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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[ 258158, 15058]*) (*NotebookOutlinePosition[ 303712, 16636]*) (* CellTagsIndexPosition[ 303516, 16626]*) (*WindowFrame->Normal*) Notebook[{ Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg"], "Graphics", ShowCellBracket->False, CellMargins->{{25, 24}, {5, 7}}, ImageSize->{81, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "Approximation\n", StyleBox[ "Authors: Bill Davis, Horacio Porta and Jerry Uhl ", "Subtitle"], StyleBox["\[Copyright]1999", "Subtitle", FontSize->12], StyleBox["\nProducer: Bruce Carpenter\n", "Subtitle"], StyleBox["Publisher: ", "Subtitle", FontSize->12], StyleBox[ButtonBox["Math Everywhere, Inc.", ButtonData:>{ URL[ "http://www.matheverywhere.com"], None}, ButtonStyle->"MEIHyperlink"], FontSize->12], StyleBox[" Distributor: ", "Subtitle", FontSize->12], StyleBox[ButtonBox["Wolfram Research, Inc.", ButtonData:>{ URL[ "http://www.wolfram.com"], None}, ButtonStyle->"MEIHyperlink", ButtonNote->"Makers of Mathematica!"], FontSize->12] }], "PrefaceTitle", CellMargins->{{Inherited, Inherited}, {Inherited, 0}}], Cell[TextData[{ "3.01 Splines\n", StyleBox["Samples", FontSize->16, FontSlant->"Italic"] }], "Title"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " Initializations" }], "Special2"], Cell[BoxData[{ \(\(Off[General::spell]; \)\), \(\(Off[General::spell1]; \)\), \(\(Off[Plot::plnr]; \)\), \(\(Off[ParametricPlot3D::ppcom]; \)\), \(SetOptions[Limit, Analytic \[Rule] True]; \n\n If[MemberQ[{"\", \ "\", \ "\"}, \n\ \ \ \ Context[Gray]], \ Remove["\<*`Gray\>"]]; \n<< "\"; \n Remove["\<*`Gray\>"]; \n<< "\"; \n Graphics`Colors`GosiaGreen = RGBColor[0, \ 0.392187, \ 0]; \n\n Clear[Derivative]; \n$Pre\ = \ Chop; \)}], "Input", InitializationCell->True], Cell[CellGroupData[{ Cell["ThreeAxes[u,v]", "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{27, Inherited}, {Inherited, Inherited}}], Cell[BoxData[{ \(\(Axes3D::"\" = "\"; \)\), \(\(Axes3D[u_, v_] := Graphics3D[{{Blue, Line[{{\(-\(u\/3\)\), 0, 0}, {u, 0, 0}}]}, Text["\", {u + v, 0, 0}], {Blue, Line[{{0, \(-\(u\/3\)\), 0}, {0, u, 0}}]}, Text["\", {0, u + v, 0}], {Blue, Line[{{0, 0, \(-\(u\/3\)\)}, {0, 0, u}}]}, Text["\", {0, 0, u + v}]}]; \)\), \(\(Axes3D[u_] := Axes3D[u, u\/8]; \)\)}], "Input"] }, Closed]], Cell[BoxData[ \(\(CMView\ = \ {2.7, \ 1.6, \ 1.2}; \)\)], "Input", InitializationCell->True] }, Closed]], Cell["Basic Problems", "Subsubsection"], Cell[CellGroupData[{ Cell["B.1) Some remarkable plots explained by order of contact", "Subsection", CellTags->"3.01.B1"], Cell["\<\ Sometimes functions whose formulas are strikingly different have \ plots that are strikingly similar. 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But there's a serious aspect as \ well: \nLaying out the curves on expressways and railroads amounts to \ joining curved plots to relatively straight plots at knots of a spline. It \ is unacceptable to have a hitch (corner) in the middle of the roadway.\nThe \ higher the order of contact at the knots, the safer the highway or roadbed.\n\ Any order of contact less than ", Cell[BoxData[ \(2\)]], " is considered unsafe, and this may be pushing it." }], "SmallText"] }, Closed]] }, Closed]], Cell["Tutorial Problem", "Subsubsection"], Cell[CellGroupData[{ Cell["T.1) Splining functions and polynomials", "Subsection", CellTags->"3.01.T1"], Cell["T.1.a.i)", "Subsubsection"], Cell[CellGroupData[{ Cell[TextData[{ "Find the polynomial ", Cell[BoxData[ \(g[x]\)]], " of degree ", Cell[BoxData[ \(2\)]], " that has the highest possible order of contact with ", Cell[BoxData[ \(f[x]\ = \ e\^x\)]], " at ", Cell[BoxData[ \(x\ = \ 0\)]], ".\nPlot the spline knotted at ", Cell[BoxData[ \({0, 1}\)]], " with ", Cell[BoxData[ \(e\^x\)]], " on the right and your polynomial on the left.\nAlso show a plot of ", Cell[BoxData[ \(f[x]\)]], ", the polynomial, and the spline." }], "Text"], Cell["Answer:", "Special1"], Cell[TextData[{ "Enter ", Cell[BoxData[ \(f[x]\)]], " and the general form of a second degree polynomial:" }], "SmallText"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[f, g, x, a, k];\)\), "\n", \(\(f[x_]\ = \ E\^x;\)\), "\n", \(g[x_]\ = \ Sum[a[k]\ x\^k, {k, 0, 2}]\)}], "Input"], Cell[BoxData[ \(a[0] + x\ a[1] + x\^2\ a[2]\)], "Output"] }, Open ]], Cell["You need:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(eqn1 = f[0] == g[0]\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(1 == a[0]\)], "Output"] }, Open ]], Cell["And:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(eqn2 = \(f'\)[0] == \(g'\)[0]\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(1 == a[1]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(eqn3 = \(\(f'\)'\)[0] == \(\(g'\)'\)[0]\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(1 == 2\ a[2]\)], "Output"] }, Open ]], Cell[TextData[{ "Now you've got three equations with the three unknowns ", Cell[BoxData[ \(a[1]\)]], ", ", Cell[BoxData[ \(a[2]\)]], ", and ", Cell[BoxData[ \(a[3]\)]], ". Going for a fourth equation will only overdetermine the system of \ equations, so solve:" }], "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(coeffs = Solve[{eqn1, eqn2, eqn3}]\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \({{a[0] \[Rule] 1, a[1] \[Rule] 1, a[2] \[Rule] 1\/2}}\)], "Output"] }, Open ]], Cell["The polynomial you are after is:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[poly];\)\), "\n", \(poly[x_] = g[x] /. coeffs\[LeftDoubleBracket]1\[RightDoubleBracket]\)}], "Input", AspectRatioFixed->True], Cell[BoxData[ \(1 + x + x\^2\/2\)], "Output"] }, Open ]], Cell["Check:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[{D[f[x], {x, k}], D[poly[x], {x, k}]} /. x -> 0, {k, 0, 3}]\)], "Input"], Cell[BoxData[ \({{1, 1}, {1, 1}, {1, 1}, {1, 0}}\)], "Output"] }, Open ]], Cell[TextData[{ "This gives you order of contact ", Cell[BoxData[ \(2\)]], " between ", Cell[BoxData[ \(f[x]\)]], " and the polynomial at ", Cell[BoxData[ \(x\ = \ 0\)]], ". 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", "SmallText"] }, Closed]], Cell["T.1.a.ii)", "Subsubsection"], Cell[CellGroupData[{ Cell[TextData[{ "Find the polynomial ", Cell[BoxData[ \(g[x]\)]], " of degree ", Cell[BoxData[ \(6\)]], " that has the highest possible order of contact with ", Cell[BoxData[ \(f[x]\ = \ e\^x\)]], " at ", Cell[BoxData[ \(x\ = \ 0\)]], ".\nPlot the spline knotted at ", Cell[BoxData[ \({0, 1}\)]], " with ", Cell[BoxData[ \(e\^x\)]], " on the right and your polynomial on the left.\nAlso show a plot of ", Cell[BoxData[ \(f[x]\)]], ", the polynomial, and the spline." }], "Text"], Cell["Answer:", "Special1"], Cell[TextData[{ "Enter ", Cell[BoxData[ \(f[x]\)]], " and the general form of a sixth degree polynomial:" }], "SmallText"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[f, g, x, a, k];\)\), "\n", \(\(f[x_]\ = \ E^x;\)\), "\n", \(g[x_]\ = \ Sum[a[k]\ x^k, {k, 0, 6}]\)}], "Input"], Cell[BoxData[ \(a[0] + x\ a[1] + x\^2\ a[2] + x\^3\ a[3] + x\^4\ a[4] + x\^5\ a[5] + x\^6\ a[6]\)], "Output"] }, Open ]], Cell[TextData[{ "This leaves seven unknowns \n ", Cell[BoxData[ \(a[0]\)]], ", ", Cell[BoxData[ \(a[1]\)]], ", ", Cell[BoxData[ \(a[2]\)]], ", ", Cell[BoxData[ \(a[3]\)]], ", ", Cell[BoxData[ \(a[4]\)]], ", ", Cell[BoxData[ \(a[5]\)]], ", and ", Cell[BoxData[ \(a[6]\)]], " \nto determine.\nYou need seven equations to do this:" }], "SmallText"], Cell[CellGroupData[{ Cell[BoxData[{ \(eqn1\ = \ f[0]\ == \ g[0]\), "\n", \(eqn2\ = \ \(f'\)[0]\ == \ \(g'\)[0]\), "\n", \(eqn3\ = \ \(\(f'\)'\)[0]\ == \ \(\(g'\)'\)[0]\), "\n", \(eqn4\ = \ \(\(\(f'\)'\)'\)[0]\ == \ \(\(\(g'\)'\)'\)[0]\), "\n", \(eqn5\ = \ \(\(\(\(f'\)'\)'\)'\)[0]\ == \ \(\(\(\(g'\)'\)'\)'\)[ 0]\), "\n", \(eqn6\ = \ \(\(\(\(\(f'\)'\)'\)'\)'\)[ 0]\ == \ \(\(\(\(\(g'\)'\)'\)'\)'\)[0]\), "\n", \(eqn7\ = \ \(\(\(\(\(\(f'\)'\)'\)'\)'\)'\)[ 0]\ == \ \(\(\(\(\(\(g'\)'\)'\)'\)'\)'\)[0]\)}], "Input"], Cell[BoxData[ \(1 == a[0]\)], "Output"], Cell[BoxData[ \(1 == a[1]\)], "Output"], Cell[BoxData[ \(1 == 2\ a[2]\)], "Output"], Cell[BoxData[ \(1 == 6\ a[3]\)], "Output"], Cell[BoxData[ \(1 == 24\ a[4]\)], "Output"], Cell[BoxData[ \(1 == 120\ a[5]\)], "Output"], Cell[BoxData[ \(1 == 720\ a[6]\)], "Output"] }, Open ]], Cell["\<\ Now you've got the seven equations in the seven unknowns. Going for \ an eighth equation will only overdetermine the system of equations, so solve:\ \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(coeffs = Solve[{eqn1, eqn2, eqn3, eqn4, eqn5, eqn6, eqn7}]\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \({{a[0] \[Rule] 1, a[1] \[Rule] 1, a[2] \[Rule] 1\/2, a[3] \[Rule] 1\/6, a[4] \[Rule] 1\/24, a[5] \[Rule] 1\/120, a[6] \[Rule] 1\/720}}\)], "Output"] }, Open ]], Cell["The polynomial you are after is:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[poly];\)\), "\n", \(poly[x_] = g[x] /. coeffs[\([1]\)]\)}], "Input", AspectRatioFixed->True], Cell[BoxData[ \(1 + x + x\^2\/2 + x\^3\/6 + x\^4\/24 + x\^5\/120 + x\^6\/720\)], "Output"] }, Open ]], Cell["Check:", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[{D[f[x], {x, k}], D[poly[x], {x, k}]} /. x -> 0, {k, 0, 7}]\)], "Input"], Cell[BoxData[ \({{1, 1}, {1, 1}, {1, 1}, {1, 1}, {1, 1}, {1, 1}, {1, 1}, {1, 0}}\)], "Output"] }, Open ]], Cell[TextData[{ "This gives you order of contact ", Cell[BoxData[ \(6\)]], " between ", Cell[BoxData[ \(f[x]\)]], " and the polynomial at ", Cell[BoxData[ \(x\ = \ 0\)]], ". 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TextAlignment->Center, FontSize->16, FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], ShowCellBracket->False, ShowClosedCellArea->True, CellMargins->{{6, Inherited}, {0, 0}}, CellGroupingRules->{"TitleGrouping", 10}, PageBreakBelow->False, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Left, FontFamily->"Times", FontSize->14], Cell[StyleData["Subtitle", "Presentation"], CellFrame->False, CellMargins->{{24, Inherited}, {6, Inherited}}], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{14, Inherited}, {2, 2}}], Cell[StyleData["Subtitle", "TwoColumn"], CellMargins->{{14, Inherited}, {2, 2}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellFrame->True, ShowClosedCellArea->True, CellMargins->{{6, Inherited}, {6, Inherited}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Center, FontFamily->"Times", FontSize->24, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Subsubtitle", "Presentation"], CellFrame->True, CellMargins->{{24, Inherited}, {6, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{14, Inherited}, {2, 2}}, FontColor->GrayLevel[0]], Cell[StyleData["Subsubtitle", "TwoColumn"], CellMargins->{{14, Inherited}, {2, 2}}, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[GraySquare]", ShowCellBracket->True, ShowGroupOpenCloseIcon->True, CellMargins->{{22, Inherited}, {Inherited, 20}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1.5, 1}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Times", FontSize->16], Cell[StyleData["Section", "Presentation"], CellMargins->{{24, Inherited}, {Inherited, 20}}, LineSpacing->{1.5, 0}, FontSize->18], Cell[StyleData["Section", "Printout"], CellMargins->{{14, Inherited}, {2, 10}}], Cell[StyleData["Section", "TwoColumn"], CellMargins->{{14, Inherited}, {2, 10}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"", ShowCellBracket->True, ShowGroupOpenCloseIcon->True, CellMargins->{{19, Inherited}, {Inherited, 18}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1.5, 1}, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Times", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[0, 0.392187, 0]], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{24, Inherited}, {Inherited, 15}}], Cell[StyleData["Subsection", "Printout"], CellMargins->{{14, Inherited}, {2, 5}}, FontSize->12, FontColor->GrayLevel[0]], Cell[StyleData["Subsection", "TwoColumn"], CellFrame->{{0, 0}, {0, 1}}, CellMargins->{{14, Inherited}, {2, 10}}, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[EmptySquare]", ShowClosedCellArea->True, CellMargins->{{18, Inherited}, {Inherited, 12}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1.5, 1}, CounterIncrements->"Subsubsection", FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0.689998, 0.0899977, 0.119997]], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{24, Inherited}, {Inherited, 12}}, LineSpacing->{1, 0}], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{14, Inherited}, {2, 3}}, FontSize->12, FontColor->GrayLevel[0]], Cell[StyleData["Subsubsection", "TwoColumn"], CellMargins->{{14, Inherited}, {2, 3}}, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["PrefaceText"], CellMargins->{{15, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1, 1}, LimitsPositioningTokens->{}, StyleMenuListing->None, FontFamily->"Times", FontSize->10, FontWeight->"Plain"], Cell[StyleData["PrefaceText", "Presentation"], CellMargins->{{24, Inherited}, {Inherited, Inherited}}, LineSpacing->{2, 0}, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["PrefaceText", "Printout"], CellMargins->{{0, Inherited}, {2, 2}}, LineSpacing->{1, 1}, FontSize->12, FontColor->GrayLevel[0], Background->None], Cell[StyleData["PrefaceText", "TwoColumn"], CellMargins->{{0, Inherited}, {2, 2}}, LineSpacing->{1, 1}, FontSize->12, FontColor->GrayLevel[0], Background->None] }, Closed]], Cell[StyleData["PrefaceHyperlink"], CellMargins->{{15, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1, 1}, LimitsPositioningTokens->{}, StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontSize->10, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[CellGroupData[{ Cell[StyleData["Text"], ShowClosedCellArea->True, CellMargins->{{15, 10}, {Inherited, Inherited}}, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1.5, 1}, LimitsPositioningTokens->{}, FontFamily->"Times", FontSize->16, FontColor->RGBColor[0, 0, 0.500008]], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, Inherited}, {Inherited, Inherited}}, LineSpacing->{2, 0}, FontSize->16, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Text", "Printout"], CellMargins->{{14, Inherited}, {3, 1}}, PageBreakWithin->True, GroupPageBreakWithin->True, LineSpacing->{1, 2}, FontColor->GrayLevel[0], Background->None], Cell[StyleData["Text", "TwoColumn"], CellMargins->{{14, Inherited}, {3, 1}}, PageBreakWithin->True, GroupPageBreakWithin->True, LineSpacing->{1, 2}, FontSize->14, FontColor->GrayLevel[0], Background->None] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], ShowClosedCellArea->True, CellMargins->{{15, Inherited}, {Inherited, Inherited}}, DefaultInlineFormatType->DefaultInputInlineFormatType, LineSpacing->{1.5, 1}, LimitsPositioningTokens->{}, FontFamily->"Times", FontSize->16], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["SmallText", "Printout"], CellMargins->{{14, Inherited}, {2, 2}}, PageBreakWithin->True, GroupPageBreakWithin->True], Cell[StyleData["SmallText", "TwoColumn"], CellMargins->{{14, Inherited}, {2, 2}}, PageBreakWithin->True, GroupPageBreakWithin->True, FontSize->14] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellFrame->{{3, 0}, {0, 0}}, CellMargins->{{45, Inherited}, {Inherited, Inherited}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellFrame->{{3, 0}, {0, 0}}, CellMargins->{{45, Inherited}, {20, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Printout"], CellFrame->{{3, 0}, {0, 0}}, CellMargins->{{30, Inherited}, {2, 2}}, PageBreakWithin->True, GroupPageBreakWithin->True, FontSize->9], Cell[StyleData["Input", "TwoColumn"], CellFrame->{{3, 0}, {0, 0}}, CellMargins->{{30, Inherited}, {2, 2}}, PageBreakWithin->True, GroupPageBreakWithin->True, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1.5, 0}, FormatType->StandardForm, FontFamily->"Courier", FontSize->14, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Output", "Presentation"], CellMargins->{{45, Inherited}, {20, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Printout"], CellMargins->{{30, Inherited}, {2, 2}}, PageBreakWithin->True, GroupPageBreakWithin->True, LineSpacing->{1, 0}, FontSize->10, FontColor->GrayLevel[0]], Cell[StyleData["Output", "TwoColumn"], CellMargins->{{30, Inherited}, {2, 2}}, PageBreakWithin->True, GroupPageBreakWithin->True, LineSpacing->{1, 0}, FontSize->12, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, StyleMenuListing->None, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Printout"], CellMargins->{{30, Inherited}, {2, 2}}, FontSize->9, FontColor->GrayLevel[0]], Cell[StyleData["Message", "TwoColumn"], CellMargins->{{30, Inherited}, {2, 2}}, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Printout"], CellMargins->{{30, Inherited}, {2, 2}}, FontSize->9], Cell[StyleData["Print", "TwoColumn"], CellMargins->{{30, Inherited}, {2, 2}}, FontSize->16] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Info"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, StyleMenuListing->None], Cell[StyleData["Info", "Presentation"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Info", "Printout"], CellMargins->{{30, Inherited}, {Inherited, Inherited}}, FontSize->10], Cell[StyleData["Info", "TwoColumn"], CellMargins->{{30, Inherited}, {Inherited, Inherited}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{15, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, ImageMargins->{{35, Inherited}, {Inherited, 0}}, AnimationDisplayTime->0.2, StyleMenuListing->None, FontSize->14], Cell[StyleData["Graphics", "Presentation"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Graphics", "Printout"], CellMargins->{{30, Inherited}, {0, 0}}, CellFrameMargins->False, ImageSize->{Inherited, 150}, ImageMargins->{{45, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, FontSize->9], Cell[StyleData["Graphics", "TwoColumn"], CellMargins->{{20, Inherited}, {0, 0}}, CellFrameMargins->False, ImageSize->{Inherited, 150}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Times", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->14], Cell[StyleData["CellLabel", "Printout"], FontColor->GrayLevel[1]], Cell[StyleData["CellLabel", "TwoColumn"], FontColor->GrayLevel[1]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Special Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["PrefaceTitle"], CellFrame->{{1, 1}, {1, 5}}, ShowCellBracket->False, CellMargins->{{24, 24}, {0, 10}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, CellFrameMargins->{{15, Inherited}, {Inherited, Inherited}}, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Center, LineSpacing->{1.4, 1}, FontFamily->"Times", FontSize->24, FontWeight->"Bold", FontColor->GrayLevel[1], Background->RGBColor[0, 0.392187, 0]], Cell[StyleData["PrefaceTitle", "Presentation"], CellMargins->{{24, Inherited}, {60, Inherited}}, TextAlignment->Center, FontSize->38, FontColor->GrayLevel[1], Background->RGBColor[0.596078, 0.65098, 0.0196078]], Cell[StyleData["PrefaceTitle", "Printout"], CellMargins->{{0, Inherited}, {0, Inherited}}, FontSize->16, FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[StyleData["PrefaceTitle", "TwoColumn"], CellFrame->{{1, 1}, {0, 5}}, CellMargins->{{0, Inherited}, {0, Inherited}}, FontSize->16, FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Special Body Text and Index", "Section"], Cell[CellGroupData[{ Cell[StyleData["Accident"], CellFrame->3, ShowCellBracket->False, CellMargins->{{24, 24}, {0, 10}}, CellFrameMargins->{{15, Inherited}, {Inherited, Inherited}}, TextAlignment->Center, LineSpacing->{1.4, 1}, FontFamily->"Times", FontSize->24, FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Accident", "Presentation"], CellMargins->{{24, Inherited}, {60, Inherited}}, TextAlignment->Center, FontSize->36], Cell[StyleData["Accident", "Printout"], CellFrame->2, CellMargins->{{0, Inherited}, {0, Inherited}}, FontSize->16, FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[StyleData["Accident", "TwoColumn"], CellFrame->2, CellMargins->{{0, Inherited}, {0, Inherited}}, FontSize->16, FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ContentsText"], CellMargins->{{50, 10}, {5, 5}}, FontFamily->"Times", FontSize->16], Cell[StyleData["ContentsText", "Presentation"]], Cell[StyleData["ContentsText", "Printout"], FontColor->GrayLevel[0], Background->None], Cell[StyleData["ContentsText", "TwoColumn"], FontColor->GrayLevel[0], Background->None] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Special1"], CellDingbat->"\[EmptySquare]", ShowClosedCellArea->True, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0.689998, 0.0899977, 0.119997]], Cell[StyleData["Special1", "Presentation"], FontSize->16], Cell[StyleData["Special1", "Printout"], FontSize->12, FontColor->GrayLevel[0]], Cell[StyleData["Special1", "TwoColumn"], FontSize->12, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Special2"], CellMargins->{{6, 0}, {0, 0}}, CellGroupingRules->{"SectionGrouping", 40}, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Center, FontFamily->"Courier", FontSize->10, FontColor->GrayLevel[0.333333]], Cell[StyleData["Special2", "Presentation"], FontSize->12], Cell[StyleData["Special2", "Printout"], FontSize->10, FontColor->GrayLevel[0]], Cell[StyleData["Special2", "TwoColumn"], FontSize->10, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Special3"], CellDingbat->"\[GraySquare]", ShowClosedCellArea->True, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Left, FontFamily->"Courier", FontSize->10, FontColor->GrayLevel[0.333333]], Cell[StyleData["Special3", "Presentation"]], Cell[StyleData["Special3", "Printout"], FontColor->GrayLevel[0]], Cell[StyleData["Special3", "TwoColumn"], FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Special4"], ShowClosedCellArea->True, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Center, FontFamily->"Courier", FontSize->10, FontColor->GrayLevel[0.333333]], Cell[StyleData["Special4", "Presentation"], FontSize->12], Cell[StyleData["Special4", "Printout"], FontColor->GrayLevel[0]], Cell[StyleData["Special4", "TwoColumn"], FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Special5"], ShowClosedCellArea->True, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, TextAlignment->Center, FontFamily->"Courier", FontSize->10, FontColor->GrayLevel[0.333333]], Cell[StyleData["Special5", "Presentation"], FontSize->12], Cell[StyleData["Special5", "Printout"]], Cell[StyleData["Special5", "TwoColumn"]] }, Closed]], Cell[StyleData["IndexEntry"], ShowCellBracket->False, CellMargins->{{15, 5}, {0, 5}}, PageBreakBelow->False, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, ParagraphIndent->-40, StyleMenuListing->None, FontSize->16], Cell[StyleData["IndexSubEntry"], ShowCellBracket->False, CellMargins->{{45, 5}, {0, 0}}, DefaultFormatType->DefaultTextFormatType, DefaultInlineFormatType->DefaultInputInlineFormatType, ParagraphIndent->-40, StyleMenuListing->None, FontSize->16] }, Closed]], Cell[CellGroupData[{ Cell["Styles for License Agreement", "Section"], Cell[CellGroupData[{ Cell[StyleData["LicenseHeading"], ShowCellBracket->True, ShowGroupOpenCloseIcon->True, CellMargins->{{24, 24}, {-1, 2}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->12, FontWeight->"Bold", FontColor->RGBColor[0.4, 0.300008, 0.6]], Cell[StyleData["LicenseHeading", "Presentation"], FontSize->12], Cell[StyleData["LicenseHeading", "Printout"], FontSize->10, FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[StyleData["LicenseHeading", "TwoColumn"], FontSize->10, FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["LicenseText"], CellFrame->True, ShowCellBracket->False, CellMargins->{{24, 24}, {5, -1}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->12, Background->RGBColor[1, 0.537743, 0.509071]], Cell[StyleData["LicenseText", "Presentation"], FontSize->18], Cell[StyleData["LicenseText", "Printout"], FontSize->10, FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[StyleData["LicenseText", "TwoColumn"], FontSize->10, FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, \ etc. They automatically give the cell a FrameLabel containing a reference to \ a particular counter, and also increment that counter.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CounterIncrements->"NumberedEquation"], Cell[StyleData["NumberedEquation", "Presentation"]], Cell[StyleData["NumberedEquation", "Printout"]], Cell[StyleData["NumberedEquation", "TwoColumn"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedFigure"], CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Figure ", CounterBox[ "NumberedFigure"]}]], None}}, CounterIncrements->"NumberedFigure", FormatTypeAutoConvert->False, FontFamily->"Times"], Cell[StyleData["NumberedFigure", "Presentation"], CellMargins->{{24, Inherited}, {20, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["NumberedFigure", "Printout"], CellMargins->{{14, Inherited}, {Inherited, Inherited}}, FontSize->10], Cell[StyleData["NumberedFigure", "TwoColumn"], CellMargins->{{14, Inherited}, {Inherited, Inherited}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedTable"], CellMargins->{{6, Inherited}, {Inherited, 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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]}]&)}], 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