(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 22223, 766] NotebookOptionsPosition[ 18036, 611] NotebookOutlinePosition[ 18695, 636] CellTagsIndexPosition[ 18617, 631] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " Review" }], "Title", CellChangeTimes->{{3.559395254922027*^9, 3.5593952610013747`*^9}}], Cell[CellGroupData[{ Cell["How to Format Your Notebook", "Section", CellChangeTimes->{{3.559395738266055*^9, 3.5593957748949194`*^9}}], Cell[CellGroupData[{ Cell["Remember to first remove all the previously used variables", \ "Subsection", CellChangeTimes->{{3.5593952699098845`*^9, 3.559395272088009*^9}, { 3.559395324823025*^9, 3.559395325317054*^9}, {3.559395358263938*^9, 3.559395376338972*^9}, {3.559395507970891*^9, 3.559395529951329*^9}, { 3.559399859449692*^9, 3.559399859733708*^9}}], Cell[BoxData[ RowBox[{"Remove", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.559395534100937*^9, 3.559395579668617*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["THIS IS VERY IMPORTANT !", "Subtitle", CellChangeTimes->{{3.559395594083042*^9, 3.5593956247094965`*^9}, { 3.5593956573175125`*^9, 3.5593956584095144`*^9}, 3.5593957967817574`*^9}], Cell[CellGroupData[{ Cell["Here\[CloseCurlyQuote]s why", "Subsection", CellChangeTimes->{{3.5593957200608225`*^9, 3.559395722088826*^9}, { 3.559395793474552*^9, 3.5593957938645525`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"var", " ", "=", " ", "4"}]], "Input", CellChangeTimes->{{3.559395798684961*^9, 3.559395799745763*^9}, { 3.5593971631140704`*^9, 3.559397169187418*^9}}], Cell[BoxData["4"], "Output", CellChangeTimes->{3.5594066338781548`*^9, 3.5594077193192387`*^9}] }, Open ]] }, Open ]], Cell["At the top of the notebook please include your name", "Subsection", CellChangeTimes->{{3.559395833363822*^9, 3.5593958582146654`*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["The Three Rules of Mathematica", "Section", CellChangeTimes->{{3.559395955699237*^9, 3.5593959692868605`*^9}}], Cell["Functions Start With a Capital Letter", "Subsection", CellChangeTimes->{{3.5593959793176785`*^9, 3.5593959937633038`*^9}}], Cell["\<\ Function Inputs are Surrounded by [ ]\ \>", "Subsection", CellChangeTimes->{{3.559396182687993*^9, 3.559396211918665*^9}, { 3.5593962718890953`*^9, 3.559396273682198*^9}, {3.5594033111519876`*^9, 3.5594033149802065`*^9}}], Cell[CellGroupData[{ Cell["\<\ Lists and Ranges are Surrounded by { }\ \>", "Subsection", CellChangeTimes->{{3.5593962875929937`*^9, 3.559396298113595*^9}, 3.559396427611002*^9, 3.559398122118922*^9, {3.559403316419289*^9, 3.559403319150445*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.5594035338517256`*^9, 3.559403588491851*^9}, { 3.5594068330145445`*^9, 3.5594068379218254`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"x", "^", "k"}], "*", RowBox[{"Sin", "[", RowBox[{"k", "*", RowBox[{"Exp", "[", "x", "]"}]}], "]"}]}], ",", RowBox[{"x", "^", "k"}], ",", RowBox[{"-", RowBox[{"x", "^", "k"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "3"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "10"}], ",", " ", "10"}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"k", ",", "0", ",", " ", "3"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5594067631565495`*^9, 3.559406841577035*^9}, { 3.5594069305081215`*^9, 3.5594070314968977`*^9}, {3.559407403786191*^9, 3.559407406826365*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`k$$ = 0, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`k$$], 0, 3}}, Typeset`size$$ = {360., {111., 116.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`k$8115$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`k$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`k$$, $CellContext`k$8115$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{$CellContext`x^$CellContext`k$$ Sin[$CellContext`k$$ Exp[$CellContext`x]], $CellContext`x^$CellContext`k$$, \ -$CellContext`x^$CellContext`k$$}, {$CellContext`x, 0, 3}, PlotRange -> {-10, 10}], "Specifications" :> {{$CellContext`k$$, 0, 3}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{409., {157., 162.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.5594067971504936`*^9, 3.559406949288195*^9, {3.5594069885634413`*^9, 3.559407032800972*^9}, 3.5594077193692417`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"q", "^", "2"}], "*", RowBox[{"Sin", "[", "q", "]"}]}], ",", RowBox[{"{", RowBox[{"q", ",", " ", "0", ",", " ", RowBox[{"10", "*", "Pi"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5594068454792576`*^9, 3.5594068784731445`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"-", "100"}], " ", SuperscriptBox["\[Pi]", "2"]}]], "Output", CellChangeTimes->{{3.559406862417227*^9, 3.5594068791181817`*^9}, 3.5594077196042547`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"y", "^", "2"}]}], "\[Equal]", "2"}], ",", RowBox[{ RowBox[{"x", "+", "y"}], "\[Equal]", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.559406885152527*^9, 3.559406920295537*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", SqrtBox["3"]}], ")"}]}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", SqrtBox["3"]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", SqrtBox["3"]}], ")"}]}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", SqrtBox["3"]}], ")"}]}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.559406920905572*^9, 3.559407719628256*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Syntax and Some Little Things to Know", "Section", CellChangeTimes->{{3.55939814726136*^9, 3.5593981836424413`*^9}, { 3.5593982210765824`*^9, 3.5593982269379177`*^9}, {3.559401440579623*^9, 3.559401441782692*^9}}], Cell[CellGroupData[{ Cell["\[OpenCurlyDoubleQuote]==\[CloseCurlyDoubleQuote] vs. \ \[OpenCurlyDoubleQuote]=\[CloseCurlyDoubleQuote]", "Subsection", CellChangeTimes->{{3.5593999332639136`*^9, 3.559399970719056*^9}, { 3.5594025632608366`*^9, 3.5594025751915193`*^9}, 3.559403253575694*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"y", " ", "=", " ", "4"}]], "Input", CellChangeTimes->{{3.5593999759143534`*^9, 3.559399993202342*^9}}], Cell[BoxData["4"], "Output", CellChangeTimes->{3.559407059847519*^9, 3.5594077196462574`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["y"], "Input", CellChangeTimes->{{3.5593999832907753`*^9, 3.559400000741773*^9}}], Cell[BoxData["4"], "Output", CellChangeTimes->{3.5594070626536794`*^9, 3.5594077196642585`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Cos", "[", RowBox[{"Pi", "/", "4"}], "]"}], " ", "\[Equal]", " ", RowBox[{"Sin", "[", RowBox[{"Pi", "/", "4"}], "]"}]}]], "Input", CellChangeTimes->{{3.5594000071331387`*^9, 3.5594000279223275`*^9}}], Cell[BoxData["True"], "Output", CellChangeTimes->{3.5594070777315416`*^9, 3.559407719682259*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Cos", "[", RowBox[{"3", " ", RowBox[{"Pi", "/", "4"}]}], "]"}], " ", "\[Equal]", " ", RowBox[{"Sin", "[", RowBox[{"3", " ", RowBox[{"Pi", "/", "4"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.5594000395959954`*^9, 3.5594000423591537`*^9}}], Cell[BoxData["False"], "Output", CellChangeTimes->{3.559407083266858*^9, 3.55940771970026*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Functions", "Subsection", CellChangeTimes->{{3.559398192806966*^9, 3.5593981937190175`*^9}, { 3.559398526212035*^9, 3.559398531487337*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], " ", ":=", " ", RowBox[{"4", " ", RowBox[{"Log", "[", "x", "]"}]}]}]], "Input", CellChangeTimes->{{3.559398197226218*^9, 3.559398231326169*^9}, { 3.5593992918452263`*^9, 3.559399295555439*^9}, {3.5593994111390495`*^9, 3.5593994579917297`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"f", "[", "3", "]"}]], "Input", CellChangeTimes->{{3.559398534381502*^9, 3.559398535842586*^9}}], Cell[BoxData[ RowBox[{"4", " ", RowBox[{"Log", "[", "3", "]"}]}]], "Output", CellChangeTimes->{3.559407120786004*^9, 3.559407719730262*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{"f", "[", "3", "]"}], "]"}]], "Input", CellChangeTimes->{{3.5593985394357915`*^9, 3.5593985473922462`*^9}}], Cell[BoxData["4.394449154672439`"], "Output", CellChangeTimes->{3.5594071265053315`*^9, 3.559407719750263*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\[OpenCurlyDoubleQuote] /. \[CloseCurlyDoubleQuote] is called \ ReplaceAll", "Subsection", CellChangeTimes->{{3.5593985632361526`*^9, 3.559398577714981*^9}, { 3.559400347874628*^9, 3.559400353828968*^9}, {3.5594011326690116`*^9, 3.55940113840934*^9}, {3.5594032930369515`*^9, 3.559403298801281*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"x", " ", "+", "c"}], " ", "/.", " ", RowBox[{"x", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "2", ",", " ", "3"}], "}"}]}]}]], "Input", CellChangeTimes->{{3.5593985806081467`*^9, 3.55939858888362*^9}, { 3.559400399275568*^9, 3.5594004028547726`*^9}, {3.559401466705117*^9, 3.559401469926302*^9}, {3.5594071348458085`*^9, 3.559407166618626*^9}, { 3.559407209281066*^9, 3.5594072158204403`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"1", "+", "c"}], ",", RowBox[{"2", "+", "c"}], ",", RowBox[{"3", "+", "c"}]}], "}"}]], "Output", CellChangeTimes->{{3.559407147307521*^9, 3.559407167182658*^9}, 3.5594072164094734`*^9, 3.5594077197682643`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"sol", " ", "=", " ", RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"f", "[", "x", "]"}], "\[Equal]", "9"}], ",", " ", "x"}], "]"}]}]], "Input", CellChangeTimes->{{3.55939860444351*^9, 3.559398613843047*^9}, { 3.559399175042546*^9, 3.5593993932520266`*^9}, {3.5593994822951193`*^9, 3.5593994996161103`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"x", "\[Rule]", SuperscriptBox["\[ExponentialE]", RowBox[{"9", "/", "4"}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.5594071765041914`*^9, 3.5594077197862654`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x", "]"}], " ", "/.", " ", "sol"}]], "Input", CellChangeTimes->{{3.559399489725545*^9, 3.559399514956988*^9}}], Cell[BoxData[ RowBox[{"{", "9", "}"}]], "Output", CellChangeTimes->{3.559407189143914*^9, 3.5594077198052664`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Cos", "[", "x", "]"}], "/.", RowBox[{"Cos", "\[Rule]", " ", "Sin"}]}]], "Input", CellChangeTimes->{{3.559401176924543*^9, 3.55940118736114*^9}, { 3.5594018713132596`*^9, 3.559401872910351*^9}}], Cell[BoxData[ RowBox[{"Sin", "[", "x", "]"}]], "Output", CellChangeTimes->{3.5594072035737395`*^9, 3.5594077198232675`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["There are many different ways to do things in Mathematica", "Subsection", CellChangeTimes->{{3.559399609023368*^9, 3.559399642188265*^9}}], Cell[CellGroupData[{ Cell["Dont Freak Out", "Subsubsection", CellChangeTimes->{{3.55939979752415*^9, 3.5593998027114463`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"3", "*", RowBox[{"Cos", "[", "4", "]"}]}]], "Input", CellChangeTimes->{{3.5593997121362658`*^9, 3.5593997232999043`*^9}}], Cell[BoxData[ RowBox[{"3", " ", RowBox[{"Cos", "[", "4", "]"}]}]], "Output", CellChangeTimes->{3.5594072338924737`*^9, 3.5594077198452682`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"3", " ", RowBox[{"Cos", "[", "4", "]"}]}]], "Input", CellChangeTimes->{{3.559399715394452*^9, 3.55939973090934*^9}}], Cell[BoxData[ RowBox[{"3", " ", RowBox[{"Cos", "[", "4", "]"}]}]], "Output", CellChangeTimes->{3.5594072357735815`*^9, 3.5594077198622694`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", "+", " ", RowBox[{"c", "^", "2"}]}], " ", "\[Equal]", " ", "2"}], ",", " ", RowBox[{ RowBox[{"x", "+", "c"}], "\[Equal]", "1"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "c"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.559399663934509*^9, 3.559399698327476*^9}, { 3.559399747456286*^9, 3.55939975696383*^9}, {3.5594075504085774`*^9, 3.5594075564659243`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", SqrtBox["3"]}], ")"}]}]}], ",", RowBox[{"c", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", SqrtBox["3"]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", SqrtBox["3"]}], ")"}]}]}], ",", RowBox[{"c", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", SqrtBox["3"]}], ")"}]}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.5594072540376263`*^9, 3.559407271976652*^9}, 3.5594077198832707`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", "+", " ", RowBox[{"c", "^", "2"}]}], " ", "\[Equal]", " ", "2"}], " ", "&&", " ", RowBox[{ RowBox[{"x", "+", "c"}], "\[Equal]", "1"}]}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "c"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5593997663743677`*^9, 3.5593997723307085`*^9}, { 3.5594075587330537`*^9, 3.559407562154249*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", SqrtBox["3"]}], ")"}]}]}], ",", RowBox[{"c", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", SqrtBox["3"]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", SqrtBox["3"]}], ")"}]}]}], ",", RowBox[{"c", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", SqrtBox["3"]}], ")"}]}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.5594072759868813`*^9, 3.559407719906272*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Exp", "[", "5", "]"}]], "Input", CellChangeTimes->{{3.5593998066506715`*^9, 3.559399810693903*^9}}], Cell[BoxData[ SuperscriptBox["\[ExponentialE]", "5"]], "Output", CellChangeTimes->{3.559407282864275*^9, 3.5594077199242735`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"E", "^", "5"}]], "Input", CellChangeTimes->{{3.5593998155831823`*^9, 3.5593998171602726`*^9}}], Cell[BoxData[ SuperscriptBox["\[ExponentialE]", "5"]], "Output", CellChangeTimes->{3.559407291192751*^9, 3.559407719942274*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, ScreenStyleEnvironment->"Working", WindowSize->{1008, 633}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, TooltipBoxOptions->{TooltipDelay->Automatic}, FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (February 23, 2011)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "SlideShowHeader"->{ Cell[2336, 80, 64, 1, 66, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[8022, 258, 64, 1, 66, "SlideShowNavigationBar", CellTags->"SlideShowHeader"]} } *) (*CellTagsIndex CellTagsIndex->{ {"SlideShowHeader", 18418, 623} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 156, 5, 83, "Title"], Cell[CellGroupData[{ Cell[760, 31, 114, 1, 71, "Section"], Cell[CellGroupData[{ Cell[899, 36, 343, 5, 36, "Subsection"], Cell[1245, 43, 140, 2, 31, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[1434, 51, 190, 2, 49, "Subtitle"], Cell[CellGroupData[{ Cell[1649, 57, 168, 2, 36, "Subsection"], Cell[CellGroupData[{ Cell[1842, 63, 178, 3, 31, "Input"], Cell[2023, 68, 96, 1, 30, "Output"] }, Open ]] }, Open ]], Cell[2146, 73, 141, 1, 36, "Subsection"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[2336, 80, 64, 1, 66, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[2425, 85, 117, 1, 71, "Section"], Cell[2545, 88, 129, 1, 36, "Subsection"], Cell[2677, 91, 237, 5, 28, "Subsection"], Cell[CellGroupData[{ Cell[2939, 100, 234, 5, 28, "Subsection"], Cell[3176, 107, 147, 2, 31, "Input"], Cell[CellGroupData[{ Cell[3348, 113, 895, 25, 31, "Input"], Cell[4246, 140, 1796, 38, 336, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6079, 183, 333, 9, 31, "Input"], Cell[6415, 194, 194, 5, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6646, 204, 421, 13, 31, "Input"], Cell[7070, 219, 879, 31, 47, "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[8022, 258, 64, 1, 66, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[8111, 263, 225, 3, 71, "Section"], Cell[CellGroupData[{ Cell[8361, 270, 270, 3, 36, "Subsection"], Cell[CellGroupData[{ Cell[8656, 277, 127, 2, 31, "Input"], Cell[8786, 281, 94, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8917, 287, 95, 1, 31, "Input"], Cell[9015, 290, 96, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9148, 296, 246, 6, 31, "Input"], Cell[9397, 304, 97, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9531, 310, 296, 8, 31, "Input"], Cell[9830, 320, 95, 1, 30, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9974, 327, 148, 2, 36, "Subsection"], Cell[10125, 331, 313, 7, 31, "Input"], Cell[CellGroupData[{ Cell[10463, 342, 120, 2, 31, "Input"], Cell[10586, 346, 144, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10767, 354, 152, 3, 31, "Input"], Cell[10922, 359, 111, 1, 30, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[11082, 366, 311, 4, 36, "Subsection"], Cell[CellGroupData[{ Cell[11418, 374, 452, 9, 31, "Input"], Cell[11873, 385, 273, 7, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12183, 397, 358, 9, 31, "Input"], Cell[12544, 408, 237, 6, 33, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12818, 419, 156, 3, 31, "Input"], Cell[12977, 424, 116, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13130, 431, 234, 5, 31, "Input"], Cell[13367, 438, 125, 2, 30, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[13541, 446, 145, 1, 36, "Subsection"], Cell[CellGroupData[{ Cell[13711, 451, 106, 1, 27, "Subsubsection"], Cell[CellGroupData[{ Cell[13842, 456, 149, 3, 31, "Input"], Cell[13994, 461, 148, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14179, 469, 144, 3, 31, "Input"], Cell[14326, 474, 148, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14511, 482, 557, 15, 31, "Input"], Cell[15071, 499, 911, 32, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16019, 536, 486, 13, 31, "Input"], Cell[16508, 551, 881, 31, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17426, 587, 124, 2, 31, "Input"], Cell[17553, 591, 131, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17721, 598, 119, 2, 31, "Input"], Cell[17843, 602, 129, 2, 30, "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)