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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 16337, 634]*) (*NotebookOutlinePosition[ 40317, 1484]*) (* CellTagsIndexPosition[ 40273, 1480]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Simpson's Rule", "Title"], Cell["\<\ By Robin Sue Sanders, Buffalo State College copyright 1998\ \>", "Subsubtitle", TextAlignment->Center], Cell[CellGroupData[{ Cell["Parabolas", "Section"], Cell["Through every three points there is a parabola", "Text"], Cell[BoxData[ \(\(dots\ = \ ListPlot[{{0, 2}, {\(-1\), 5}, {7, 8}}, \n\t\t\t\t\t\t\t\t\t PlotStyle -> {Green, \ PointSize[ .04]}]; \)\)], "Input"], Cell["We find the parabola's coeffiecients.", "Text"], Cell[BoxData[ \(Clear[a, \ b, \ c]; Solve[{2\ == \ \ \ a\ + \ b*0\ + \ c*0\^2, \n \t\ \ \ \ \ \ \ \ \ \ \ \ \ 5\ == \ \ \ a\ + \ b*\((\(-1\))\)\ + \ c*\((\(-1\))\)\^2, \n \t\ \ \ \ \ \ \ \ \ \ \ \ \ 8\ == \ \ \ a\ + \ b*7\ + \ c*7\^2}, { a, b, c}]\)], "Input"], Cell["We plot the parabola.", "Text"], Cell["\<\ ParabolaPlot = Plot[2 - (141/56)x + (27/56)x^2, \t{x, -2, 8}, \tPlotStyle->Thickness[0.01]];\ \>", "Input"], Cell["We confirm the Solve does what we think it does.", "Text"], Cell[BoxData[ \(\(Show[dots, \ ParabolaPlot]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Geometry of Simpson's Rule", "Section"], Cell["Our working example in this notebook is:", "Text"], Cell[BoxData[ FormBox[ RowBox[{ StyleBox[ RowBox[{"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t", StyleBox["\t", FontSize->24]}]], StyleBox[ \(\[Integral]\_0\%\(\@\[Pi]\)sin \((x\^2)\) \[DifferentialD]x\), FontSize->24]}], TextForm]], "Text"], Cell[TextData[{ "This integral is equal to the area under the curve y = ", Cell[BoxData[ \(TraditionalForm\`sin(x\^2)\)]], " over the interval \n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"0", " ", "\[LessEqual]", " ", "x", " ", "\[LessEqual]", StyleBox[\(\@\[Pi]\), FontSize->16]}], " "}], TraditionalForm]]], ". We can plot this:" }], "Text"], Cell["\<\ f[x_] := Sin[x^2]; a=0; b= Sqrt[Pi]; Plot[f[x], {x, a, b}, PlotStyle->Thickness[0.01]];\ \>", "Input"], Cell["We slice the area we're trying to find,", "Text"], Cell["\<\ f[x_] := Sin[x^2]; a=0; b= Sqrt[Pi]; Slices[4];\ \>", "Input"], Cell["and put a parabola over each pair of neighboring slices", "Text"], Cell["Parabolas[2];", "Input"], Cell["\<\ We can compare (geometrically) to other standard Calculus II \ numerical approximation rules:\ \>", "Text"], Cell["RightRectangles[4];", "Input"], Cell["LeftRectangles[4];", "Input"], Cell["Trapezoids[4];", "Input"], Cell[TextData[{ "Playing around let's the students see that Simpson's Rule ", StyleBox["should", FontSlant->"Italic"], " work better (and faster) than any of the others." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Derivation of Simpson's Rule", "Section"], Cell["\<\ Algebraic erivation of Simpson's Rule is provided in text cells for \ the students to read. Code for Simpson's Rule is provided.\ \>", "Text"], Cell[BoxData[ \(Clear[SimpsonsRule]; \n SimpsonsRule[n_]\ := \ \n\t\ N[\ \ \(\(b - a\)\/\(6\ n\)\) \((f[a]\ + f[b]\ + \ \[Sum]\+\(i = 1\)\%\(n - 1\)\(( 2\ f[a\ + \ 2\ i\ \ \(b - a\)\/\(2 n\)]\ )\) + \ \[Sum]\+\(i = 0\)\%\(n - 1\)\((\ 4 f[a\ + \ \((2\ i\ + 1)\)\ \(b - a\)\/\(2 n\)])\))\)] \)], "Input"], Cell["And approximations can easily be generated: ", "Text"], Cell["SimpsonsRule[2]", "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Error Term and Accuracy of Estimates", "Section"], Cell["\<\ The second lab of the set has the students studying the error in \ Simpson's Rule estimates by comparing the estimates to the exact value of \ certain known integrals. \ \>", "Text"], Cell["\<\ Students also investigate how rapidly Simpson's Rule converges by \ looking at \"error ratios\"---a way to measure how much smaller the error \ becomes when we double the number of parabolas used. Students have done this \ same kind of exercise with the other rules previously in the semester. They \ can see that these ratios are much smaller for Simpson's Rule, which \ indicates much more rapid convergence.\ \>", "Text"], Cell["\<\ In the third lab, the \"Error Term\" for Simpson's Rule is \ introduced to let the students determine the accuracy of their estimates. \ This is stated as a theorem:\ \>", "Text"], Cell[TextData[{ "Theorem: (Error Term for Simpson's Rule) If ", Cell[BoxData[ \(TraditionalForm\`f[x]\)]], " has a continuous ", StyleBox["fourth", FontSlant->"Italic"], " derivative on the interval [", StyleBox["a", FontSlant->"Italic"], ", ", StyleBox["b", FontSlant->"Italic"], "], then the error in using ", StyleBox["n", FontSlant->"Italic"], " parabolas (and 2", StyleBox["n ", FontSlant->"Italic"], "slices) in Simpson's Rule to approximate ", Cell[BoxData[ FormBox[ StyleBox[\(\[Integral]\_a\%bf[x] \[DifferentialD]x\), FontSize->19], TraditionalForm]]], " satisfies the inequality:" }], "Text", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "\t", Cell[BoxData[ \(TraditionalForm \`SimpsonsError[n]\ \[LessEqual] \ \((b - a)\)\/180\ M\ \ \((width\ of\ one\ slice)\)\^4 = \((b - a)\)\/180\ M\ \ \((\ \(b - a\)\/\(2 n\))\)\^4\)]], " " }], "Text", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "where ", StyleBox["M", FontSlant->"Italic"], " is an ", StyleBox["upper bound ", FontSlant->"Italic"], " for ", Cell[BoxData[ \(TraditionalForm\`\(|\( f\^\((4)\)\)[x]\ | \)\)]], " on the interval [", StyleBox["a", FontSlant->"Italic"], ", ", StyleBox["b", FontSlant->"Italic"], "]. In other words, for all ", StyleBox["x", FontSlant->"Italic"], " in the interval [", StyleBox["a", FontSlant->"Italic"], ", ", StyleBox["b", FontSlant->"Italic"], "], we know that ", Cell[BoxData[ \(TraditionalForm \`\(\(-M\) \[LessEqual] \(f\^\((4)\)\)[x] \[LessEqual] \ M\ \)\)]], "." }], "Text", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "We can feed ", StyleBox["Mathematica", FontSlant->"Italic"], " a formula for the theorectical error bound using ", StyleBox["n", FontSlant->"Italic"], " parabolas in terms of ", StyleBox["f", FontSlant->"Italic"], ", ", StyleBox["a", FontSlant->"Italic"], ", ", StyleBox["b", FontSlant->"Italic"], ", and ", StyleBox["M", FontSlant->"Italic"], ". " }], "Text"], Cell[BoxData[ \(Clear[TheorecticalError, \ M]; TheorecticalError[n_]\ := \ N[\((\ \(b - a\)\/180)\)\ M\ \((\ \(b - a\)\/\(2 n\))\)\^4]\)], "Input",\ InitializationCell->True], Cell[TextData[{ "We can make ", StyleBox["Mathematica", FontSlant->"Italic"], " find the fourth derivative:" }], "Text"], Cell[BoxData[ \(\(\(\(\(f'\)'\)'\)'\)[x]\)], "Input"], Cell[TextData[{ "To get ", StyleBox["M", FontSlant->"Italic"], ", weplot the fourth derivative" }], "Text"], Cell["\<\ Plot[f''''[x], {x, a, b}, PlotStyle->Thickness[.01]];\ \>", "Input"], Cell["We can even check our guess", "Text"], Cell["\<\ Plot[{(* FILL IN *), \t f''''[x], \t (*FILL IN *)}, \t {x, 0, Sqrt[Pi]}, PlotStyle->{{Red,Thickness[.01]}, {Black,Thickness[.01]}, {Red,Thickness[.01]}}];\ \>", "Input"], Cell[TextData[{ "And use the ", StyleBox["M", FontSlant->"Italic"], " we get from the plot to find the Theorectical Error in our estimate." }], "Text"], Cell[BoxData[ \(\(\n\(M\ = \)\ (*\ FILL\ IN\ *) ; \n\(n = \) (*\ FILL\ IN\ *) ; 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x2 = a + (2 k - 1)jump[2 n]; x1 = a + (2 k - 2)jump[2 n]; coeffs = Solve[{ f[x1] == a0 + a1 x1 + a2 (x1)^2, f[x2] == a0 + a1 x2 + a2 (x2)^2, f[x3] == a0 + a1 x3 + a2 (x3)^2}, \t\t {a0, a1, a2}]; c0 = If[coeffs[[1,1,1]] === a0, c0 = coeffs[[1,1,2]], \t\tIf[coeffs[[1,2,1]] === a0, \t\t c0 = coeffs[[1,2,2]], \t\t c0 = coeffs[[1,3,2]] \t\t]]; c1 = If[coeffs[[1,1,1]] === a1, c1 = coeffs[[1,1,2]], \t\tIf[coeffs[[1,2,1]] === a1, \t\t c1 = coeffs[[1,2,2]], \t\t c1 = coeffs[[1,3,2]] \t\t]]; c2 = If[coeffs[[1,1,1]] === a2, c2 = coeffs[[1,1,2]], \t\tIf[coeffs[[1,2,1]] === a2, \t\t c2 = coeffs[[1,2,2]], \t\t c2 = coeffs[[1,3,2]] \t\t]]; Plot[c0 + c1 x + c2 x^2, {x, x1, x3}, \t\t PlotStyle->{Green, Thickness[.01]}, \t\t DisplayFunction->Identity] } ]\ \>", "Input", InitializationCell->True], Cell["\<\ Parabolas[n_] := Show[picture, Table[SliceLine[k,2 n], {k,0,2 n}], Table[ParabolaTop[k,n],{k,1,n}], DisplayFunction->$DisplayFunction]\ \>", "Input", InitializationCell->True], Cell["Commands for showing Right-hand rule rectangles", "Text", Evaluatable->False], Cell["\<\ Clear[RightRectangles, RightHandTop] RightHandTop[k_,n_] := Graphics[{{Blue,Thickness[0.01], Line[{ {a + (k-1) jump[n], f[a + k jump[n]]}, {a + k jump[n], f[a + k jump[n]]} }] }, If[ f[a + k jump[n]] > f[a + (k-1) jump[n]], {Blue, Thickness[0.01], Line[{ {a + (k-1) jump[n], f[a + k jump[n]]}, {a + (k-1) jump[n], f[a + (k-1)jump[n]]} }] }, {Blue, Point[{a + (k-1) jump[n], f[a + (k-1) jump[n]]}] }]}]\ \>", "Input", InitializationCell->True], Cell["\<\ RightRectangles[n_] := Show[picture, Table[SliceLine[k,n],{k,0,n}], Table[RightHandTop[k,n],{k,1,n}], DisplayFunction->$DisplayFunction]\ \>", "Input", InitializationCell->True], Cell["\<\ The commands for drawing the picture for Left-hand rule rectangles.\ \ \>", "Text", Evaluatable->False], Cell["\<\ Clear[LeftRectangles, LeftHandTop] LeftHandTop[k_,n_] := Graphics[{{Red, Thickness[0.01], Line[{ {a + (k-1) jump[n], f[a + (k-1) jump[n]]}, {a + k jump[n], f[a + (k-1) jump[n]]}}] }, If[f[a + k jump[n]] < f[a + (k-1) jump[n]], {Red,Thickness[0.01], Line[{ {a + k jump[n], f[a + k jump[n]]}, {a + k jump[n], f[a + (k-1) jump[n]]} }] }, {Red, Point[{a + k jump[n], f[a + k jump[n]]}] }]}]\ \>", "Input", InitializationCell->True], Cell["\<\ LeftRectangles[n_] := Show[picture, Table[SliceLine[k,n],{k,0,n}], Table[LeftHandTop[k,n],{k,1,n}], DisplayFunction->$DisplayFunction]\ \>", "Input", InitializationCell->True], Cell["Commands for showing \"Midpoint Rule\" rectangles.", "Text", Evaluatable->False], Cell["\<\ Clear[MiddleRectangles, MidpointTop] MidpointTop[k_,n_] := Graphics[ {{Brick,Thickness[0.01], Line[{ {a + (k-1) jump[n], f[(a + (k-1) jump[n] + a + k jump[n])/2]}, {a + k jump[n], f[(a + (k-1) jump[n] + a + k jump[n])/2]} }]}, If[f[a + k jump[n]] < f[(a + (k-1) jump[n] + a + k jump[n])/2], {Brick,Thickness[.01], Line[{ {a + k jump[n], f[a + k jump[n]]}, {a + k jump[n], f[(a + (k-1) jump[n] + a + k jump[n])/2]} }] }, {Brick,Thickness[0.01], Point[{a + k jump[n], f[(a + (k-1) jump[n] + a + k jump[n])/2]}] }], If[f[a + (k-1) jump[n]] < f[(a + (k-1) jump[n] + a + k jump[n])/2], {Brick,Thickness[0.01], Line[{ {a + (k-1) jump[n], f[a + (k-1) jump[n]]}, {a + (k-1) jump[n], f[(a + (k-1) jump[n] + a + k jump[n])/2]} }] }, {Brick,Thickness[0.01], Point[{a + (k-1) jump[n], f[(a + (k-1) jump[n] + a + k jump[n])/2]}] }] }]\ \>", "Input", InitializationCell->True], Cell["\<\ MiddleRectangles[n_] := Show[picture, Table[SliceLine[k,n],{k,0,n}], Table[MidpointTop[k,n],{k,1,n}], DisplayFunction->$DisplayFunction]\ \>", "Input", InitializationCell->True], Cell["\<\ Clear[Trapezoids, TrapTop] TrapTop[k_,n_] := Graphics[{Orange,Thickness[0.01], Line[{ {a + (k-1) jump[n], f[a + (k-1) jump[n]]}, {a + k jump[n], f[a + k jump[n]]}}] }]\ \>", "Input", InitializationCell->True], Cell["\<\ Trapezoids[n_] := Show[picture, Table[SliceLine[k,n],{k,0,n}], Table[TrapTop[k,n],{k,1,n}], DisplayFunction->$DisplayFunction]\ \>", "Input", InitializationCell->True] }, Closed]] }, Open ]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 800}, {0, 580}}, AutoGeneratedPackage->None, ScreenStyleEnvironment->"Presentation", WindowSize->{654, 509}, WindowMargins->{{29, Automatic}, {Automatic, 6}}, StyleDefinitions -> Notebook[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of \ all cells in a given style. 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Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8, FontColor->GrayLevel[0]] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->9, Magnification->0.8] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Open ]], Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]], Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10], Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]], Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }], MacintoshSystemPageSetup->"\<\ 00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001 0000I00000400`<300000BL?00400@0000000000000006P801T1T00000000000 00000000000000000000000000000000\>" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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