(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 82842, 1899] NotebookOptionsPosition[ 13929, 452] NotebookOutlinePosition[ 81882, 1866] CellTagsIndexPosition[ 81839, 1863] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["Natural Modes of the Rectangular Membrane", "Title"], Cell[CellGroupData[{ Cell["Natural Modes of Oscillation ", "Section"], Cell[TextData[{ StyleBox["Problem 1", FontWeight->"Bold"], ": Consider a rectangular membrane ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"0", "\[LessEqual]", "x", "\[LessEqual]", "a"}], ",", " ", RowBox[{"0", "\[LessEqual]", "y", "\[LessEqual]", "b"}]}], TraditionalForm]]], " with homogeneous BC for the displacement on all four sides. Show that the \ method of separation of variables leads to the following family of solutions \ satisfying the wave equation and the BC:\n\n\t\t\t\t", Cell[BoxData[ FormBox[ RowBox[{ StyleBox[ RowBox[{ SubscriptBox["u", RowBox[{"m", ",", "n"}]], "(", RowBox[{"x", ",", "y", ",", "t"}], ")"}], "DisplayFormula"], StyleBox["=", "DisplayFormula"], RowBox[{ StyleBox[ RowBox[{"sin", "(", FractionBox[ RowBox[{"m", " ", "\[Pi]", " ", "x"}], "a"], ")"}], "DisplayFormula"], StyleBox[ RowBox[{"sin", "(", FractionBox[ RowBox[{"n", " ", "\[Pi]", " ", "y"}], "b"], ")"}], "DisplayFormula"], RowBox[{ StyleBox["cos", "DisplayFormula"], StyleBox["(", "DisplayFormula"], RowBox[{ StyleBox["c", "DisplayFormula"], StyleBox[" ", "DisplayFormula"], SqrtBox[ SubscriptBox["\[Lambda]", RowBox[{"m", ",", "n"}]]], "t"}], ")"}]}]}], TraditionalForm]]], "\n\t\t\t\t\nwhere \n\t\t\t\t", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ SubscriptBox["\[Lambda]", RowBox[{"m", ",", "n"}]], "=", RowBox[{ RowBox[{"(", RowBox[{ FractionBox[ SuperscriptBox["m", "2"], SuperscriptBox["a", "2"]], "+", FractionBox[ SuperscriptBox["n", "2"], SuperscriptBox["b", "2"]]}], ")"}], SuperscriptBox["\[Pi]", "2"]}]}], "DisplayFormula"], TraditionalForm]]], "\n\t\t\t\t\nSuch solutions are called \"natural modes of oscillation\" or \ \"standing waves\" and have the property that all points of the membrane \ oscillate up and down with the same frequency. " }], "Text", CellChangeTimes->{{3.45105256371875*^9, 3.4510525684375*^9}, { 3.451052633125*^9, 3.451052648203125*^9}, {3.45105274325*^9, 3.45105278890625*^9}, 3.45105287746875*^9}], Cell[TextData[{ StyleBox["Problem 2", FontWeight->"Bold"], ": Using the values of ", Cell[BoxData[ FormBox[ RowBox[{"a", ",", " ", "b", ",", " ", RowBox[{"and", " ", "c", " ", "given", " ", "below"}], ",", " ", "c"}], TraditionalForm]], FormatType->"TraditionalForm"], "omplete the definitions given below to define ", StyleBox["Mathematica", FontSlant->"Italic"], " functions for \n\n\t\t\t\t", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ RowBox[{"\[Lambda]", "(", RowBox[{"m", ",", "n"}], ")"}], "=", RowBox[{ RowBox[{"(", RowBox[{ FractionBox[ SuperscriptBox["m", "2"], SuperscriptBox["a", "2"]], "+", FractionBox[ SuperscriptBox["n", "2"], SuperscriptBox["b", "2"]]}], ")"}], SuperscriptBox["\[Pi]", "2"]}]}], "DisplayFormula"], TraditionalForm]], FormatType->"TraditionalForm"], "\n\t\t\t\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Phi]", "(", RowBox[{"m", ",", "n", ",", "x", ",", "y"}], ")"}], "=", StyleBox[ RowBox[{ RowBox[{"sin", "(", FractionBox[ RowBox[{"m", " ", "\[Pi]", " ", "x"}], "a"], ")"}], RowBox[{"sin", "(", FractionBox[ RowBox[{"n", " ", "\[Pi]", " ", "y"}], "b"], ")"}]}], "DisplayFormula"]}], TraditionalForm]], FormatType->"TraditionalForm"], "\n\t\t\t\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"T", "(", RowBox[{"m", ",", "n", ",", "t"}], ")"}], "=", RowBox[{ StyleBox["cos", "DisplayFormula"], StyleBox["(", "DisplayFormula"], RowBox[{ StyleBox["c", "DisplayFormula"], StyleBox[" ", "DisplayFormula"], SqrtBox[ SubscriptBox["\[Lambda]", RowBox[{"m", ",", "n"}]]], "t"}], ")"}]}], TraditionalForm]], FormatType->"TraditionalForm"], "\n\t\t\t\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"u", "(", RowBox[{"m", ",", "n", ",", "x", ",", "y", ",", "t"}], ")"}], "=", RowBox[{ RowBox[{"\[Phi]", "(", RowBox[{"m", ",", "n", ",", "x", ",", "y"}], ")"}], RowBox[{"T", "(", RowBox[{"m", ",", "n", ",", "t"}], ")"}]}]}], TraditionalForm]], FormatType->"TraditionalForm"] }], "Text", CellChangeTimes->{{3.4510529353125*^9, 3.451053050109375*^9}, { 3.451053087734375*^9, 3.451053379234375*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"a", "=", "1."}], ";"}], "\n", RowBox[{ RowBox[{"b", "=", "2."}], ";"}], "\n", RowBox[{ RowBox[{"c", "=", "2."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Lambda]", "[", RowBox[{"m_", ",", "n_"}], "]"}], ":=", " ", "\n", RowBox[{ RowBox[{"\[Phi]", "[", RowBox[{"m_", ",", "n_", ",", "x_", ",", "y_"}], "]"}], ":=", " ", "\[IndentingNewLine]", "\n", RowBox[{ RowBox[{"T", "[", RowBox[{"m_", ",", "n_", ",", "t_"}], "]"}], ":=", " ", "\[IndentingNewLine]", "\n", RowBox[{ RowBox[{"u", "[", RowBox[{"m_", ",", "n_", ",", "x_", ",", "y_", ",", "t_"}], "]"}], ":=", " "}]}]}]}]}], "Input", CellChangeTimes->{{3.451053406546875*^9, 3.451053415828125*^9}, { 3.451053535640625*^9, 3.451053543828125*^9}, {3.451053573890625*^9, 3.45105358621875*^9}}], Cell[CellGroupData[{ Cell["Surface Plot and Animation", "Subsection"], Cell[TextData[{ StyleBox["Problem 3:", FontWeight->"Bold"], " Take ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"m", "=", "2"}], ",", " ", RowBox[{"n", "=", "3"}]}], TraditionalForm]]], " and use Plot3D to give a plot of the solution surface at ", Cell[BoxData[ FormBox[ RowBox[{"t", "=", "2."}], TraditionalForm]], FormatType->"TraditionalForm"], " Use ColorFunction->Hue to color the plot." }], "Text", CellChangeTimes->{{3.45105360778125*^9, 3.451053667921875*^9}, { 3.45105599390625*^9, 3.451056013140625*^9}}], Cell[TextData[{ StyleBox["Problem 4:", FontWeight->"Bold"], " Wrap your plot from Problem 3 in Manipulate to obtain an animation of the \ mode as ", Cell[BoxData[ FormBox["t", TraditionalForm]], FormatType->"TraditionalForm"], " goes from 0 to 5. 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Do these plots indicate that the solution is or is not a mode." }], "Text", CellChangeTimes->{{3.451057181703125*^9, 3.4510572214375*^9}, { 3.451057254234375*^9, 3.45105730215625*^9}, {3.45105739384375*^9, 3.45105743940625*^9}}], Cell[TextData[{ StyleBox["Problem 9 ", FontWeight->"Bold"], ": Make plots showing where the three functions from Problem 8 are 0." }], "Text", CellChangeTimes->{{3.4510575755*^9, 3.451057626875*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["The Case of Repeated Eigenvalues", "Section"], Cell[TextData[{ StyleBox["Problem 10", FontWeight->"Bold"], ": Suppose ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"a", "=", RowBox[{ RowBox[{"1", " ", "and", " ", "b"}], "=", "2"}]}], ",", " ", RowBox[{"c", "=", "2."}]}], TraditionalForm]]], " Then ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ SubscriptBox["\[Lambda]", RowBox[{"2", ",", "2"}]], "=", SubscriptBox["\[Lambda]", RowBox[{"1", ",", "4"}]]}], "DisplayFormula"], TraditionalForm]]], " so we can construct additional modes of oscillation as follows:\n\n\t\t\t\t\ ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ RowBox[{ SubscriptBox["v", " "], "(", RowBox[{"x", ",", "y", ",", "t"}], ")"}], "=", RowBox[{ RowBox[{ StyleBox["(", "DisplayFormula"], RowBox[{ StyleBox[ RowBox[{"p", " ", RowBox[{"sin", "(", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "x"}], "a"], ")"}], RowBox[{"sin", "(", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "y"}], "b"], ")"}]}], "DisplayFormula"], StyleBox["+", "DisplayFormula"], RowBox[{ StyleBox["q", "DisplayFormula"], StyleBox[ RowBox[{ StyleBox[" ", "DisplayFormula"], " "}]], RowBox[{"sin", "(", FractionBox[ RowBox[{"1", " ", "\[Pi]", " ", "x"}], "a"], ")"}], RowBox[{"sin", "(", FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "y"}], "b"], ")"}]}]}], " ", ")"}], RowBox[{"cos", "(", RowBox[{ StyleBox["c", "DisplayFormula"], StyleBox[" ", "DisplayFormula"], SqrtBox[ SubscriptBox["\[Lambda]", RowBox[{"2", ",", "2"}]]], "t"}], ")"}]}]}], "DisplayFormula"], TraditionalForm]]], "\n\t\t\t\t\nwhere ", Cell[BoxData[ FormBox[ RowBox[{"p", " ", "and", " ", "q", " "}], TraditionalForm]]], "are constants. 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"\[FilledSquare]", CellMargins -> {{25, Inherited}, {8, 12}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 9}, CounterIncrements -> "Subsubsection", FontFamily -> "Times", FontSize -> 13, FontWeight -> "Bold"], Cell[ StyleData["Subsubsection", "Presentation"], CellMargins -> {{34, 10}, {18, 28}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Subsubsection", "Condensed"], CellMargins -> {{22, Inherited}, {2, 12}}, FontSize -> 10], Cell[ StyleData["Subsubsection", "Printout"], CellMargins -> {{21, 0}, {4, 20}}, FontSize -> 11]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Text"], CellFrame -> 3, CellMargins -> {{12, 10}, {5, 5}}, CellFrameColor -> RGBColor[1, 1, 0], InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 3}, ParagraphSpacing -> {0, 12}, CounterIncrements -> "Text", FontFamily -> "Times", FontColor -> RGBColor[1, 1, 0], Background -> RGBColor[0, 0, 0.627451]], Cell[ StyleData["Text", "Presentation"], CellMargins -> {{15, 10}, {8, 10}}, LineSpacing -> {1, 5}, ParagraphSpacing -> {0, 12}, FontSize -> 18], Cell[ StyleData["Text", "Condensed"], CellMargins -> {{8, 10}, {4, 4}}, LineSpacing -> {1, 1}, ParagraphSpacing -> {0, 4}], Cell[ StyleData["Text", "Printout"], CellFrame -> False, CellMargins -> {{9, 0}, {4, 4}}, Hyphenation -> True, ParagraphSpacing -> {0, 6}, FontColor -> GrayLevel[0], Background -> None]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["SmallText"], CellMargins -> {{12, 10}, {5, 5}}, InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 3}, ParagraphSpacing -> {0, 6}, CounterIncrements -> "SmallText", FontFamily -> "Helvetica", FontSize -> 9], Cell[ StyleData["SmallText", "Presentation"], CellMargins -> {{15, 10}, {8, 10}}, LineSpacing -> {1, 5}, FontSize -> 14], Cell[ StyleData["SmallText", "Condensed"], CellMargins -> {{8, 10}, {2, 2}}, LineSpacing -> {1, 2}, FontSize -> 9], Cell[ StyleData["SmallText", "Printout"], CellMargins -> {{9, 0}, {4, 4}}, Hyphenation -> True, FontSize -> 7]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell["Inline Formatting", "Section"], Cell[ "These styles are for modifying individual words or letters in a \ cell exclusive of the cell tag.", "Text"], Cell[ StyleData["RM"], StyleMenuListing -> None, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["BF"], StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["IT"], StyleMenuListing -> None, FontSlant -> "Italic"], Cell[ StyleData["TR"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["TI"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["TB"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["TBI"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ StyleData["SR"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["SO"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["SB"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["SBO"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ CellGroupData[{ Cell[ StyleData["SO10"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["SO10", "Printout"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 7, FontWeight -> "Plain", FontSlant -> "Italic"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Inert"], StyleMenuListing -> None, Background -> RGBColor[0.870588, 0.905882, 0.972549]], Cell[ StyleData["Inert", "Printout"], StyleMenuListing -> None, Background -> GrayLevel[1]]}, Closed]]}, Open]], 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 -> {{52, 10}, {8, 8}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{5, Inherited}, {Inherited, Inherited}}, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", FormatType -> InputForm, ShowStringCharacters -> True, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", FontWeight -> "Bold", Background -> RGBColor[1, 0.700008, 0.4]], Cell[ StyleData["Input", "Presentation"], CellFrame -> {{5, 0}, {0, 0}}, CellMargins -> {{74, 10}, {8, 10}}, CellFrameMargins -> {{10, 10}, {14, 14}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Input", "Condensed"], CellMargins -> {{40, Inherited}, {1, 4}}], Cell[ StyleData["Input", "Printout"], CellMargins -> {{44, 0}, {2, 6}}, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineInput"], Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, FormatType -> InputForm, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", FontWeight -> "Bold"], Cell[ StyleData["InlineInput", "Presentation"], FontSize -> 18], Cell[ StyleData["InlineInput", "Condensed"]], Cell[ StyleData["InlineInput", "Printout"], FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Output"], CellFrame -> {{3, 0}, {0, 0}}, CellMargins -> {{52, 10}, {8, 8}}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, CellLabelMargins -> {{3, Inherited}, {Inherited, Inherited}}, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", FormatType -> InputForm, CounterIncrements -> "Output", Background -> RGBColor[0.784314, 0.54902, 0]], Cell[ StyleData["Output", "Presentation"], CellFrame -> {{5, 0}, {0, 0}}, CellMargins -> {{74, 10}, {12, 5}}, CellFrameMargins -> {{10, 10}, {14, 14}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Output", "Condensed"], CellMargins -> {{40, Inherited}, {4, 1}}], Cell[ StyleData["Output", "Printout"], CellMargins -> {{44, 0}, {6, 2}}, Background -> GrayLevel[0.900008]]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Message"], CellMargins -> {{62, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "OutputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, FormatType -> InputForm, CounterIncrements -> "Message", StyleMenuListing -> None, FontColor -> RGBColor[1, 0, 0]], Cell[ StyleData["Message", "Presentation"], CellMargins -> {{86, 20}, {10, 10}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Message", "Condensed"], CellMargins -> {{50, Inherited}, {Inherited, Inherited}}], Cell[ StyleData["Message", "Printout"], CellMargins -> {{54, Inherited}, {Inherited, Inherited}}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Print"], CellMargins -> {{62, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, FormatType -> InputForm, CounterIncrements -> "Print", StyleMenuListing -> None], Cell[ StyleData["Print", "Presentation"], CellMargins -> {{86, 20}, {4, 4}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Print", "Condensed"], CellMargins -> {{50, Inherited}, {Inherited, Inherited}}], Cell[ StyleData["Print", "Printout"], CellMargins -> {{54, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Graphics"], CellMargins -> {{62, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, FormatType -> InputForm, CounterIncrements -> "Graphics", StyleMenuListing -> None], Cell[ StyleData["Graphics", "Presentation"], CellMargins -> {{86, 20}, {8, 8}}, FontSize -> 18], Cell[ StyleData["Graphics", "Condensed"], CellMargins -> {{52, Inherited}, {Inherited, Inherited}}, ImageSize -> {175, 175}], Cell[ StyleData["Graphics", "Printout"], CellMargins -> {{54, Inherited}, {Inherited, Inherited}}, ImageSize -> {250, 250}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["CellLabel"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 11, FontWeight -> "Bold", FontColor -> RGBColor[0.571389, 0.19675, 0.570504]], Cell[ StyleData["CellLabel", "Presentation"], FontSize -> 12], Cell[ StyleData["CellLabel", "Condensed"], FontSize -> 8], Cell[ StyleData["CellLabel", "Printout"], FontSize -> 8, FontColor -> GrayLevel[0]]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell["Unique Styles", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Author"], ShowCellBracket -> False, CellMargins -> {{10, 4}, {2, 10}}, LineSpacing -> {1, 5}, FontSize -> 16, FontSlant -> "Italic"], Cell[ StyleData["Author", "Presentation"], CellMargins -> {{15, 10}, {4, 16}}, LineSpacing -> {1, 5}, ParagraphSpacing -> {0, 12}, FontSize -> 24], Cell[ StyleData["Author", "Condensed"], CellMargins -> {{8, 10}, {1, 4}}, LineSpacing -> {1, 1}, ParagraphSpacing -> {0, 4}, FontSize -> 12], Cell[ StyleData["Author", "Printout"], CellMargins -> {{9, 0}, {4, 12}}, ParagraphSpacing -> {0, 6}, FontSize -> 14]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Copyright"], ShowCellBracket -> False, CellMargins -> {{10, 10}, {40, 2}}, FontFamily -> "Helvetica", FontSize -> 9], Cell[ StyleData["Copyright", "Presentation"], CellMargins -> {{15, 10}, {50, 4}}, LineSpacing -> {1, 5}, FontSize -> 14], Cell[ StyleData["Copyright", "Condensed"], CellMargins -> {{8, 10}, {12, 1}}, LineSpacing -> {1, 2}, FontSize -> 9], Cell[ StyleData["Copyright", "Printout"], CellMargins -> {{9, 0}, {72, 4}}, FontSize -> 7]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Example"], CellMargins -> {{12, 10}, {5, 12}}, LineSpacing -> {1, 3}, ParagraphSpacing -> {0, 12}, CounterIncrements -> "Example", FontFamily -> "Times", FontWeight -> "Bold"], Cell[ StyleData["Example", "Presentation"], CellMargins -> {{18, 10}, {8, 20}}, LineSpacing -> {1, 5}, ParagraphSpacing -> {0, 12}, FontSize -> 18], Cell[ StyleData["Example", "Condensed"], CellMargins -> {{8, 10}, {4, 8}}, LineSpacing -> {1, 1}, ParagraphSpacing -> {0, 4}], Cell[ StyleData["Example", "Printout"], CellMargins -> {{9, 0}, {4, 10}}, ParagraphSpacing -> {0, 6}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Definition"], CellFrame -> {{3, 0}, {0, 0}}, CellMargins -> {{52, 10}, {8, 8}}, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, ShowStringCharacters -> True, CounterIncrements -> "Definition", FontFamily -> "Helvetica", FontWeight -> "Bold", FontColor -> GrayLevel[1], Background -> RGBColor[0.2, 0.700008, 0.700008]], Cell[ StyleData["Definition", "Presentation"], CellFrame -> {{5, 0}, {0, 0}}, CellMargins -> {{74, 10}, {8, 12}}, CellFrameMargins -> {{10, 10}, {14, 14}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Definition", "Condensed"], CellMargins -> {{40, 10}, {1, 4}}], Cell[ StyleData["Definition", "Printout"], CellMargins -> {{44, 0}, {2, 6}}, Hyphenation -> True, Background -> GrayLevel[0.6]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Theorem"], CellFrame -> {{3, 0}, {0, 0}}, CellMargins -> {{52, 10}, {8, 8}}, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, ShowStringCharacters -> True, CounterIncrements -> "Theorem", FontFamily -> "Helvetica", FontWeight -> "Bold", FontColor -> GrayLevel[1], Background -> RGBColor[0.571389, 0.19675, 0.570504]], Cell[ StyleData["Theorem", "Presentation"], CellFrame -> {{5, 0}, {0, 0}}, CellMargins -> {{74, 10}, {8, 12}}, CellFrameMargins -> {{10, 10}, {14, 14}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Theorem", "Condensed"], CellMargins -> {{40, 10}, {1, 4}}], Cell[ StyleData["Theorem", "Printout"], CellMargins -> {{44, 0}, {2, 6}}, Hyphenation -> True, Background -> GrayLevel[0.4]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ExerciseMain"], CellFrame -> {{6, 0}, {0, 1}}, CellMargins -> {{12, Inherited}, {4, 20}}, CellGroupingRules -> {"SectionGrouping", 30}, PageBreakBelow -> False, CellFrameColor -> RGBColor[0.571389, 0.19675, 0.570504], LineSpacing -> {1, 7}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold", FontColor -> RGBColor[0.571389, 0.19675, 0.570504]], Cell[ StyleData["ExerciseMain", "Presentation"], CellFrame -> {{8, 0}, {0, 2}}, CellMargins -> {{18, 10}, {12, 32}}, CellFrameMargins -> {{10, 10}, {14, 14}}, LineSpacing -> {1, 2}, FontSize -> 24, FontTracking -> "Condensed"], Cell[ StyleData["ExerciseMain", "Condensed"], CellMargins -> {{8, Inherited}, {2, 12}}, FontSize -> 12], Cell[ StyleData["ExerciseMain", "Printout"], CellMargins -> {{9, 0}, {2, 50}}, CellFrameColor -> GrayLevel[0.500008], FontSize -> 14, FontTracking -> "Plain", FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Exercise"], CellDingbat -> "\[FilledDownTriangle]", CellMargins -> {{23, Inherited}, {4, 18}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 7}, CounterIncrements -> "Subsubsection", FontFamily -> "Times", FontSize -> 13, FontWeight -> "Bold", FontColor -> RGBColor[0.571389, 0.19675, 0.570504]], Cell[ StyleData["Exercise", "Presentation"], CellMargins -> {{28, 10}, {10, 34}}, LineSpacing -> {1, 0}, FontSize -> 22], Cell[ StyleData["Exercise", "Condensed"], CellMargins -> {{17, Inherited}, {2, 12}}, FontSize -> 10], Cell[ StyleData["Exercise", "Printout"], CellFrame -> {{0, 0}, {0.5, 0}}, CellDingbat -> None, CellMargins -> {{9, 0}, {6, 20}}, Hyphenation -> True, FontSize -> 11, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ExerciseText"], CellMargins -> {{62, 10}, {5, 5}}, LineSpacing -> {1, 3}, ParagraphSpacing -> {0, 8}, CounterIncrements -> "ExerciseText", FontFamily -> "Times"], Cell[ StyleData["ExerciseText", "Presentation"], CellMargins -> {{100, 10}, {8, 8}}, LineSpacing -> {1, 5}, ParagraphSpacing -> {0, 12}, FontSize -> 18], Cell[ StyleData["ExerciseText", "Condensed"], CellMargins -> {{52, 10}, {2, 2}}, LineSpacing -> {1, 1}, ParagraphSpacing -> {0, 4}], Cell[ StyleData["ExerciseText", "Printout"], CellMargins -> {{54, 0}, {4, 4}}, Hyphenation -> True, ParagraphSpacing -> {0, 6}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Solution"], CellDingbat -> None, CellMargins -> {{23, Inherited}, {4, 18}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 7}, CounterIncrements -> "Subsubsection", FontFamily -> "Times", FontSize -> 13, FontWeight -> "Bold", FontColor -> RGBColor[0.300008, 0, 0.8], Background -> GrayLevel[0.900008]], Cell[ StyleData["Solution", "Presentation"], CellMargins -> {{28, 10}, {10, 34}}, LineSpacing -> {1, 0}, FontSize -> 22], Cell[ StyleData["Solution", "Condensed"], CellMargins -> {{17, Inherited}, {2, 12}}, FontSize -> 10], Cell[ StyleData["Solution", "Printout"], CellFrame -> {{0, 0}, {0.5, 0}}, CellDingbat -> None, CellMargins -> {{9, 0}, {6, 20}}, Hyphenation -> True, FontSize -> 11, FontColor -> GrayLevel[0], Background -> None]}, Open]]}, Open]], Cell[ CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["DisplayFormula"], CellMargins -> {{62, 10}, {2, 10}}, CellHorizontalScrolling -> True, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", ScriptLevel -> 0, SingleLetterItalics -> True, FontFamily -> "Times New Roman", UnderoverscriptBoxOptions -> {LimitsPositioning -> True}], Cell[ StyleData["DisplayFormula", "Presentation"], CellMargins -> {{100, 10}, {8, 16}}, FontSize -> 18], Cell[ StyleData["DisplayFormula", "Condensed"], CellMargins -> {{52, 10}, {2, 10}}, FontSize -> 10], Cell[ StyleData["DisplayFormula", "Printout"], CellMargins -> {{54, 10}, {2, 10}}, FontSize -> 10]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["ChemicalFormula"], CellMargins -> {{62, 10}, {2, 10}}, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", AutoSpacing -> False, ScriptBaselineShifts -> {0.6, Automatic}, ScriptLevel -> 1, SingleLetterItalics -> False, ZeroWidthTimes -> True], Cell[ StyleData["ChemicalFormula", "Presentation"], CellMargins -> {{100, 10}, {8, 12}}, FontSize -> 18], Cell[ StyleData["ChemicalFormula", "Condensed"], CellMargins -> {{52, 10}, {2, 10}}, FontSize -> 10], Cell[ StyleData["ChemicalFormula", "Printout"], CellMargins -> {{54, 10}, {2, 10}}, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Program"], CellMargins -> {{12, 10}, {Inherited, 6}}, Hyphenation -> False, LanguageCategory -> "Formula", FontFamily -> "Courier"], Cell[ StyleData["Program", "Presentation"], CellMargins -> {{20, 30}, {4, 4}}, FontSize -> 18], Cell[ StyleData["Program", "Condensed"], CellMargins -> {{8, 10}, {Inherited, 4}}, FontSize -> 9.5], Cell[ StyleData["Program", "Printout"], CellMargins -> {{9, 0}, {Inherited, 4}}, FontSize -> 9.5]}, Closed]]}, Open]], 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"], CellMargins -> {{62, 10}, {Inherited, Inherited}}, CellFrameLabels -> {{None, Cell[ TextData["(", CounterBox["Section"], ".", CounterBox["NumberedEquation"], ")"]]}, {Inherited, None}}, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, CounterIncrements -> "NumberedEquation", FormatTypeAutoConvert -> False, FontColor -> RGBColor[1, 1, 0], Background -> RGBColor[0, 0, 0.501961]], Cell[ StyleData["NumberedEquation", "Presentation"], CellMargins -> {{100, 10}, {6, 8}}, FontSize -> 18], Cell[ StyleData["NumberedEquation", "Condensed"], CellMargins -> {{52, 10}, {Inherited, Inherited}}], Cell[ StyleData["NumberedEquation", "Printout"], CellMargins -> {{54, 0}, {Inherited, Inherited}}]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["NumberedFigure"], CellMargins -> {{62, 145}, {Inherited, Inherited}}, CellFrameLabels -> {{None, None}, { Cell[ TextData[{"Figure ", CounterBox["NumberedFigure"]}]], None}}, CounterIncrements -> "NumberedFigure", ImageMargins -> {{43, Inherited}, {Inherited, 0}}, FormatTypeAutoConvert -> False], Cell[ StyleData["NumberedFigure", "Presentation"], CellMargins -> {{100, 145}, {8, 6}}, FontSize -> 18], Cell[ StyleData["NumberedFigure", "Condensed"]], Cell[ StyleData["NumberedFigure", "Printout"]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["NumberedTable"], CellMargins -> {{62, 145}, {Inherited, Inherited}}, CellFrameLabels -> {{None, None}, { Cell[ TextData[{"Table ", CounterBox["NumberedTable"]}]], None}}, TextAlignment -> Center, CounterIncrements -> "NumberedTable", FormatTypeAutoConvert -> False], Cell[ StyleData["NumberedTable", "Presentation"], CellMargins -> {{100, 145}, {8, 8}}, FontSize -> 18], Cell[ StyleData["NumberedTable", "Condensed"]], Cell[ StyleData["NumberedTable", "Printout"]]}, Closed]], Cell["Styles for Headers and Footers", "Author"], Cell[ StyleData["Header"], CellMargins -> {{0, 0}, {4, 1}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 9, FontSlant -> "Italic"], Cell[ StyleData["Footer"], CellMargins -> {{0, 0}, {0, 4}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 6], Cell[ StyleData["PageNumber"], CellMargins -> {{0, 0}, {4, 1}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 9, FontWeight -> "Bold"]}, Open]], Cell[ CellGroupData[{ 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[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["Hyperlink", "Presentation"], FontSize -> 16], Cell[ StyleData["Hyperlink", "Condensed"], FontSize -> 11], Cell[ StyleData["Hyperlink", "SlideShow"]], Cell[ StyleData["Hyperlink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, 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[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["MainBook", #]}]& )}], Cell[ StyleData["MainBookLink", "Presentation"], FontSize -> 16], Cell[ StyleData["MainBookLink", "Condensed"], FontSize -> 11], Cell[ StyleData["MainBookLink", "SlideShow"]], Cell[ StyleData["MainBookLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AddOnsLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Courier", FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["AddOns", #]}]& )}], Cell[ StyleData["AddOnsLink", "Presentation"], FontSize -> 16], Cell[ StyleData["AddOnsLink", "Condensed"], FontSize -> 11], Cell[ StyleData["AddOnsLink", "SlideShow"]], Cell[ StyleData["AddOnsLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["RefGuideLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Courier", FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["RefGuide", #]}]& )}], Cell[ StyleData["RefGuideLink", "Presentation"], FontSize -> 16], Cell[ StyleData["RefGuideLink", "Condensed"], FontSize -> 11], Cell[ StyleData["RefGuideLink", "SlideShow"]], Cell[ StyleData["RefGuideLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["RefGuideLinkText"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["RefGuide", #]}]& )}], Cell[ StyleData["RefGuideLinkText", "Presentation"], FontSize -> 16], Cell[ StyleData["RefGuideLinkText", "Condensed"], FontSize -> 11], Cell[ StyleData["RefGuideLinkText", "SlideShow"]], Cell[ StyleData["RefGuideLinkText", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GettingStartedLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["GettingStarted", #]}]& )}], Cell[ StyleData["GettingStartedLink", "Presentation"], FontSize -> 16], Cell[ StyleData["GettingStartedLink", "Condensed"], FontSize -> 11], Cell[ StyleData["GettingStartedLink", "SlideShow"]], Cell[ StyleData["GettingStartedLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemosLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["Demos", #]}]& )}], Cell[ StyleData["DemosLink", "SlideShow"]], Cell[ StyleData["DemosLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TourLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["Tour", #]}]& )}], Cell[ StyleData["TourLink", "SlideShow"]], Cell[ StyleData["TourLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OtherInformationLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["OtherInformation", #]}]& )}], Cell[ StyleData["OtherInformationLink", "Presentation"], FontSize -> 16], Cell[ StyleData["OtherInformationLink", "Condensed"], FontSize -> 11], Cell[ StyleData["OtherInformationLink", "SlideShow"]], Cell[ StyleData["OtherInformationLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["MasterIndexLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["MasterIndex", #]}]& )}], Cell[ StyleData["MasterIndexLink", "SlideShow"]], Cell[ StyleData["MasterIndexLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ 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], FrontEnd`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]}]& )}]}, Closed]], Cell[ CellGroupData[{ Cell["Slide Show Styles", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["SlideShowNavigationBar"], Editable -> False, CellFrame -> True, CellMargins -> {{0, 0}, {3, 3}}, CellElementSpacings -> {"CellMinHeight" -> 0.8125}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> False, CellFrameColor -> GrayLevel[1], CellFrameLabelMargins -> False, TextAlignment -> Center, CounterIncrements -> "SlideShowNavigationBar", StyleMenuListing -> None, FontSize -> 10, Magnification -> 1, Background -> GrayLevel[0.8], GridBoxOptions -> { BaselinePosition -> Center, GridBoxAlignment -> { "Columns" -> { Center, Center, Center, Center, Center, Center, Right, { Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> { "Columns" -> {3.5, 3.5, 3.5, 3.5, 13, 5, {4}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["SlideShowNavigationBar", "Presentation"]], Cell[ StyleData["SlideShowNavigationBar", "SlideShow"], Deletable -> False, ShowCellBracket -> False, CellMargins -> {{-1, -1}, {-1, -1}}, PageBreakAbove -> True, CellFrameMargins -> {{1, 1}, {0, 0}}], Cell[ StyleData["SlideShowNavigationBar", "Printout"], CellMargins -> {{18, 4}, {4, 4}}, LineSpacing -> {1, 3}, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideShowSection"], CellFrame -> {{0, 0}, {0, 0.5}}, CellMargins -> {{0, 0}, {10, 0}}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, CellFrameMargins -> {{12, 4}, {6, 12}}, InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 18, FontWeight -> "Plain", FontColor -> GrayLevel[1], Background -> RGBColor[0.408011, 0.440726, 0.8]], Cell[ StyleData["SlideShowSection", "Presentation"], CellFrameMargins -> {{18, 10}, {10, 16}}, FontSize -> 27], Cell[ StyleData["SlideShowSection", "SlideShow"], ShowCellBracket -> False, PageBreakAbove -> True], Cell[ StyleData["SlideShowSection", "Printout"], CellMargins -> {{18, 30}, {0, 30}}, CellFrameMargins -> 5, FontSize -> 14]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideHyperlink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontSize -> 26, FontColor -> GrayLevel[0.400015], ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonMargins -> 0.5, ButtonMinHeight -> 0.85, ButtonNote -> None}], Cell[ StyleData["SlideHyperlink", "Presentation"], CellMargins -> {{10, 10}, {8, 12}}, FontSize -> 36], Cell[ StyleData["SlideHyperlink", "SlideShow"]], Cell[ StyleData["SlideHyperlink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideTOCLink"], CellMargins -> {{24, Inherited}, {Inherited, Inherited}}, StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Helvetica", ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonMargins -> 1.5, ButtonNote -> ButtonData}], Cell[ StyleData["SlideTOCLink", "Presentation"], CellMargins -> {{35, 10}, {4, 6}}, FontSize -> 18], Cell[ StyleData["SlideTOCLink", "SlideShow"]], Cell[ StyleData["SlideTOCLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideTOC"], CellDingbat -> "\[Bullet]", CellMargins -> {{18, Inherited}, {Inherited, Inherited}}, StyleMenuListing -> None, FontFamily -> "Helvetica"], Cell[ StyleData["SlideTOC", "Presentation"], CellMargins -> {{25, 10}, {8, 6}}, FontSize -> 18], Cell[ StyleData["SlideTOC", "SlideShow"], FontSize -> 14], Cell[ StyleData["SlideTOC", "Printout"], FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]]}, Closed]]}, Open]]}, Visible -> False, FrontEndVersion -> "7.0 for Microsoft Windows (32-bit) (November 10, 2008)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 58, 0, 61, "Title"], Cell[CellGroupData[{ Cell[628, 24, 48, 0, 67, "Section"], Cell[679, 26, 2241, 63, 317, "Text"], Cell[2923, 91, 2356, 77, 227, "Text"], Cell[5282, 170, 865, 24, 209, "Input"], Cell[CellGroupData[{ Cell[6172, 198, 48, 0, 64, "Subsection"], Cell[6223, 200, 546, 17, 47, "Text"], Cell[6772, 219, 508, 12, 65, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[7317, 236, 50, 0, 64, "Subsection"], Cell[7370, 238, 568, 19, 47, "Text"], Cell[7941, 259, 334, 7, 65, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[8324, 272, 49, 0, 67, "Section"], Cell[8376, 274, 809, 20, 83, "Text"], Cell[CellGroupData[{ Cell[9210, 298, 48, 0, 64, 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