(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 25151, 797] NotebookOptionsPosition[ 21208, 677] NotebookOutlinePosition[ 21575, 693] CellTagsIndexPosition[ 21532, 690] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Introduction to Mathematica", "Title", CellChangeTimes->{{3.6660391054616375`*^9, 3.666039123583289*^9}}], Cell["Vito, March 2017", "Text", CellChangeTimes->{{3.6660391342891912`*^9, 3.6660391478536825`*^9}, { 3.6819866909501514`*^9, 3.6819866947018976`*^9}, {3.698487660116933*^9, 3.698487664544757*^9}}], Cell[CellGroupData[{ Cell["Uses (according S. Wolfram)", "Section", CellChangeTimes->{{3.666039229395526*^9, 3.666039230559862*^9}, { 3.6660392624523444`*^9, 3.6660392731425543`*^9}}], Cell["\<\ Numerical and symbolic calculator Visualization system Programming language Modeling and data analysis framework Environment for developing Interactive documents: animations in general and \ active calculations Accessing curated databases of everything\ \>", "Text", CellChangeTimes->{{3.6660392440705442`*^9, 3.666039421147496*^9}, 3.6819909634281273`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Class 1 - Basic calculations and plotting", "Section", CellChangeTimes->{{3.6819872339244375`*^9, 3.6819872360021133`*^9}, { 3.6821363940678835`*^9, 3.6821364094406724`*^9}}], Cell[CellGroupData[{ Cell["Arithmetics and common functions", "Subsubsection", CellChangeTimes->{{3.5854807042128243`*^9, 3.5854807143070984`*^9}, { 3.6819870598421955`*^9, 3.68198707185104*^9}}], Cell[BoxData[ RowBox[{"2", "+", "2"}]], "Input", CellChangeTimes->{{3.5854793014681425`*^9, 3.58547930307761*^9}}], Cell[BoxData[ RowBox[{"33", "/", "66"}]], "Input", CellChangeTimes->{{3.585479309874835*^9, 3.585479330282152*^9}}], Cell[BoxData[ RowBox[{"3", " ", "8"}]], "Input", CellChangeTimes->{{3.585479340345139*^9, 3.5854793437515907`*^9}}], Cell[BoxData[ RowBox[{"34", "-", "12"}]], "Input", CellChangeTimes->{{3.5854793495331106`*^9, 3.5854793519238873`*^9}}], Cell[BoxData[ RowBox[{"2", "^", "4"}]], "Input", CellChangeTimes->{{3.585479357783537*^9, 3.585479361955652*^9}}], Cell[BoxData[ RowBox[{"23", "^", "78"}]], "Input", CellChangeTimes->{{3.58547936453391*^9, 3.5854793666590185`*^9}}], Cell[BoxData[ RowBox[{"Sqrt", "[", "2", "]"}]], "Input", CellChangeTimes->{{3.585479374925063*^9, 3.585479386628793*^9}}], Cell[BoxData[ RowBox[{"Sqrt", "[", "2.", "]"}]], "Input", CellChangeTimes->{{3.585479389691451*^9, 3.5854793943791904`*^9}}], Cell[BoxData[ RowBox[{"%", "/", RowBox[{"Sqrt", "[", "8", "]"}]}]], "Input", CellChangeTimes->{{3.5854793981137323`*^9, 3.5854794125363426`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Sqrt", "[", "2", "]"}], "/", RowBox[{"Sqrt", "[", "8", "]"}]}]], "Input", CellChangeTimes->{{3.5854794185991545`*^9, 3.5854794301778755`*^9}}], Cell[BoxData[ RowBox[{"E", "/", "Pi"}]], "Input", CellChangeTimes->{{3.5854794433348*^9, 3.5854794636796217`*^9}}], Cell[BoxData[ RowBox[{"%", "//", "N"}]], "Input", CellChangeTimes->{{3.5854794687111015`*^9, 3.5854794738051414`*^9}}], Cell[BoxData[ RowBox[{"E", "^", RowBox[{"(", RowBox[{"I", " ", "Pi"}], ")"}]}]], "Input", CellChangeTimes->{{3.5854794800554624`*^9, 3.5854794896184225`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"E", "^", "I"}], " ", "Pi"}]], "Input", CellChangeTimes->{{3.5854795044316845`*^9, 3.5854795116195817`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Exp", "[", "3", "]"}], "//", "N"}]], "Input", CellChangeTimes->{{3.5854795415429635`*^9, 3.585479575263444*^9}}], Cell["\<\ %, %%, %%%, ... identify the last result, next to the last, two before the \ last, ... . %n identifies the result shown as Out[n]. Out[n] and In[n] are kept in memory even if you delete the line - you can get them back just by typing In[number of interest] or Out[number of \ interest]\ \>", "Text", CellChangeTimes->{{3.585482725629053*^9, 3.585482809992757*^9}, { 3.601997462140052*^9, 3.6019974622650623`*^9}, {3.681987105109064*^9, 3.681987111960533*^9}, {3.681987348252921*^9, 3.681987439602057*^9}, { 3.681987608852069*^9, 3.6819876528682566`*^9}, {3.6819881141242228`*^9, 3.6819882373399*^9}, {3.6819887551523046`*^9, 3.6819887990104723`*^9}, { 3.6820864416035604`*^9, 3.6820864444041395`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Defining variables", "Subsubsection", CellChangeTimes->{{3.58547956202839*^9, 3.585479563544118*^9}, { 3.5854807275733814`*^9, 3.58548073998027*^9}, {3.6819882486987615`*^9, 3.6819882549191523`*^9}}], Cell[TextData[StyleBox["Never start a variable name with a capital letter, \ specially a single letter", "Text", FontSize->18]], "Text", CellChangeTimes->{{3.662101424288385*^9, 3.66210147881507*^9}, { 3.681988257552291*^9, 3.681988295783367*^9}}], Cell[BoxData[ RowBox[{"x", "=", "12"}]], "Input", CellChangeTimes->{{3.5854800365608535`*^9, 3.585480048655224*^9}}], Cell[BoxData[ RowBox[{"Sqrt", "[", "x", "]"}]], "Input", CellChangeTimes->{{3.5854800612183676`*^9, 3.58548006943754*^9}}], Cell[BoxData[ RowBox[{"%", "//", "N"}]], "Input", CellChangeTimes->{{3.585480080047431*^9, 3.5854800916574316`*^9}}], Cell[BoxData[ RowBox[{"y", "=", RowBox[{"2", "x"}]}]], "Input", CellChangeTimes->{{3.5854801230965137`*^9, 3.5854801333626957`*^9}}], Cell[BoxData[ RowBox[{"y", "=", RowBox[{"2", "z"}]}]], "Input", CellChangeTimes->{{3.585480149269732*^9, 3.5854801539262457`*^9}}], Cell[BoxData[ RowBox[{"alfa", "=", RowBox[{"x", "+", "y"}]}]], "Input", CellChangeTimes->{{3.585480158598336*^9, 3.585480162457909*^9}, { 3.6819886950474005`*^9, 3.6819886996119747`*^9}}], Cell[BoxData[ RowBox[{"anyLongVariableName", "=", RowBox[{"y", "+", "z"}]}]], "Input", CellChangeTimes->{{3.585480171911529*^9, 3.5854801746460643`*^9}, { 3.6819887126820884`*^9, 3.6819887220684853`*^9}}], Cell[BoxData[ RowBox[{"y", "+", "z"}]], "Input", CellChangeTimes->{{3.5854801860841217`*^9, 3.5854801896468344`*^9}}], Cell[BoxData[ RowBox[{"f", "=", RowBox[{ RowBox[{"3", RowBox[{"x", "^", "2"}]}], " ", "+", " ", RowBox[{"8", "x"}], " ", "-", "7"}]}]], "Input", CellChangeTimes->{{3.5854807462305827`*^9, 3.585480757543672*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "x", "]"}]], "Input", CellChangeTimes->{{3.5854807634345903`*^9, 3.5854807657941136`*^9}}], Cell[BoxData[ RowBox[{"In", "[", RowBox[{"-", "2"}], "]"}]], "Input", CellChangeTimes->{{3.681988845376768*^9, 3.681988847777811*^9}}], Cell[BoxData[ RowBox[{"f", "=", RowBox[{ RowBox[{"3", RowBox[{"x", "^", "2"}]}], " ", "+", " ", RowBox[{"8", "x"}], " ", "-", "7"}]}]], "Input"], Cell["\<\ All Mathematica functions and internal variables have names starting with a \ capital letter or $. This is why we, users, use names where the first letter is not capital. There are priority rules for homographs, but they are complicated.\ \>", "Text", CellChangeTimes->{{3.5854828511198654`*^9, 3.585483031941638*^9}, { 3.681988433618002*^9, 3.6819885366733956`*^9}, {3.6819886290939326`*^9, 3.68198866819151*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Symbolic operations", "Subsubsection", CellChangeTimes->{{3.585481077169448*^9, 3.5854810901076326`*^9}, { 3.5854811318285227`*^9, 3.5854811336410975`*^9}, {3.681988740364397*^9, 3.6819887488278913`*^9}}], Cell[BoxData[ RowBox[{"FullSimplify", "[", "f", "]"}]], "Input", CellChangeTimes->{{3.5854808335475616`*^9, 3.5854808915505414`*^9}}], Cell[BoxData[ RowBox[{"Roots", "[", RowBox[{ RowBox[{"f", "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.585480895878895*^9, 3.585480923270926*^9}}], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{"f", ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.5854811368756256`*^9, 3.5854811433447185`*^9}}], Cell[BoxData[ RowBox[{"D", "[", RowBox[{"%", ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.5854811499700756`*^9, 3.5854811586580253`*^9}}], Cell[BoxData[ RowBox[{"Sum", "[", RowBox[{"f", ",", RowBox[{"{", RowBox[{"x", ",", "1", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5854811769870615`*^9, 3.585481191456563*^9}}], Cell[BoxData["f"], "Input", CellChangeTimes->{3.5854812247395196`*^9}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{"f", ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.585481234911909*^9, 3.5854812476156993`*^9}}], Cell[BoxData[ RowBox[{"Sum", "[", RowBox[{ RowBox[{"x", "^", "i"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5854812743201895`*^9, 3.5854813043529987`*^9}}], Cell[BoxData[ RowBox[{"Sum", "[", RowBox[{ RowBox[{"x", "^", "i"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "Infinity"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.585481327854206*^9, 3.5854813314481125`*^9}}], Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"x", " ", RowBox[{"Sin", "[", "x", "]"}], RowBox[{"Exp", "[", "x", "]"}]}], "\[Equal]", "3"}], ",", RowBox[{"{", RowBox[{"x", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.585481375278516*^9, 3.5854814819402385`*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"x", " ", RowBox[{"Sin", "[", "x", "]"}], RowBox[{"Exp", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "5"}], ",", "0"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5854814964878397`*^9, 3.585481520051567*^9}}], Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"x", " ", RowBox[{"Sin", "[", "x", "]"}], RowBox[{"Exp", "[", "x", "]"}]}], "\[Equal]", "0"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "3"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5854815661633387`*^9, 3.585481576445059*^9}}], Cell[BoxData[ RowBox[{"Reduce", "[", RowBox[{ RowBox[{ RowBox[{"x", " ", RowBox[{"Sin", "[", "x", "]"}], RowBox[{"Exp", "[", "x", "]"}]}], "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.5854815952897987`*^9, 3.5854816180565715`*^9}}], Cell[BoxData[ RowBox[{"Reduce", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"3", RowBox[{"x", "^", "2"}]}], "+", RowBox[{"8", "x"}], "-", "5"}], ">", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.5854816972012825`*^9, 3.5854817477976017`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Lists", "Subsubsection", CellChangeTimes->{{3.5854817885497203`*^9, 3.5854817983002195`*^9}, 3.6819889468882422`*^9}], Cell[BoxData[ RowBox[{"u", "=", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}]}]], "Input", CellChangeTimes->{{3.5854818013316083`*^9, 3.585481813566631*^9}}], Cell[BoxData[ RowBox[{"s", "=", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}]}]], "Input", CellChangeTimes->{{3.5854818172230387`*^9, 3.5854818276454487`*^9}}], Cell[BoxData[ RowBox[{"u", " ", "s"}]], "Input", CellChangeTimes->{{3.5854818311456285`*^9, 3.58548183269261*^9}}], Cell[BoxData[ RowBox[{"u", "+", "s"}]], "Input", CellChangeTimes->{{3.5854818374272003`*^9, 3.5854818385522842`*^9}}], Cell[BoxData[ RowBox[{"u", "/", "s"}]], "Input", CellChangeTimes->{{3.5854818423805795`*^9, 3.585481844958867*^9}}], Cell[BoxData[ RowBox[{"u", "^", "2"}]], "Input", CellChangeTimes->{{3.585481849099675*^9, 3.5854818504122443`*^9}}], Cell[BoxData[ RowBox[{"u", ".", "s"}]], "Input", CellChangeTimes->{{3.5854818559906826`*^9, 3.5854818591314487`*^9}}], Cell[BoxData[ RowBox[{"r", "=", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]], "Input", CellChangeTimes->{{3.5854818673974886`*^9, 3.585481881476362*^9}, { 3.585481918931408*^9, 3.5854819556989193`*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "y", "]"}]], "Input", CellChangeTimes->{{3.585481961636699*^9, 3.585481965355666*^9}}], Cell[BoxData[ RowBox[{"r", "=", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{"Cross", "[", RowBox[{"s", ",", "r"}], "]"}]], "Input", CellChangeTimes->{{3.5854819762311983`*^9, 3.585481986216113*^9}}], Cell[BoxData[ RowBox[{"a", "=", RowBox[{"{", RowBox[{"ax", ",", "ay", ",", "az"}], "}"}]}]], "Input", CellChangeTimes->{{3.585481996935388*^9, 3.585482019155301*^9}}], Cell[BoxData[ RowBox[{"b", "=", RowBox[{"{", RowBox[{"bx", ",", "by", ",", "bz"}], "}"}]}]], "Input", CellChangeTimes->{{3.585482024514926*^9, 3.5854820309996605`*^9}}], Cell[BoxData[ RowBox[{"a", ".", "b"}]], "Input", CellChangeTimes->{{3.5854820357342787`*^9, 3.585482036812461*^9}}], Cell[BoxData[ RowBox[{"Cross", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellChangeTimes->{{3.585482039703205*^9, 3.5854820440159564`*^9}}], Cell[BoxData[ RowBox[{"a", " ", "b"}]], "Input", CellChangeTimes->{{3.585482135395614*^9, 3.5854821363800406`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Plot", "Subsection"]], "Subsubsection", CellChangeTimes->{{3.6819891517014112`*^9, 3.6819891530996475`*^9}, { 3.681989207685025*^9, 3.681989208970394*^9}}], Cell[BoxData[ RowBox[{"sin", "=", RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"5", "Pi"}]}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6819892182568903`*^9, 3.6819892350391226`*^9}, { 3.68198927211191*^9, 3.6819892733497524`*^9}}], Cell[BoxData[ RowBox[{"tan", "=", RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"Tan", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"5", "Pi"}]}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6819892474045277`*^9, 3.6819892478421745`*^9}, { 3.681991012703698*^9, 3.6819910140511723`*^9}}], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"sin", ",", "tan"}], "]"}]], "Input", CellChangeTimes->{{3.681989293862477*^9, 3.681989301516598*^9}, { 3.681991022909258*^9, 3.681991023241135*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"5", "Pi"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.681989415833213*^9, 3.681989421868989*^9}, { 3.6819910281972494`*^9, 3.6819910287825174`*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"5", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Blue"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.6819894389082146`*^9, 3.6819894484114275`*^9}, 3.6819910404214263`*^9}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Blue"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "6"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.68198947523874*^9, 3.6819895068515034`*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Blue"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "6"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.681989606152384*^9, 3.681989619787644*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Blue"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "6"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\\""}], "}"}]}]}], " ", "]"}]], "Input", CellChangeTimes->{{3.6819896393360696`*^9, 3.681989672247565*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"2.5", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Blue"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "6"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotLegends", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], " ", "]"}]], "Input", CellChangeTimes->{{3.681989693214761*^9, 3.6819897097341566`*^9}, { 3.681989769689475*^9, 3.6819897979837112`*^9}, {3.6820816913558464`*^9, 3.682081694809567*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"Tan", "[", "x", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"2.4", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Blue"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "6"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotLegends", "\[Rule]", "Automatic"}]}], " ", "]"}]], "Input", CellChangeTimes->{{3.681989754865531*^9, 3.6819897578670206`*^9}, { 3.681989806901615*^9, 3.681989811317479*^9}, {3.6820817309813585`*^9, 3.682081732827077*^9}}], Cell[BoxData["f"], "Input", CellChangeTimes->{{3.681989879720001*^9, 3.6819898814040747`*^9}, 3.6819899126993484`*^9}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{"f", ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6819899166206226`*^9, 3.68198993798011*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{"f", ",", RowBox[{"4", "x"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.681989948699255*^9, 3.681989969552937*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Exerc\[IAcute]cio com Plot[ ]", "Section", CellChangeTimes->{{3.6990864245399427`*^9, 3.6990864333844175`*^9}}], Cell["\<\ 1) Um exerc\[IAcute]cio para resolver graficamente Os polin\[OHat]mios : p1 = 4 x^3 - 8 x^2 - 15 x e p2 = 4 x^6 - 16 x^5 + 4 x^4 + 44 x^3 - 24 x^2 - 47 x s\[ATilde]o praticamente coincidentes em duas regi\[OTilde]es contidas no \ intervalo - 2 < x < 3. Encontre essas regi\[OTilde]es a partir dos gr\[AAcute]ficos dos dois polin\ \[OHat]mios. Dica: Voc\[EHat] n\[ATilde]o precisa digitar os polin\[OHat]mios - copie das \ linhas acima com Ctrl-v e devolva com Ctrl-v no lugar desejado. \ \>", "Text", CellChangeTimes->{{3.699086439465071*^9, 3.6990865693831625`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Exercise with Plot[ ]", "Section", CellChangeTimes->{{3.6658670545297694`*^9, 3.665867066976886*^9}, { 3.666437146206273*^9, 3.6664371498744273`*^9}, {3.681991301183191*^9, 3.681991309493249*^9}}], Cell["\<\ The polynomials: p1 = 4 x^3 - 8 x^2 - 15 x and p2 = 4 x^6 - 16 x^5 + 4 x^4 + 44 x^3 - 24 x^2 - 47 x practically coincide in two regions inside the interval [-2, 3]. Find these regions from the graphics of the polynomials. Hint: you do not need to type the polynomials - just cut and paste from above.\ \>", "Text", CellChangeTimes->{{3.681991114419036*^9, 3.6819912915963516`*^9}, { 3.6819914846150093`*^9, 3.681991504392989*^9}}] }, Open ]] }, Open ]] }, WindowSize->{1271, 651}, WindowMargins->{{Automatic, 28}, {Automatic, 0}}, Magnification->1.5, FrontEndVersion->"11.0 for Microsoft Windows (64-bit) (September 21, 2016)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 112, 1, 150, "Title"], Cell[694, 25, 204, 3, 45, "Text"], Cell[CellGroupData[{ Cell[923, 32, 165, 2, 106, "Section"], Cell[1091, 36, 372, 10, 188, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[1500, 51, 183, 2, 106, "Section"], Cell[CellGroupData[{ Cell[1708, 57, 177, 2, 58, "Subsubsection"], Cell[1888, 61, 116, 2, 45, "Input"], Cell[2007, 65, 117, 2, 45, "Input"], Cell[2127, 69, 117, 2, 45, "Input"], Cell[2247, 73, 121, 2, 45, "Input"], Cell[2371, 77, 115, 2, 45, "Input"], Cell[2489, 81, 118, 2, 45, "Input"], Cell[2610, 85, 123, 2, 45, "Input"], Cell[2736, 89, 126, 2, 45, "Input"], Cell[2865, 93, 150, 3, 45, "Input"], Cell[3018, 98, 181, 4, 45, "Input"], Cell[3202, 104, 116, 2, 45, "Input"], Cell[3321, 108, 120, 2, 45, "Input"], Cell[3444, 112, 167, 4, 45, "Input"], Cell[3614, 118, 143, 3, 45, "Input"], Cell[3760, 123, 148, 3, 45, "Input"], Cell[3911, 128, 727, 13, 131, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[4675, 146, 211, 3, 58, "Subsubsection"], Cell[4889, 151, 251, 4, 53, "Text"], Cell[5143, 157, 118, 2, 45, "Input"], Cell[5264, 161, 124, 2, 45, "Input"], Cell[5391, 165, 118, 2, 45, "Input"], Cell[5512, 169, 137, 3, 45, "Input"], Cell[5652, 174, 135, 3, 45, "Input"], Cell[5790, 179, 194, 4, 45, "Input"], Cell[5987, 185, 211, 4, 45, "Input"], Cell[6201, 191, 119, 2, 45, "Input"], Cell[6323, 195, 228, 6, 45, "Input"], Cell[6554, 203, 128, 2, 45, "Input"], Cell[6685, 207, 139, 3, 45, "Input"], Cell[6827, 212, 160, 5, 45, "Input"], Cell[6990, 219, 430, 8, 102, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[7457, 232, 216, 3, 58, "Subsubsection"], Cell[7676, 237, 135, 2, 45, "Input"], Cell[7814, 241, 178, 4, 45, "Input"], Cell[7995, 247, 155, 3, 45, "Input"], Cell[8153, 252, 147, 3, 45, "Input"], Cell[8303, 257, 206, 5, 45, "Input"], Cell[8512, 264, 71, 1, 45, "Input"], Cell[8586, 267, 207, 5, 45, "Input"], Cell[8796, 274, 232, 6, 45, "Input"], Cell[9031, 282, 237, 6, 45, "Input"], Cell[9271, 290, 328, 9, 45, "Input"], Cell[9602, 301, 321, 9, 45, "Input"], Cell[9926, 312, 349, 10, 45, "Input"], Cell[10278, 324, 282, 8, 45, "Input"], Cell[10563, 334, 280, 8, 45, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[10880, 347, 128, 2, 58, "Subsubsection"], Cell[11011, 351, 174, 4, 45, "Input"], Cell[11188, 357, 176, 4, 45, "Input"], Cell[11367, 363, 116, 2, 45, "Input"], Cell[11486, 367, 119, 2, 45, "Input"], Cell[11608, 371, 117, 2, 45, "Input"], Cell[11728, 375, 117, 2, 45, "Input"], Cell[11848, 379, 119, 2, 45, "Input"], Cell[11970, 383, 225, 5, 45, "Input"], Cell[12198, 390, 124, 2, 45, "Input"], Cell[12325, 394, 106, 3, 45, "Input"], Cell[12434, 399, 149, 3, 45, "Input"], Cell[12586, 404, 175, 4, 45, "Input"], Cell[12764, 410, 177, 4, 45, "Input"], Cell[12944, 416, 117, 2, 45, "Input"], Cell[13064, 420, 149, 3, 45, "Input"], Cell[13216, 425, 117, 2, 45, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[13370, 432, 182, 2, 60, "Subsubsection"], Cell[13555, 436, 347, 9, 45, "Input"], Cell[13905, 447, 348, 9, 45, "Input"], Cell[14256, 458, 199, 4, 45, "Input"], Cell[14458, 464, 400, 11, 45, "Input"], Cell[14861, 477, 483, 14, 45, "Input"], Cell[15347, 493, 573, 17, 45, "Input"], Cell[15923, 512, 671, 20, 75, "Input"], Cell[16597, 534, 693, 20, 75, "Input"], Cell[17293, 556, 926, 26, 75, "Input"], Cell[18222, 584, 853, 23, 75, "Input"], Cell[19078, 609, 123, 2, 45, "Input"], Cell[19204, 613, 227, 6, 45, "Input"], Cell[19434, 621, 296, 9, 45, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[19779, 636, 118, 1, 106, "Section"], Cell[19900, 639, 583, 14, 302, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[20520, 658, 208, 3, 106, "Section"], Cell[20731, 663, 449, 10, 216, "Text"] }, Open ]] }, Open ]] } ] *)