(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 50191, 1961] NotebookOptionsPosition[ 40612, 1703] NotebookOutlinePosition[ 41129, 1723] CellTagsIndexPosition[ 41086, 1720] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["Ficheiros", FontWeight->"Bold"], " *.nb (", StyleBox["Mathematica", FontSlant->"Italic"], " notebook):\nConjunto de c\[EAcute]lulas de v\[AAcute]rios tipos" }], "Text", FontSize->14], Cell[TextData[{ StyleBox["Tipos de c\[EAcute]lulas", FontWeight->"Bold"], ":\n* ", StyleBox["input", FontWeight->"Bold"], "\n* ", StyleBox["output", FontWeight->"Bold"], "\n* gr\[AAcute]ficos\n* texto, etc." }], "Text", FontSize->14], Cell[TextData[{ StyleBox["C\[EAcute]lulas de input", FontWeight->"Bold"], ": podem ser avaliadas\n", StyleBox["C\[EAcute]lulas de output", FontWeight->"Bold"], ": normalmente s\[ATilde]o produzidas pela avalia\[CCedilla]\[ATilde]o de c\ \[EAcute]lulas de input" }], "Text", FontSize->14], Cell[TextData[{ "Quando se come\[CCedilla]a a escrever, o ", StyleBox["Mathematica", FontSlant->"Italic"], " assume autom\[AAcute]ticamente que se vai criar um ", StyleBox["input", FontWeight->"Bold"], " e cria uma c\[EAcute]lula desse tipo." }], "Text", FontSize->14], Cell[TextData[{ "Para avaliar uma c\[EAcute]lula de input, carregar ", StyleBox["Shift+Enter", FontWeight->"Bold"], " com o cursor na c\[EAcute]lula ou com a c\[EAcute]lula selecionada.\n\ \[CapitalEAcute] poss\[IAcute]vel seleccionar mais do que uma c\[EAcute]lula \ simult\[AHat]neamente." }], "Text", FontSize->14], Cell["\<\ Exemplo de uma c\[EAcute]lula de input que ao ser avaliada produz uma c\ \[EAcute]lula de output:\ \>", "Text", FontSize->14], Cell[BoxData[ RowBox[{"2", "+", "2"}]], "Input", FontSize->14], Cell["\<\ Exemplo de uma c\[EAcute]lula de input que ao ser avaliada cria uma \ c\[EAcute]lula de gr\[AAcute]ficos e uma c\[EAcute]lula de output\ \>", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Sin", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"-", "Pi"}], ",", "Pi"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell["\<\ O output assinalado por \".Graphics.\" cont\[EAcute]m a informa\[CCedilla]\ \[ATilde]o para desenhar o gr\[AAcute]fico tal como se v\[EHat] acima\ \>", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"Out", "[", "2", "]"}], "]"}]], "Input", FontSize->14], Cell[TextData[{ "As ", StyleBox["c\[EAcute]lulas de texto", FontWeight->"Bold"], " n\[ATilde]o s\[ATilde]o avaliadas mas s\[ATilde]o \[UAcute]teis para v\ \[AAcute]rios fins:\n* Produzir textos, relat\[OAcute]rios, etc, combinando \ elementos \"matem\[AAcute]ticos\" com explica\[CCedilla]\[OTilde]es, t\ \[IAcute]tulos, etc..\n* Introduzir coment\[AAcute]rios num ficheiro *.nb \ puramente matem\[AAcute]tico, para o tornar mais intelig\[IAcute]vel\nExemplo:" }], "Text", FontSize->14], Cell[CellGroupData[{ Cell["A sucess\[ATilde]o x(i+1)=f(x(i),a) converge para raiz de a:", "Text", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"f", "[", RowBox[{"x_", ",", "a_"}], "]"}], "=", RowBox[{ RowBox[{"(", RowBox[{"a", "+", RowBox[{"x", "^", "2"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", "x"}], ")"}]}]}], ";"}]], "Input", FontSize->14] }, Open ]], Cell[TextData[{ "C\[EAcute]lulas de texto s\[ATilde]o produzidas carregando ", StyleBox["Alt+7", FontWeight->"Bold"] }], "Text", FontSize->14], Cell[TextData[{ "O tipo de uma determinada c\[EAcute]lula pode ser modificado \ atrav\[EAcute]s do menu ", StyleBox["Format -> Style", FontWeight->"Bold"] }], "Text", FontSize->14], Cell["\<\ Cada tipo de c\[EAcute]lulas tem propriedades espec\[IAcute]ficas que podem \ ser alteradas\ \>", "Text", FontSize->14], Cell["\<\ As c\[EAcute]lulas podem ser apresentadas com diferentes aspectos que podem \ ser modificados atrav\[EAcute]s dos menus Cell->Default Input Format Type, Cell->Default Ouput Format Type, etc.\ \>", "Text", FontSize->14], Cell[TextData[{ "Eu prefiro as op\[CCedilla]\[OTilde]es\nDefault Input Format Type = \ StandardForm : d\[AAcute] um controlo exacto daquilo que se quer que o ", StyleBox["Mathematica", FontSlant->"Italic"], " fa\[CCedilla]a\nDefault Ouput Format Type = TraditionalForm : permite ler \ os outputs na nota\[CCedilla]\[ATilde]o matem\[AAcute]tica habitual" }], "Text", FontSize->14], Cell["Exemplo:", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "a", ",", "b"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell[TextData[{ StyleBox["HELP", FontWeight->"Bold"], " do ", StyleBox["Mathematica", FontSlant->"Italic"], ":\nPara aceder ao Help, carregar ", StyleBox["F1", FontWeight->"Bold"], "." }], "Text", FontSize->14], Cell[TextData[{ "O Help est\[AAcute] organizado em v\[AAcute]rias categorias. As mais \ importantes s\[ATilde]o:\n", StyleBox["Built-in functions", FontWeight->"Bold"], ": Explica o uso das fun\[CCedilla]\[OTilde]es nativas do ", StyleBox["Mathematica\n", FontSlant->"Italic"], StyleBox["The Mathematica Book", FontWeight->"Bold"], ": Manual em formato electr\[OAcute]nico." }], "Text", FontSize->14], Cell[TextData[{ "Para aceder directamente \[AGrave] informa\[CCedilla]\[ATilde]o relativa a \ qualquer objecto presente no notebook basta seleccionar o objecto ", StyleBox["antes", FontWeight->"Bold"], " de carregar F1" }], "Text", FontSize->14], Cell["\<\ Exemplo: ao escrever um input com a fun\[CCedilla]\[ATilde]o Sum surge uma d\ \[UAcute]vida sobre a sua sintaxe\ \>", "Text", FontSize->14], Cell[TextData[{ "Exemplo: o ", StyleBox["Mathematica", FontSlant->"Italic"], " devolve um output cujo significado n\[ATilde]o entendemos:" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Exp", "[", RowBox[{"-", RowBox[{"x", "^", "2"}]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "a", ",", "b"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell[TextData[{ "Capacidades do ", StyleBox["Mathematica", FontSlant->"Italic"], ":\n* C\[AAcute]lculo num\[EAcute]rico\n* C\[AAcute]lculo simb\[OAcute]lico\n\ * Gr\[AAcute]ficos, sons, etc" }], "Text", FontSize->14], Cell["C\[CapitalAAcute]LCULO SIMB\[CapitalOAcute]LICO:", "Text", FontSize->14, FontWeight->"Bold"], Cell[TextData[{ "\[CapitalEAcute] baseado na manipula\[CCedilla]\[ATilde]o de ", StyleBox["s\[IAcute]mbolos", FontSlant->"Italic"], " segundo regras bem definidas.\n", "Exemplo:" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"6", "+", "x", "-", RowBox[{"2", "x"}], "+", "1", "+", "y"}]], "Input", FontSize->14], Cell[TextData[{ "Os s\[IAcute]mbolos s\[ATilde]o caracterizados por um ", StyleBox["nome", FontWeight->"Bold"], " (sequ\[EHat]ncia de caracteres)" }], "Text", FontSize->14], Cell[TextData[{ "Existem ", StyleBox["conven\[CCedilla]\[OTilde]es", FontWeight->"Bold"], " na atribui\[CCedilla]\[ATilde]o de nomes a s\[IAcute]mbolos. \nEstas \ conven\[CCedilla]\[OTilde]es n\[ATilde]o s\[ATilde]o obrigat\[OAcute]rias \ (i.e., o seu desrespeito n\[ATilde]o provoca autom\[AAcute]ticamente uma \ situa\[CCedilla]\[ATilde]o de erro) mas \[EAcute] mais f\[AAcute]cil escrever \ ficheiros sem erros respeitando as conven\[CCedilla]\[OTilde]es." }], "Text", FontSize->14], Cell[TextData[{ "Principais conven\[CCedilla]\[OTilde]es:\n* ", StyleBox["s\[IAcute]mbolos definidos pelo utilizador", FontWeight->"Bold"], " come\[CCedilla]am por letra min\[UAcute]scula\n* ", StyleBox["s\[IAcute]mbolos pr\[EAcute]definidos", FontWeight->"Bold"], " come\[CCedilla]am por letra mai\[UAcute]scula\n*", StyleBox[" vari\[AAcute]veis globais", FontWeight->"Bold"], " ou de sistema come\[CCedilla]am por ", StyleBox["$", FontWeight->"Bold"] }], "Text", FontSize->14], Cell["Exemplos:", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Sin", "[", "x", "]"}]], "Input", FontSize->14], Cell[BoxData["$RecursionLimit"], "Input", FontSize->14], Cell[TextData[{ "C\[AAcute]lculos simb\[OAcute]licos s\[ATilde]o sempre ", StyleBox["exactos", FontWeight->"Bold"], ":" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"2", "/", "6"}]], "Input", FontSize->14], Cell[TextData[{ "Para obter um valor num\[EAcute]rico (aproximado ) de 1/3 \[EAcute] necess\ \[AAcute]rio proceder \[AGrave] sua ", StyleBox["avalia\[CCedilla]\[ATilde]o num\[EAcute]rica", FontWeight->"Bold"] }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"%", " ", "//", "N"}]], "Input", FontSize->14], Cell[TextData[{ "S\[IAcute]mbolos podem ser ", StyleBox["substitu\[IAcute]dos", FontWeight->"Bold"], " por valores concretos ou por outros s\[IAcute]mbolos\nExemplos:" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x", "*", "y"}], "+", RowBox[{"y", "^", "2"}]}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x", "*", "y"}], "+", RowBox[{"y", "^", "2"}]}], "/.", RowBox[{"x", "\[Rule]", "1"}]}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x", "*", "y"}], "+", RowBox[{"y", "^", "2"}]}], "/.", RowBox[{"x", "\[Rule]", "y"}]}]], "Input", FontSize->14], Cell[TextData[{ "Aos s\[IAcute]mbolos podem ser ", StyleBox["atribu\[IAcute]dos", FontWeight->"Bold"], " valores\nSe um s\[IAcute]mbolo tem um valor atribu\[IAcute]do, ele ser\ \[AAcute] substituido pelo seu valor em todos os c\[AAcute]lculos simb\ \[OAcute]licos\no valor atribu\[IAcute]do a um s\[IAcute]mbolo pode ser outro \ s\[IAcute]mbolo ou uma express\[ATilde]o\nExemplos:" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"x", "=", "2"}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x", "*", "y"}], "+", RowBox[{"y", "^", "2"}]}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{"x", "=", RowBox[{"z", "+", "1"}]}]], "Input", FontSize->14], Cell[BoxData[ 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Exemplo:\ \>", "Text", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", "x", "]"}], ";", RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x", "*", "y"}], "+", RowBox[{"y", "^", "2"}]}]}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{"x", "=."}], ";", RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x", "*", "y"}], "+", RowBox[{"y", "^", "2"}]}]}]], "Input", FontSize->14], Cell[TextData[{ "Quando se avalia uma c\[EAcute]lula que cont\[EAcute]m um s\[IAcute]mbolo \ at\[EAcute] a\[IAcute] inexistente, o ", StyleBox["Mathematica", FontSlant->"Italic"], " cria autom\[AAcute]ticamente o s\[IAcute]mbolo indicado, mesmo que n\ \[ATilde]o lhe seja atribu\[IAcute]do nenhum valor.\nExemplo:" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"x", "+", "1"}]], "Input", FontSize->14], Cell["\<\ A fun\[CCedilla]\[ATilde]o Clear ou =. n\[ATilde]o destr\[OAcute]i os s\ \[IAcute]mbolos (apenas destr\[OAcute]i as atribui\[CCedilla]\[OTilde]es que \ lhes foram feitas). Para destruir um s\[IAcute]mbolo \[EAcute] \ necess\[AAcute]rio usar Remove[symbol]\ \>", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Remove", "[", "x", "]"}]], "Input", FontSize->14], Cell[TextData[{ "O ", StyleBox["Mathematica", FontSlant->"Italic"], " disp\[OTilde]e de v\[AAcute]rias fun\[CCedilla]\[OTilde]es para ", StyleBox["manipular express\[OTilde]es simb\[OAcute]licas", FontWeight->"Bold"], "\nExemplos" }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"2", "x"}], "+", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "^", "2"}]}], ")"}]}], "]"}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{"Expand", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "^", "3"}], RowBox[{ RowBox[{"(", RowBox[{"x", "+", "2"}], ")"}], "^", "2"}]}], "]"}]], "Input", FontSize->14], Cell[TextData[{ StyleBox["Para outras fun\[CCedilla]\[OTilde]es que manipulam express\ \[OTilde]es simb\[OAcute]licas, ver no Help (Built-in Functions) \n", FontSize->14], StyleBox["Algebraic Computation > Formula Manipulation", FontSize->14, FontWeight->"Bold"] }], "Text", FontSize->14], Cell["\<\ H\[AAcute] s\[IAcute]mbolos pr\[EAcute]definidos que t\[EHat]m \ atribu\[IAcute]dos os valores de certas constantes importantes\ \>", "Text", FontSize->14], Cell[BoxData["E"], "Input", FontSize->14], Cell[BoxData["Pi"], "Input", FontSize->14], Cell[BoxData["I"], "Input", FontSize->14], Cell[BoxData["Infinity"], "Input", FontSize->14], Cell[TextData[{ "Al\[EAcute]m das fun\[CCedilla]\[OTilde]es alg\[EAcute]bricas (+, -, *, /), \ o ", StyleBox["Mathematica", FontSlant->"Italic"], " inclui v\[AAcute]rias fun\[CCedilla]\[OTilde]es matem\[AAcute]ticas pr\ \[EAcute]definidas que podem ser usadas tanto em c\[AAcute]lculo \ num\[EAcute]rico como em c\[AAcute]lculo simb\[OAcute]lico:" }], "Text", FontSize->14], Cell["Sqrt[x] : Ra\[IAcute]z quadrada", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Sqrt", "[", "4", "]"}]], "Input", FontSize->14], Cell["Exp[x] : Exponencial", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Exp", "[", "x", "]"}]], "Input", FontSize->14], Cell["Log[x] : Logaritmo natural", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Log", "[", "E", "]"}]], "Input", FontSize->14], Cell["Log[b,x]:Logaritmo de x na base b", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Log", "[", RowBox[{"2", ",", "8"}], "]"}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{"Log", "[", RowBox[{"2", ",", "9"}], "]"}]], "Input", FontSize->14], Cell["Sin[x]; Cos[x], Tan[x]: fun\[CCedilla]\[OTilde]es \ trigonom\[EAcute]tricas", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Sin", "[", "Pi", "]"}]], "Input", FontSize->14], Cell["\<\ ArcSin[x], ArcCos[x], ArcTan[x]: fun\[CCedilla]\[OTilde]es \ trigonom\[EAcute]tricas inversas\ \>", "Text", FontSize->14], Cell[BoxData[ RowBox[{"ArcSin", "[", "1", "]"}]], "Input", FontSize->14], Cell["n! : factorial", "Text", FontSize->14], Cell[BoxData[ RowBox[{"5", "!"}]], "Input", FontSize->14], Cell[TextData[StyleBox["OPERA\[CapitalCCedilla]\[CapitalOTilde]ES MATEM\ \[CapitalAAcute]TICAS EM CALCULO SIMB\[CapitalOAcute]LICO", FontWeight->"Bold"]], "Text", FontSize->14], Cell[TextData[StyleBox["Deriva\[CCedilla]\[ATilde]o", FontWeight->"Bold"]], "Text", FontSize->14], Cell["Derivadas parciais:", "Text", FontSize->14], Cell[BoxData[ RowBox[{"D", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", RowBox[{"Log", "[", RowBox[{"x", "+", "y"}], "]"}]}], ",", "x"}], "]"}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{"D", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", RowBox[{"Log", "[", RowBox[{"x", "+", "y"}], "]"}]}], ",", "y"}], "]"}]], "Input", FontSize->14], Cell["Derivadas parciais de ordem superior", "Text", FontSize->14], Cell[BoxData[ RowBox[{"D", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", RowBox[{"Log", "[", RowBox[{"x", "+", "y"}], "]"}]}], ",", "x", ",", "y"}], "]"}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{"D", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", RowBox[{"Log", "[", RowBox[{"x", "+", "y"}], "]"}]}], ",", "x", ",", "y", ",", "x", ",", "x"}], "]"}]], "Input", FontSize->14], Cell[TextData[StyleBox["Integra\[CCedilla]\[ATilde]o e primitiva\[CCedilla]\ \[ATilde]o", FontWeight->"Bold"]], "Text", FontSize->14], Cell["Primitiva\[CCedilla]\[ATilde]o", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], RowBox[{"Sin", "[", "y", "]"}]}], ",", "x"}], "]"}]], "Input", FontSize->14], Cell["Integra\[CCedilla]\[ATilde]o", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], RowBox[{"Sin", "[", "y", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "a", ",", "b"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell[TextData[{ "O ", StyleBox["Mathematica", FontSlant->"Italic"], " consegue calcular integrais com alguma complexidade ..." }], "Text", FontSize->14], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Log", "[", "t", "]"}], "^", "2"}], RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"t", "^", "2"}]}], ")"}], "/", "t"}]}], ",", RowBox[{"{", RowBox[{"t", ",", "1", ",", "x"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell["... Mas n\[ATilde]o todos", "Text", FontSize->14], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"Sin", "[", "x", "]"}], "]"}], ",", "x"}], "]"}]], "Input", FontSize->14], Cell[TextData[StyleBox["Somat\[OAcute]rios", FontWeight->"Bold"]], "Text", FontSize->14], Cell[BoxData[ RowBox[{"Sum", "[", RowBox[{ RowBox[{"x", "+", "i"}], ",", RowBox[{"{", RowBox[{"i", ",", "5"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell[TextData[StyleBox["Produtos", FontWeight->"Bold"]], "Text", FontSize->14], Cell[BoxData[ RowBox[{"Product", "[", RowBox[{ RowBox[{"(", RowBox[{"x", "+", "i"}], ")"}], ",", RowBox[{"{", RowBox[{"i", ",", "4"}], "}"}]}], "]"}]], "Input", FontSize->14], Cell[TextData[StyleBox["RELA\[CapitalCCedilla]\[CapitalOTilde]ES ", FontWeight->"Bold"]], "Text", FontSize->14], Cell["x==y: igual", "Text", FontSize->14], Cell[BoxData[ RowBox[{"1", "\[Equal]", "1"}]], "Input", FontSize->14], Cell[BoxData[ RowBox[{"1", "\[Equal]", "2"}]], "Input", FontSize->14], 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