]es de fun\[CCedilla]\[OTilde]es \ intr\[IAcute]nsecas espec\[IAcute]ficas. Os exemplos a seguir ilustram \ algumas delas:\ \>", "Text", CellChangeTimes->{ 3.6992697457019463`*^9, {3.704547447744219*^9, 3.70454745807546*^9}, { 3.8393259642736063`*^9, 3.839325994716235*^9}},ExpressionUUID->"060befa7-8133-4147-925f-\ 99e17e5ba7ba"], Cell[BoxData[ RowBox[{ RowBox[{"TrigExpand", "[", RowBox[{"Cos", "[", RowBox[{"2", "*", "\[Theta]"}], "]"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Expande", " ", "em", " ", "uma", " ", "soma", " ", "de", " ", "termos"}], " ", "*)"}]}]], "Input", CellChangeTimes->{{3.839326029767715*^9, 3.83932605070868*^9}},ExpressionUUID->"abb087ee-3ca1-4797-abff-\ 86e2efcf7183"], Cell[BoxData[ RowBox[{ RowBox[{"TrigReduce", "[", RowBox[{ RowBox[{"Sin", "[", "\[Theta]", "]"}], "*", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Aplica", " ", "identidades", " ", "envolvendo", " ", "m\[UAcute]ltiplos", " ", "de", " ", "\[AHat]ngulos"}], " ", "*)"}]}]], "Input", CellChangeTimes->{{3.839326056238852*^9, 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"]"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Expande", " ", "supondo", " ", "que", " ", "quaisquer", " ", "vari\[AAcute]veis", " ", "s\[ATilde]o", " ", "reais"}], " ", "*)"}]}]], "Input", CellChangeTimes->{{3.839326159796673*^9, 3.8393261873301373`*^9}, { 3.839448677455133*^9, 3.839448680558666*^9}},ExpressionUUID->"28a734e4-7438-4dc7-82a2-\ 185584ec61c9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"ExpToTrig", "[", RowBox[{"Exp", "[", RowBox[{"I", "*", "\[Theta]"}], "]"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{ "Converte", " ", "exponenciais", " ", "em", " ", "fun\[CCedilla]\[OTilde]es", " ", "trigonom\[EAcute]tricas"}], " ", "*)"}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839326190834084*^9, 3.839326222125729*^9}, 3.8393262610547733`*^9},ExpressionUUID->"198ca9a2-ab33-4b29-ad4b-\ 1789bc072e09"], Cell["\<\ Encontrar a fun\[CCedilla]\[ATilde]o do Mathematica que produz a melhor \ simplifica\[CCedilla]\[ATilde]o para os seus objetivos pode ser bem \ complicado!\ \>", "SubitemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393262318689632`*^9, 3.839326261056025*^9}},ExpressionUUID->"d166acb0-18ba-4ff4-8197-\ d9353fcb68f1"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"d0653087-e6fc-4117-98fa-618b3d35e3ba"], Cell[CellGroupData[{ Cell["Fun\[CCedilla]\[OTilde]es definidas pelo usu\[AAcute]rio", "Section", CellChangeTimes->{ 3.6992696669461823`*^9, 3.70454749050467*^9, {3.704547532369433*^9, 3.704547533321432*^9}, {3.706294323875647*^9, 3.706294324495994*^9}, { 3.83933157455728*^9, 3.83933158456863*^9}},ExpressionUUID->"a6bca3fb-c161-4f12-a2a7-\ 035c628e3fe4"], Cell["\<\ Al\[EAcute]m das muitas fun\[CCedilla]\[OTilde]es intr\[IAcute]nsecas do \ Mathematica, voc\[EHat] tamb\[EAcute]m pode definir suas pr\[OAcute]prias fun\ \[CCedilla]\[OTilde]es, usando a constru\[CCedilla]\[ATilde]o mostrada no \ exemplo a seguir.\ \>", "Text", CellChangeTimes->{{3.839331597383399*^9, 3.8393316463877277`*^9}},ExpressionUUID->"d8defd24-687d-4dd2-bb21-\ 118c0ff8990b"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"x", "+", RowBox[{"x", "^", "2"}]}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839331651940278*^9, 3.839331660406026*^9}, 3.839331888939042*^9, 3.839401565111022*^9},ExpressionUUID->"ee981e59-9af6-4bb0-a50d-\ 8c92504e88fc"], Cell["H\[AAcute] dois pontos a destacar aqui:", "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839331667617505*^9, 3.83933167410791*^9}, 3.839331888940856*^9},ExpressionUUID->"18b04e79-d9e9-472c-b7f8-\ 41d7c6d46148"], Cell[TextData[{ "o argumento da fun\[CCedilla]\[ATilde]o, na defini\[CCedilla]\[ATilde]o, \ \[EAcute] escrito seguido por uma \[OpenCurlyDoubleQuote]sublinha\ \[CloseCurlyDoubleQuote], que indica que se trata de um argumento arbitr\ \[AAcute]rio, e n\[ATilde]o de uma vari\[AAcute]vel ", StyleBox["x", FontFamily->"Source Code Pro", FontWeight->"Regular"], " cujo valor tenha sido atribu\[IAcute]do anteriormente;" }], "Item", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393316879242477`*^9, 3.839331768121561*^9}, 3.8393318889425898`*^9},ExpressionUUID->"6ca5e3b1-f901-4b2b-a70c-\ eed1befe6521"], Cell[TextData[{ "a defini\[CCedilla]\[ATilde]o da fun\[CCedilla]\[ATilde]o foi feita com \ \[OpenCurlyDoubleQuote]", StyleBox[":=", FontFamily->"Source Code Pro", FontWeight->"Regular"], "\[CloseCurlyDoubleQuote] em vez de uma igualdade simples, o que indica uma \ atribui\[CCedilla]\[ATilde]o retardada, em que o c\[AAcute]lculo \[EAcute] \ feito apenas quando a fun\[CCedilla]\[ATilde]o for invocada." }], "Item", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393316879242477`*^9, 3.839331826939906*^9}, 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Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"k", "=", "3"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"g", "[", "2", "]"}], "-", RowBox[{"h", "[", "2", "]"}]}]}], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839332040842651*^9, 3.83933204674364*^9}, 3.83933209179676*^9},ExpressionUUID->"82fc8a9f-3af3-49b6-b4db-\ 74214cb09a9c"], Cell[TextData[{ "Qual \[EAcute] a diferen\[CCedilla]a entre ", StyleBox["g[x]", FontFamily->"Source Code Pro", FontWeight->"Regular"], " e ", StyleBox["h[x]", FontFamily->"Source Code Pro", FontWeight->"Regular"], "?" }], "SubitemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839332058523201*^9, 3.839332091798148*^9}},ExpressionUUID->"ad5d46ad-e4c9-40c3-919b-\ 87e2a99b529d"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"c062d2d7-d4c8-4dfd-ab21-1f0c1c86de22"], Cell["E um segundo 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Cell["Substitui\[CCedilla]\[OTilde]es", "Section", CellChangeTimes->{{3.83933219158899*^9, 3.839332194242936*^9}},ExpressionUUID->"f78330d5-f5c5-4e89-88d9-\ d7f964eb0afe"], Cell[TextData[{ "Um recurso muito \[UAcute]til do Mathematica \[EAcute] a atribui\[CCedilla]\ \[ATilde]o tempor\[AAcute]ria oferecida pelo ", StyleBox["operador de substitui\[CCedilla]\[ATilde]o", FontWeight->"Bold"], " \[OpenCurlyDoubleQuote]", StyleBox["/.", FontFamily->"Source Code Pro", FontWeight->"Regular"], "\[CloseCurlyDoubleQuote] (sem as aspas). Vamos limpar a vari\[AAcute]vel ", StyleBox["k", FontFamily->"Source Code Pro", FontWeight->"Regular"], "," }], "Text", CellChangeTimes->{{3.839332209229011*^9, 3.839332282150674*^9}},ExpressionUUID->"545eecb9-86d8-43e5-90c2-\ de7056d59eab"], Cell[BoxData[ RowBox[{"Clear", "[", "k", "]"}]], "Input", CellChangeTimes->{{3.8393322952298603`*^9, 3.839332296856209*^9}},ExpressionUUID->"7edb5983-a054-4252-8d97-\ 22b4697c5f30"], Cell[TextData[{ "e redefinir a fun\[CCedilla]\[ATilde]o ", StyleBox["f[x]", FontFamily->"Source Code Pro", FontWeight->"Regular"], " como" }], "Text", CellChangeTimes->{{3.839332168542363*^9, 3.839332170179727*^9}, { 3.8393323029778023`*^9, 3.839332315586122*^9}},ExpressionUUID->"a2371891-c298-4c8a-a7e3-\ 211142174686"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"x", "+", RowBox[{"k", "*", RowBox[{"x", "^", "2"}]}]}]}]], "Input", CellChangeTimes->{{3.8393323234216137`*^9, 3.839332331226179*^9}},ExpressionUUID->"3e91f563-8d81-4999-8ab7-\ 3a0369aa8f28"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"6449f915-2665-4a0c-a6e2-e9d6ad499c59"], Cell[TextData[{ "Formalmente, ", StyleBox["f[x]", FontFamily->"Source Code Pro", FontWeight->"Regular"], " \[EAcute] fun\[CCedilla]\[ATilde]o apenas de ", StyleBox["x", FontFamily->"Source Code Pro", FontWeight->"Regular"], ", mas, enquanto ", StyleBox["k", FontFamily->"Source Code Pro", FontWeight->"Regular"], " n\[ATilde]o for definido, claramente n\[ATilde]o \[EAcute] \ poss\[IAcute]vel obter um valor puramente num\[EAcute]rico para ", StyleBox["f[x]", FontFamily->"Source Code Pro", FontWeight->"Regular"], ":" }], "Text", CellChangeTimes->{{3.8393323479306583`*^9, 3.83933239412267*^9}},ExpressionUUID->"b1b267e2-3d02-4f6e-8b23-\ bd16992023b6"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{"f", "[", "1", "]"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.83933241821694*^9, 3.839332420302052*^9}, 3.8393325959661293`*^9},ExpressionUUID->"58294c51-40e9-4bf3-9dc1-\ 844ec4c74896"], Cell[TextData[{ "O operador \[OpenCurlyDoubleQuote]", StyleBox["/.", FontFamily->"Source Code Pro", FontWeight->"Regular"], "\[CloseCurlyDoubleQuote] (tamb\[EAcute]m chamado de ", StyleBox[ButtonBox["ReplaceAll", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/ReplaceAll.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/ReplaceAll.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], ") permite atribuir valores tempor\[AAcute]rios a vari\[AAcute]veis:" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393324335102882`*^9, 3.839332456549461*^9}, 3.839332595967922*^9, {3.870419759739304*^9, 3.870419759744101*^9}},ExpressionUUID->"f54687cb-c7b2-41fc-ab9f-\ d40819af5615"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{ RowBox[{"f", "[", "1", "]"}], "/.", RowBox[{"k", "\[Rule]", " ", RowBox[{"1", "/", "2"}]}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839332470427185*^9, 3.839332484879675*^9}, 3.8393325959693403`*^9},ExpressionUUID->"9a4f990d-58af-4141-ad7b-\ a3946037eb95"], Cell[TextData[{ "Note a sintaxe que se segue ao operador \[OpenCurlyDoubleQuote]", StyleBox["/.", FontFamily->"Source Code Pro", FontWeight->"Regular"], "\[CloseCurlyDoubleQuote]: a atribui\[CCedilla]\[ATilde]o tempor\[AAcute]ria \ \[EAcute] feita n\[ATilde]o por meio da igualdade, mas pelo sinal \ \[OpenCurlyDoubleQuote]\[Rule]\[CloseCurlyDoubleQuote] (obtido no modo de ", StyleBox["input", FontSlant->"Italic"], " pela sequ\[EHat]ncia \[OpenCurlyDoubleQuote]", StyleBox["->", FontFamily->"Source Code Pro", FontWeight->"Regular"], "\[CloseCurlyDoubleQuote]). " }], "SubitemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393324915490713`*^9, 3.839332563368626*^9}, 3.839332595971122*^9},ExpressionUUID->"46f125a4-cd40-4710-b250-\ 7038bbc2c0ff"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"33cf9c85-e456-4482-a1ca-186c865bea40"], Cell[TextData[{ "Se agora consultarmos o valor de ", StyleBox["k", FontFamily->"Source Code Pro", FontWeight->"Regular"], ", veremos que continua n\[ATilde]o estando atribu\[IAcute]do:" }], "Text", CellChangeTimes->{{3.839332652436082*^9, 3.8393326668015957`*^9}},ExpressionUUID->"2155b105-b887-47d2-aa62-\ 0b268ef35680"], Cell[BoxData["k"], "Input", CellChangeTimes->{ 3.839332675650133*^9},ExpressionUUID->"d2197a4d-62de-4f66-bc00-\ 7aa4048df260"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"2a87f1cf-cd4a-4847-9f4e-91032c3a3b5a"], Cell[TextData[{ "Para mais um exemplo, vamos limpar as vari\[AAcute]veis ", StyleBox["a", FontFamily->"Source Code Pro", FontWeight->"Regular"], ", ", StyleBox["b", FontFamily->"Source Code Pro", FontWeight->"Regular"], " e ", StyleBox["c", FontFamily->"Source Code Pro", FontWeight->"Regular"], "," }], "Text", CellChangeTimes->{{3.839332686681287*^9, 3.8393326992126627`*^9}},ExpressionUUID->"7f5d949e-5d36-4ab4-a3cd-\ a707505901b1"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Input", CellChangeTimes->{{3.839332725286643*^9, 3.8393327276764917`*^9}},ExpressionUUID->"8f7fd91b-0a5e-4871-9be5-\ c1a6ac599dcb"], Cell[TextData[{ "e redefinir mais uma vez a fun\[CCedilla]\[ATilde]o ", StyleBox["f[x]", FontFamily->"Source Code Pro", FontWeight->"Regular"], " como" }], "Text", CellChangeTimes->{{3.8393327606620073`*^9, 3.839332769942075*^9}},ExpressionUUID->"02bed125-63ab-4551-9d1e-\ ba4d73274291"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{ RowBox[{"a", "*", RowBox[{"x", "^", "2"}]}], "+", RowBox[{"b", "*", "x"}], "+", "c"}]}]], "Input", CellChangeTimes->{{3.8393327766422663`*^9, 3.839332795289834*^9}},ExpressionUUID->"999e54b9-bfcf-406f-9dd7-\ 4ec31dd26548"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"f", "[", "1", "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.83933279794897*^9, 3.839332799024023*^9}, 3.8393329090603533`*^9},ExpressionUUID->"6db15cb2-8d05-4711-91c6-\ 12c4121ef9d6"], Cell[TextData[{ "A atribui\[CCedilla]\[ATilde]o de valores tempor\[AAcute]rios para ", StyleBox["a", FontFamily->"Source Code Pro", FontWeight->"Regular"], ", ", StyleBox["b", FontFamily->"Source Code Pro", FontWeight->"Regular"], " e ", StyleBox["c", FontFamily->"Source Code Pro", FontWeight->"Regular"], " \[EAcute] feita pela sintaxe abaixo:" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839332831210791*^9, 3.839332878336495*^9}, 3.8393329090616217`*^9},ExpressionUUID->"6e35e94c-bd83-47ff-b81b-\ 587c8185352b"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "1", "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"a", "\[Rule]", " ", "1"}], ",", RowBox[{"b", "\[Rule]", " ", "2"}], ",", RowBox[{"c", "\[Rule]", " ", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}]}], "}"}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393328844182262`*^9, 3.839332909062491*^9}},ExpressionUUID->"57e67ad8-90a5-43ef-af1e-\ ae4613f5fcb8"], Cell[TextData[{ "Note que a atribui\[CCedilla]\[ATilde]o de mais de uma vari\[AAcute]vel \ \[EAcute] feita entre chaves. Mais \[AGrave] frente, veremos que valores \ entre chaves definem uma ", StyleBox["lista", FontWeight->"Bold"], ", um importante tipo de estrutura de dados em muitas linguagens de programa\ \[CCedilla]\[ATilde]o." }], "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839338680567897*^9, 3.839338740927827*^9}},ExpressionUUID->"d0e38cc6-d0d2-425f-bf89-\ 3f97af7f1b6d"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"a2ab1752-a682-455f-89b1-85252f27546b"], Cell["\<\ Voc\[EHat] pode definir uma \[OpenCurlyDoubleQuote]vari\[AAcute]vel\ \[CloseCurlyDoubleQuote] para armazenar as atribui\[CCedilla]\[OTilde]es \ tempor\[AAcute]rias, como no exemplo a seguir:\ \>", "Text", CellChangeTimes->{{3.839338770297514*^9, 3.839338791458033*^9}},ExpressionUUID->"df876ce3-0d04-492a-a1d9-\ 2e9ea07903ad"], Cell[BoxData[ RowBox[{"subs", "=", RowBox[{"{", RowBox[{ RowBox[{"a", "\[Rule]", " ", "1"}], ",", RowBox[{"b", "\[Rule]", " ", "2"}], ",", RowBox[{"c", "\[Rule]", " ", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}]}], "}"}]}]], "Input", CellChangeTimes->{{3.83933879633805*^9, 3.839338803117584*^9}},ExpressionUUID->"32153864-4c57-4f1c-85aa-\ 114b8c13e766"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "1", "]"}], "/.", "subs"}]], "Input", CellChangeTimes->{{3.839338807812275*^9, 3.839338810505219*^9}},ExpressionUUID->"3186a80e-7f5a-4e21-bd37-\ 7d8b9854ac06"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"f1939ce6-9bc7-4693-8f1f-9eb682a18971"], Cell[TextData[{ "Uma forma alternativa de usar substitui\[CCedilla]\[OTilde]es envolve \ explicitamente a fun\[CCedilla]\[ATilde]o ", StyleBox[ButtonBox["ReplaceAll", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/ReplaceAll.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/ReplaceAll.html"], FontFamily->"Source 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"ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839332986787857*^9, 3.839333018185903*^9}, 3.839338661672798*^9, {3.8393573598984537`*^9, 3.839357363542678*^9}},ExpressionUUID->"872b1678-f1b2-4c79-8797-\ cdbfd7ca67ab"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"576ec092-35df-410b-a527-98b101a3dd1c"], Cell[CellGroupData[{ Cell["Introdu\[CCedilla]\[ATilde]o \[AGrave]s capacidades gr\[AAcute]ficas", \ "Section", CellChangeTimes->{{3.839333040214677*^9, 3.8393330462885437`*^9}},ExpressionUUID->"19228b1e-227d-4e69-8c93-\ 1f65f7f93b39"], Cell[TextData[{ "A produ\[CCedilla]\[ATilde]o de gr\[AAcute]ficos no Mathematica pode ser \ feita de forma direta atrav\[EAcute]s da fun\[CCedilla]\[ATilde]o ", StyleBox[ButtonBox["Plot", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Plot.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Plot.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], " (e suas variantes que exploraremos em aulas futuras):" }], "Text", CellChangeTimes->{{3.839333085394517*^9, 3.8393331163426123`*^9}, { 3.8704372181301947`*^9, 3.870437218136032*^9}},ExpressionUUID->"c335034a-647e-4975-9680-\ e3f78c0faef0"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"Pi", "*", "x"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839333159402782*^9, 3.8393331716942883`*^9}, 3.839333264451928*^9},ExpressionUUID->"0b2a2889-2447-4745-b565-\ 7bb0d53c2217"], Cell[TextData[{ "Note a sintaxe: o primeiro argumento de ", StyleBox[ButtonBox["Plot", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Plot.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Plot.html"], FontFamily->"Source Code Pro", FontWeight->"Regular"], " \[EAcute] a fun\[CCedilla]\[ATilde]o cujo gr\[AAcute]fico queremos \ produzir, e o segundo argumento (entre chaves) indica a vari\[AAcute]vel que \ servir\[AAcute] de abscissa, seu valor inicial e seu valor final no gr\ \[AAcute]fico." }], "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.839333199639122*^9, 3.839333264453705*^9}, { 3.870437229935413*^9, 3.870437229940609*^9}},ExpressionUUID->"c56b50cb-4bc5-44aa-a5da-\ 00f5cc835237"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"addca8bf-2489-4546-8035-6bc80dc4dcb0"], Cell["Um segundo exemplo, utilizando substitui\[CCedilla]\[OTilde]es:", "Text", CellChangeTimes->{{3.839333273518186*^9, 3.839333285735359*^9}},ExpressionUUID->"da6701ca-8b2f-4608-87b0-\ 302b902843df"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"f", "[", "x", "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"a", "\[Rule]", " ", "1"}], ",", RowBox[{"b", "\[Rule]", " ", "2"}], ",", RowBox[{"c", "\[Rule]", " ", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.839333127183731*^9, 3.839333143887081*^9}, { 3.83933329253157*^9, 3.8393332952106447`*^9}},ExpressionUUID->"0a0a5507-bc47-41c1-b8b1-\ 59c8c3ccc5d6"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"84e53bac-174e-4f58-ab72-ff54f61fd868"], Cell["\<\ E se quisermos mais de um gr\[AAcute]fico no mesmo conjunto de eixos?\ \>", "Text", CellChangeTimes->{{3.839333341818688*^9, 3.839333351751588*^9}},ExpressionUUID->"64b398cc-2e38-4769-83a5-\ e964f9fc977e"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", RowBox[{"\[Pi]", "*", "x"}], "]"}], ",", RowBox[{"Cos", "[", RowBox[{"\[Pi]", "*", "x"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393333572938623`*^9, 3.8393333786848097`*^9}, 3.83933351284588*^9},ExpressionUUID->"38b53edc-4daa-4da4-a48b-\ f9a39fe1a583"], Cell["Note que as fun\[CCedilla]\[OTilde]es a tra\[CCedilla]ar devem estar \ entre chaves. ", "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393333903964863`*^9, 3.839333443986271*^9}, 3.83933351284686*^9, 3.8393386374009953`*^9},ExpressionUUID->"db115c48-2815-490e-bb73-\ 10c7662d6943"], Cell["", "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393333903964863`*^9, 3.8393334447420053`*^9}, 3.839333512847888*^9},ExpressionUUID->"878884c2-7aaa-4974-bcd0-\ 03032cefcfca"], Cell["\<\ Em aulas futuras, vamos explorar op\[CCedilla]\[OTilde]es na linguagem \ Wolfram para dar uma apar\[EHat]ncia mais profissional aos gr\[AAcute]ficos e \ como tra\[CCedilla]ar outros tipos de gr\[AAcute]ficos.\ \>", "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8393333903964863`*^9, 3.8393335128491917`*^9}},ExpressionUUID->"40dd9a8c-13a6-4698-a8e6-\ 5151b2de75a7"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"32be91fb-777d-400b-86fa-9a049cede895"], Cell[CellGroupData[{ Cell["Para a pr\[OAcute]xima aula", "Section", CellChangeTimes->{{3.839333537446044*^9, 3.839333542350568*^9}},ExpressionUUID->"22ca6e40-5203-4405-ab21-\ c6777f1f153d"], Cell["\<\ A primeira lista de exerc\[IAcute]cios para nota est\[AAcute] \ dispon\[IAcute]vel na aba \[OpenCurlyDoubleQuote]Listas de exerc\[IAcute]cio\ \[CloseCurlyDoubleQuote] do E-disciplinas. A entrega deve ser feita at\ \[EAcute] as 23h55 do dia 5 de setembro.\ \>", "Item", CellChangeTimes->{{3.839333548032505*^9, 3.839333592379475*^9}, { 3.83933705919527*^9, 3.839337097534361*^9}, {3.87041987584597*^9, 3.870419876655802*^9}},ExpressionUUID->"60f6e4f6-2c4b-47f6-9054-\ 2ac5149001f0"] }, Open ]] }, Open ]] }, ScreenStyleEnvironment->"Slideshow Working", WindowSize->{808, 911}, WindowMargins->{{249, Automatic}, {Automatic, 0}}, TaggingRules->{ "PresenterSettings" -> { "ShowNavigationBar" -> False, "SlideBreakStyles" -> {"Title", "Chapter", "Section"}, "ShowSlideBreaks" -> True, "Theme" -> { "ThemeName" -> "Default", "FontSetName" -> "Default", "ColorSetName" -> "Default"}, "WindowSize" -> {808, 911}, "WindowMargins" -> {{249, 863}, {124, 0}}, "Dialogs" -> {}}}, CellContext->Notebook, FrontEndVersion->"12.2 for Mac OS X x86 (64-bit) (December 12, 2020)", StyleDefinitions->FrontEnd`FileName[{"PresenterTools"}, "Default.nb", CharacterEncoding -> "UTF-8"], 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