(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 34375, 958]*) (*NotebookOutlinePosition[ 35494, 994]*) (* CellTagsIndexPosition[ 35450, 990]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Creating Documents", "Title", Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True], Cell[TextData[{ "Sean Mauch\nsean@caltech.edu\n", ButtonBox["http://www.its.caltech.edu/~sean", ButtonData:>{ URL[ "http://www.its.caltech.edu/~sean"], None}, ButtonStyle->"Hyperlink"], "\n", "This work is distributed under the GNU FDL. See ", ButtonBox["license.nb ", ButtonData:>{"license.nb", None}, ButtonStyle->"Hyperlink"], "for details." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Style Sheets", "Section"], Cell[TextData[{ "Open a new notebook and use the ", StyleBox["Format\[Rule]Style Sheet\[Rule]Other...", FontWeight->"Bold"], " to change to the SeanDefault.nb style sheet.\nIn your document, create \ the same section structure as this one. In your document, reproduce all the \ cells in this document that do not have a Light Bulb Dingbat. Cells with a \ Light Bulb will contain explainations and hints." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1] }, Closed]], Cell[CellGroupData[{ Cell["Greek Letters and Built-in Constants", "Section"], Cell["\<\ In this section we will introduce typing Greek letters and built in \ constants using keyboard shortcuts. Use the BasicInput palette for \ formatting as indicated. The centered formulas are Display Formulas.\ \>", "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], " there are four ways of inputing special characters. \n1) Click a button \ in a palette.\n2) Type an escape key shortcut. For \[Beta] the shortcts are \ \[EscapeKey]beta\[EscapeKey] and \[EscapeKey]b\[EscapeKey].\n3) Type a ", Cell[BoxData[ \(TraditionalForm\`\(L\_A\) \(T\_E\) X\)]], " symbol between escape keys, like \[EscapeKey]\\beta\[EscapeKey].\n4) Type \ the ", StyleBox["Mathematica", FontSlant->"Italic"], " name for the symbol, like \\[Beta\[InvisibleSpace]]. When you finish \ typing the name, it will magically turn into the symbol.\nTry the following \ ways of writing \[Beta] in a Display Formula.\n\[EscapeKey]beta\[EscapeKey] \ \[SpaceKey] \[EscapeKey]b\[EscapeKey] \[SpaceKey] \[EscapeKey]\\beta\ \[EscapeKey] \[SpaceKey] \\[Beta\[InvisibleSpace]]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm\`\[Beta]\ \[Beta]\ \[Beta]\ \[Beta]\)], "DisplayFormula"], Cell["Here is a table of escape key shortcuts for Greek letters.", "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[Cell[BoxData[ FormBox[GridBox[{ {"\[Alpha]", "\[EscapeKey]a\[EscapeKey]", "\[Nu]", "\[EscapeKey]n\[EscapeKey]", "\[CapitalGamma]", "\[EscapeKey]G\[EscapeKey]"}, {"\[Beta]", "\[EscapeKey]b\[EscapeKey]", "\[Xi]", "\[EscapeKey]x\[EscapeKey]", "\[CapitalDelta]", "\[EscapeKey]D\[EscapeKey]"}, {"\[Gamma]", "\[EscapeKey]g\[EscapeKey]", "\[Pi]", "\[EscapeKey]p\[EscapeKey]", "\[CapitalTheta]", "\[EscapeKey]Th\[EscapeKey]"}, {"\[Delta]", "\[EscapeKey]d\[EscapeKey]", "\[Rho]", "\[EscapeKey]r\[EscapeKey]", "\[CapitalLambda]", "\[EscapeKey]L\[EscapeKey]"}, {"\[Epsilon]", "\[EscapeKey]e\[EscapeKey]", "\[Sigma]", "\[EscapeKey]s\[EscapeKey]", "\[CapitalPi]", "\[EscapeKey]P\[EscapeKey]"}, {"\[Zeta]", "\[EscapeKey]z\[EscapeKey]", "\[Tau]", "\[EscapeKey]t\[EscapeKey]", "\[CapitalSigma]", "\[EscapeKey]S\[EscapeKey]"}, {"\[Eta]", "\[EscapeKey]eta\[EscapeKey]", "\[Phi]", "\[EscapeKey]phi\[EscapeKey]", "\[CapitalUpsilon]", "\[EscapeKey]Ui\[EscapeKey]"}, {"\[Theta]", "\[EscapeKey]th\[EscapeKey]", "\[CurlyPhi]", "\[EscapeKey]cphi\[EscapeKey]", "\[CapitalPhi]", "\[EscapeKey]Phi\[EscapeKey]"}, {"\[Kappa]", "\[EscapeKey]k\[EscapeKey]", "\[Chi]", "\[EscapeKey]c\[EscapeKey]", "\[CapitalChi]", "\[EscapeKey]C\[EscapeKey]"}, {"\[Lambda]", "\[EscapeKey]l\[EscapeKey]", "\[Psi]", "\[EscapeKey]y\[EscapeKey]", "\[CapitalPsi]", "\[EscapeKey]Y\[EscapeKey]"}, {"\[Mu]", "\[EscapeKey]m\[EscapeKey]", "\[Omega]", "\[EscapeKey]o\[EscapeKey]", "\[CapitalOmega]", "\[EscapeKey]O\[EscapeKey]"} }, ColumnAlignments->{Left}], TraditionalForm]]]], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Center, TextJustification->0], Cell[TextData[ "\[ControlKey]\[LeftModified]9\[RightModified] sin(\[EscapeKey]th\[EscapeKey] \ + \[EscapeKey]ph\[EscapeKey]) = sin \[SpaceKey] \[EscapeKey]th\[EscapeKey] \ \[SpaceKey] sin \[SpaceKey] \[EscapeKey]phi\[EscapeKey] + cos \[SpaceKey] \ \[EscapeKey]th\[EscapeKey] \[SpaceKey] cos \[SpaceKey] \[EscapeKey]phi\ \[EscapeKey] \[ControlKey]\[LeftModified]0\[RightModified]"], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The addition formula for for sines is ", Cell[BoxData[ \(TraditionalForm \`sin(\[Theta] + \[Phi]) = sin\ \[Theta]\ sin\ \[Phi] + cos\ \[Theta]\ cos\ \[Phi]\)]], "." }], "Text"], Cell[TextData[{ "Below are the typset forms of five ", StyleBox["Mathematica", FontSlant->"Italic"], " constants. Note that the double-struck form of the exponential, \ \[ExponentialE], and the square root of -1, \[ImaginaryI], allow you to \ distinguish between these mathematical constants and the variables, ", Cell[BoxData[ \(TraditionalForm\`e\)]], " and ", Cell[BoxData[ \(TraditionalForm\`i\)]], "." }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[Cell[BoxData[ FormBox[GridBox[{ {"Character", "Input", "Meaning"}, {"\[Pi]", "\[EscapeKey]p\[EscapeKey]", "Pi"}, {"\[ExponentialE]", "\[EscapeKey]ee\[EscapeKey]", "E"}, {"\[Degree]", "\[EscapeKey]deg\[EscapeKey]", "Degree"}, {"\[ImaginaryI]", "\[EscapeKey]ii\[EscapeKey]", "I"}, {"\[Infinity]", "\[EscapeKey]inf\[EscapeKey]", "Infinity"} }, ColumnAlignments->{Left}, RowLines->{True, False}, ColumnLines->True], TraditionalForm]]]], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Center, TextJustification->0], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " \[EscapeKey]ee\[EscapeKey] \[TabKey] \[EscapeKey]ii\[EscapeKey] \ \[EscapeKey]p\[EscapeKey] \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified] = - 1" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm\`\[ExponentialE]\^\(\[ImaginaryI]\ \[Pi]\) = \(-1\)\)], "DisplayFormula"], Cell[TextData[{ "\[EscapeKey]G\[EscapeKey] ( ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " 1 \[TabKey] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] ) = \ ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " \[EscapeKey]p\[EscapeKey] \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TextForm\`\[CapitalGamma] \((1\/2)\) = \@\[Pi]\)], "DisplayFormula"], Cell[TextData[{ "sin(45 \[EscapeKey]deg\[EscapeKey] )= ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " 1 \[TabKey] ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] " }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TextForm\`sin \((45 \[Degree])\) = 1\/\@2\)], "Text", TextAlignment->Center], Cell[TextData[{ "\[ControlKey]\[LeftModified]9\[RightModified] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " \[EscapeKey]inf\[EscapeKey] \[TabKey] \[EscapeKey]inf\[EscapeKey] \ \[ControlKey]\[LeftModified]0\[RightModified] and \ \[ControlKey]\[LeftModified]9\[RightModified] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " 1 \[TabKey] \[EscapeKey]inf\[EscapeKey] \[ControlKey]\[LeftModified]0\ \[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Infinity]\/\[Infinity]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`1\^\[Infinity]\)]], " are indeterminate forms." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Two Dimensional Input", "Section"], Cell[CellGroupData[{ Cell["Subscripts, Superscripts and Fractions", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " has the following control-key sequences for creating two dimensional \ formulas." }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[Cell[BoxData[ FormBox[GridBox[{ {"\[ControlKey]\[LeftModified]6\[RightModified]", \(Superscript\ \(position . \)\)}, {\(\[ControlKey]\[LeftModified] - 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y)\)\^\(2 n - 1\)\)], "DisplayFormula", TextAlignment->Center], Cell[TextData[ "x \[ControlKey]\[LeftModified]/\[RightModified] y \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] + x \[ControlKey]\[LeftModified]/\ \[RightModified] x + y \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm\`x\/y + x\/\(x + y\)\)], "DisplayFormula", TextAlignment->Center], Cell[TextData[{ "x+y \[ControlKey]\[LeftModified]/\[RightModified] z \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] + x \[ControlKey]\[LeftModified]/\ \[RightModified] y \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + \ y \nHighlight ", Cell[BoxData[ \(TraditionalForm\`x\/y + y\)]], "\n\[ControlKey]\[LeftModified]/\[RightModified] z \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm\`\(x + y\)\/z + \(x\/y + y\)\/z\)], "DisplayFormula", TextAlignment->Center] }, Closed]], Cell[CellGroupData[{ Cell["Integrals, Sums and Matrices", "Subsection"], Cell[TextData[ "\[EscapeKey]int\[EscapeKey] \[ControlKey]\[LeftModified]-\[RightModified]a \ \[ControlKey]\[LeftModified]5\[RightModified]b \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified] sin \ \[ControlKey]\[LeftModified]6\[RightModified]2\[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified] (x) \[EscapeKey]dd\[EscapeKey] x"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm \`\[Integral]\_a\%b\(\( sin\^2\)(x)\) \[DifferentialD]x\)], "DisplayFormula", TextAlignment->Center], Cell[TextData[ "\[EscapeKey]sum\[EscapeKey] \[ControlKey]\[LeftModified]=\[RightModified]n=1 \ \[ControlKey]\[LeftModified]5\[RightModified]\[EscapeKey]inf\[EscapeKey] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] 1 \[ControlKey]\ \[LeftModified]/\[RightModified] n\[ControlKey]\[LeftModified]6\ \[RightModified]2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = \[EscapeKey]p\ \[EscapeKey] \[ControlKey]\[LeftModified]6\[RightModified]2 \[ControlKey]\ \[LeftModified]/\[RightModified] 6 \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified] "], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm \`\[Sum]\+\(n = 1\)\%\[Infinity] 1\/n\^2 = \[Pi]\^2\/6\)], "DisplayFormula", TextAlignment->Center], Cell[TextData[{ "Select the ", Cell[BoxData[ RowBox[{"(", GridBox[{ {"\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]"} }], ")"}]]], " button from the BasicInput.nb window, or press \[ControlKey]\[ShiftKey]\ \[LeftModified]c\[RightModified]. Use the \[TabKey] to move between entries \ of the matrix. Use the Backspace key to delete a column or a row." }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {"a", "b"}, {"c", "d"} }], ")"}], RowBox[{"(", GridBox[{ {"x"}, {"y"} }], ")"}]}], "=", RowBox[{"(", GridBox[{ {"u"}, {"v"} }], ")"}]}], TraditionalForm]], "DisplayFormula", TextAlignment->Center], Cell[TextData[{ "For the right side of the equation, make a ", Cell[BoxData[ \(TraditionalForm\`2\[Times]2\)]], " matrix. Delete the parentheses that enclose the matrix. Add a left \ bracket before the matrix." }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[ RowBox[{\(H(x)\), "=", RowBox[{"{", GridBox[{ {"1", \(for\ x > 0, \)}, {"0", \(for\ x < 0. \)} }]}]}], TraditionalForm]], "DisplayFormula", TextAlignment->Center], Cell[TextData[ "Start with matrices. Add rows with \[ControlKey]\[LeftModified]\[ReturnKey]\ \[RightModified]; add columns with \[ControlKey]\[LeftModified],\ \[RightModified]. Use the following following LaTeX commands to make the \ ellipses:\n\[EscapeKey]\\cdots\[EscapeKey]\t\t\[CenterEllipsis]\n\[EscapeKey]\ \\vdots\[EscapeKey]\t\t\[VerticalEllipsis]\n\[EscapeKey]\\ddots\[EscapeKey]\t\ \t\[DescendingEllipsis]"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {\(a\_\(1, 1\)\), "\[CenterEllipsis]", \(a\_\(1, n\)\)}, {"\[VerticalEllipsis]", "\[DescendingEllipsis]", "\[VerticalEllipsis]"}, {\(a\_\(n, 1\)\), "\[CenterEllipsis]", \(a\_\(n, n\)\)} }], ")"}], RowBox[{"(", GridBox[{ {\(x\_1\)}, {"\[VerticalEllipsis]"}, {\(x\_n\)} }], ")"}]}], "=", RowBox[{"(", GridBox[{ {\(y\_1\)}, {"\[VerticalEllipsis]"}, {\(y\_n\)} }], ")"}]}], TraditionalForm]], "DisplayFormula", TextAlignment->Center], Cell[TextData[ "1 \[ControlKey]\[LeftModified]/\[RightModified] 2 \[EscapeKey]p\[EscapeKey] \ \[EscapeKey]ii\[EscapeKey] \[EscapeKey]cccint\[EscapeKey] 1\[ControlKey]\ \[LeftModified]/\[RightModified] sin \[SpaceKey] z \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] \[EscapeKey]dd\[EscapeKey]z = 1"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm \`\(1\/\(2 \[Pi]\ \[ImaginaryI]\)\) \(\[CounterClockwiseContourIntegral]\(1\/\(sin\ z\)\) \[DifferentialD]z\) = 1\)], "DisplayFormula", TextAlignment->Center] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Mathematical Symbols", "Section"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " has script and double struck fonts. ", "\n\[EscapeKey]scL\[EscapeKey] [ f ] \[EscapeKey]= = =\[EscapeKey] \ \[EscapeKey]int\[EscapeKey] \[ControlKey]\[LeftModified]-\[RightModified] 0 \ \[ControlKey]\[LeftModified]5\[RightModified] \[EscapeKey]inf\[EscapeKey] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] f(t) \[EscapeKey]ee\ \[EscapeKey] \[ControlKey]\[LeftModified]6\[RightModified] -s \[SpaceKey] t \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \[EscapeKey]dd\ \[EscapeKey] t" }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The Laplace transform of ", Cell[BoxData[ \(TraditionalForm\`f(t)\)]], " is ", Cell[BoxData[ \(TraditionalForm \`\[ScriptCapitalL][f] \[Congruent] \[Integral]\_0\%\[Infinity]\( f(t)\) \(\[ExponentialE]\^\(\(-s\)\ t\)\) \[DifferentialD]t\)]], "." }], "Text"], Cell[TextData[ "\[EscapeKey]scF\[EscapeKey] [ f ] \[EscapeKey]= = =\[EscapeKey] \ \[EscapeKey]int\[EscapeKey] \[ControlKey]\[LeftModified]-\[RightModified] -\ \[EscapeKey]inf\[EscapeKey] \[ControlKey]\[LeftModified]5\[RightModified] \ \[EscapeKey]inf\[EscapeKey] \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified] f(x) \[EscapeKey]ee\[EscapeKey] \ \[ControlKey]\[LeftModified]6\[RightModified] -\[EscapeKey]ii\[EscapeKey] \ \[SpaceKey] \[EscapeKey]o\[EscapeKey] \[SpaceKey] x \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] \[EscapeKey]dd\[EscapeKey] x"], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The Fourier transform of ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], " can be defined ", Cell[BoxData[ \(TraditionalForm \`\[ScriptCapitalF][f] \[Congruent] \(1\/\(2 \[Pi]\)\) \(\[Integral]\_\(-\[Infinity]\)\%\[Infinity]\ \(f(x)\)\ \(\[ExponentialE]\^\(\(-\[ImaginaryI]\)\ \[Omega]\ x\)\) \[DifferentialD]x\)\)]], "." }], "Text"], Cell[TextData[ "\[EscapeKey]dsZ\[EscapeKey]; \[EscapeKey]dsR\[EscapeKey]; \[EscapeKey]dsC\ \[EscapeKey]."], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The set of integers is ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalZ]\)]], "; the set of real numbers is \[DoubleStruckCapitalR]; the set of complex \ numbers is \[DoubleStruckCapitalC]." }], "Text"], Cell[BoxData[ \(TraditionalForm \`\[Integral]\_\(- \[Infinity]\)\%\[Infinity]\( \[ExponentialE]\^\(\[ImaginaryI]\ \[Omega]\ x\)\/\(x\^2 + 1 \)\) \[DifferentialD]x = \[Pi]\ \[ExponentialE]\^\(-\( | \[Omega] | \)\)\ \ \ \ for\ \[Omega] \[Element] \[DoubleStruckCapitalR]\)], "DisplayFormula", TextAlignment->Center], Cell[TextData[ "\[EscapeKey]dsR\[EscapeKey] \[ControlKey]\[LeftModified]6\[RightModified]+\ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \[EscapeKey]un\ \[EscapeKey] \[EscapeKey]dsR\[EscapeKey] \[ControlKey]\[LeftModified]6\ \[RightModified]-\[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = \ \[EscapeKey]dsR\[EscapeKey] \[EscapeKey]\\\[EscapeKey] {0}"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TextForm \`\(\[DoubleStruckCapitalR]\^+\) \[Union] \(\[DoubleStruckCapitalR]\^-\) = \[DoubleStruckCapitalR]\[Backslash]{0}\)], "DisplayFormula"], Cell[TextData[ "\[EscapeKey]dsR\[EscapeKey] \[ControlKey]\[LeftModified]6\[RightModified]+\ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \[EscapeKey]inter\ \[EscapeKey] \[EscapeKey]dsR\[EscapeKey] \[ControlKey]\[LeftModified]6\ \[RightModified]-\[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = \ \[EscapeKey]es\[EscapeKey]"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TextForm \`\(\[DoubleStruckCapitalR]\^+\) \[Intersection] \(\[DoubleStruckCapitalR]\^-\) = \[EmptySet]\)], "DisplayFormula"], Cell[TextData[ "\[EscapeKey]dd\[EscapeKey] \[ControlKey]\[LeftModified]/\[RightModified] \ \[EscapeKey]dd\[EscapeKey] x f(u,v)= \[EscapeKey]pd\[EscapeKey] f \ \[ControlKey]\[LeftModified]/\[RightModified] \[EscapeKey]pd\[EscapeKey] u \ \[EscapeKey]pd\[EscapeKey] u \[ControlKey]\[LeftModified]/\[RightModified] \ \[EscapeKey]pd\[EscapeKey] x + \[EscapeKey]pd\[EscapeKey] f \[ControlKey]\ \[LeftModified]/\[RightModified] \[EscapeKey]pd\[EscapeKey] v \[EscapeKey]pd\ \[EscapeKey] v \[ControlKey]\[LeftModified]/\[RightModified] \[EscapeKey]pd\ \[EscapeKey] x \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] ."], "Text", CellDingbat->"\[LightBulb]"], Cell["The chain rule is,", "Text"], Cell[BoxData[ \(TraditionalForm \`\(\[DifferentialD]\/\[DifferentialD]x\) \(f(u, v)\) = \(\[PartialD]f\/\[PartialD]u\) \[PartialD]u\/\[PartialD]x + \(\[PartialD]f\/\[PartialD]v\) \(\[PartialD]v\/\[PartialD]x . \)\)], "DisplayFormula"], Cell[TextData[ "lim \[ControlKey]\[LeftModified]=\[RightModified] z \[EscapeKey]->\ \[EscapeKey] 0 \[ControlKey]\[LeftModified]6\[RightModified] + \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified] \[EscapeKey]ee\[EscapeKey] \[ControlKey]\ \[LeftModified]6\[RightModified] -1/z \[ControlKey]\[LeftModified]6\ \[RightModified] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = 0"], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm \`lim\+\(z \[Rule] \(0\^+\)\)\ \[ExponentialE]\^\(\(-1\)/z\^2\) = 0\)], "DisplayFormula", TextAlignment->Center] }, Closed]], Cell[CellGroupData[{ Cell["Using Invisible Space to Force Formatting", "Section"], Cell[TextData[ "If you type a single character in an inline formula, it will have italic \ face. If you type two characters in a row, they will have plain face. You \ can force an italic face by putting an invisible space, (\[EscapeKey]\ \[SpaceKey]\[EscapeKey]), or an invisible comma, (\[EscapeKey],\[EscapeKey]), \ between the characters"], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[ "\[ControlKey]\[LeftModified]9\[RightModified] x \[EscapeKey]\[SpaceKey]\ \[EscapeKey] y \[ControlKey]\[LeftModified]0\[RightModified]"], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "Consider a curve in the ", Cell[BoxData[ \(TraditionalForm\`x\[VeryThinSpace]y\)]], " plane." }], "Text"], Cell[TextData[ "\[EscapeKey]D\[EscapeKey] \[SpaceKey] \[EscapeKey]u\[EscapeKey] \ \[EscapeKey]= = =\[EscapeKey] \[EscapeKey]del\[EscapeKey] \[EscapeKey].\ \[EscapeKey] ( \[EscapeKey]del\[EscapeKey] \[SpaceKey] u )\n\[EscapeKey]D\ \[EscapeKey] \[SpaceKey] \[EscapeKey]phi\[EscapeKey] = \[EscapeKey]phi\ \[EscapeKey] \[ControlKey]\[LeftModified]-\[RightModified] x \[EscapeKey],\ \[EscapeKey] x \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + \ \[EscapeKey]phi\[EscapeKey] \[ControlKey]\[LeftModified]-\[RightModified] y \ \[EscapeKey],\[EscapeKey] y \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified]"], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The Laplacian is ", Cell[BoxData[ \(TraditionalForm \`\[CapitalDelta]\ u \[Congruent] \[Del]\(\[CenterDot]\((\[Del]\ u)\)\)\)]], ". In 2D rectangular coordinates it is ", Cell[BoxData[ \(TraditionalForm \`\[CapitalDelta]\ \[Phi] = \[Phi]\_\(x\[InvisibleComma] x\) + \[Phi]\_\(y\[InvisibleComma] y\)\)]], "." }], "Text"], Cell[TextData[{ "Within inline formulas,", StyleBox[" Mathematica", FontSlant->"Italic"], " will not let you use the bottom position with words that it recognizes as \ functions, like lim and max. To force this, follow the word with an \ invisible space.\nlim \[EscapeKey]is\[EscapeKey] \ \[ControlKey]\[LeftModified]=\[RightModified] z \[EscapeKey]->\[EscapeKey] 0 \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] sin \[SpaceKey] z \ ``select ", Cell[BoxData[ \(TraditionalForm\`sin\ z\)]], "'' \[ControlKey]\[LeftModified]/\[RightModified] z \[ControlKey]\ \[LeftModified]\[SpaceKey]\[RightModified] \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified] = 0" }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The limit is ", Cell[BoxData[ \(TraditionalForm \`\(lim\[InvisibleSpace]\)\+\(z \[Rule] 0\)\ \(sin\ z\)\/z = 1\)]] }], "Text", TextAlignment->Left, TextJustification->0], Cell[TextData[{ "Ordinarily, ", StyleBox["Mathematica", FontSlant->"Italic"], " will not let you use the top and bottom positions with sums in inline \ formulas. To force this, follow the sum with an invisible space and select \ both the sum and the invisible space. Then use the top or bottom position as \ usual.\n\[EscapeKey]z\[EscapeKey] (2) = \[EscapeKey]sum\[EscapeKey] \ \[EscapeKey]sum\[EscapeKey] \[ControlKey]\[LeftModified].\[RightModified] \ \[ControlKey]\[LeftModified].\[RightModified] \[ControlKey]\[LeftModified]=\ \[RightModified] n = 1 \[ControlKey]\[LeftModified]5\[RightModified]\ \[EscapeKey]inf\[EscapeKey] \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified] 1 \[ControlKey]\[LeftModified]/\[RightModified] n\ \[ControlKey]\[LeftModified]6\[RightModified]2 \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified] \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified] = \[EscapeKey]p\[EscapeKey] \[ControlKey]\[LeftModified]6\ \[RightModified]2 \[ControlKey]\[LeftModified]/\[RightModified] 6 \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] " }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The Riemann zeta function of 2 is ", Cell[BoxData[ \(TraditionalForm \`\[Zeta](2) = \(\(\(\[Sum]\[InvisibleSpace]\)\+\(n = 1\)\%\[Infinity]\) 1\/n\^2 = \[Pi]\^2\/6\)\)]], "." }], "Text", TextAlignment->Left, TextJustification->0], Cell[TextData[{ "In order to create the display formula below, you have to put an invisible \ space, \[EscapeKey]is\[EscapeKey], between ] and its subscript/superscript. \ First try it without the invisible space. The reason ", StyleBox["Mathematica", FontSlant->"Italic"], " behaves this way is that it uses braces for functions, (like Sin[x]). \n\ 5[sin \[SpaceKey] \[EscapeKey]th\[EscapeKey] ] \[EscapeKey]is\[EscapeKey] \ \[ControlKey]\[LeftModified]-\[RightModified] 0 \[ControlKey]\[LeftModified]5\ \[RightModified] \[EscapeKey]p\[EscapeKey]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm\`\(5\ [sin\ \[Theta]]\[InvisibleSpace]\)\_0\%\[Pi]\)], "DisplayFormula", TextAlignment->Center] }, Closed]], Cell[CellGroupData[{ Cell["Alignment", "Section"], Cell[CellGroupData[{ Cell["A Sequence of Left, Right or Center Aligned Equations", "Subsection"], Cell["\<\ By default the alignment in GridBox is center. You can change this \ by showing the expression and changing the ColumnAlignments option. In the \ two display formulas below, the ColumnAlignments are the default and \ left.\ \>", "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[ RowBox[{\(f \((x)\)\), "=", RowBox[{"{", GridBox[{ {"0", \(for\ x < 0, \)}, {\(x \((1 - x)\)\), \(for\ 0 < x < 1, \)}, {"0", \(for\ 1 < x, \)} }]}]}], TextForm]], "DisplayFormula"], Cell[BoxData[ FormBox[ RowBox[{\(f \((x)\)\), "=", RowBox[{"{", GridBox[{ {"0", \(for\ x < 0, \)}, {\(x \((1 - x)\)\), \(for\ 0 < x < 1, \)}, {"0", \(for\ 1 < x, \)} }, ColumnAlignments->{Left}]}]}], TextForm]], "DisplayFormula"] }, Closed]], Cell[CellGroupData[{ Cell["Aligning by a Character", "Subsection"], Cell["\<\ In the two display formulas below, the ColumnAlignments are the \ default and \".\".\ \>", "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[GridBox[{ {"48.32"}, {"765.1"}, {"7.1234"} }], TextForm]], "DisplayFormula"], Cell[BoxData[ FormBox[GridBox[{ {"48.32"}, {"765.1"}, {"7.1234"} }, ColumnAlignments->{"."}], TextForm]], "DisplayFormula"], Cell["\<\ The display formula below was created by setting ColumnAlignments \ to \"=\".\ \>", "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[GridBox[{ { \(\[PartialD]f\/\[PartialD]x = \(\[PartialD]\/\[PartialD]x\) \(\[Integral]\_0\%1 \((p \((t\ x, t\ y)\) x + q \((t\ x, t\ y)\) y)\) \[DifferentialD]t\)\)}, { \( = \[Integral]\_0\%1 \((p \((t\ x, t\ y)\) + \(p\_x\) \((t\ x, t\ y)\) t\ x + \(q\_x\) \((t\ x, t\ y)\) t\ y)\) \[DifferentialD]t\)}, { \( = \[Integral]\_0\%1 \((p \((t\ x, t\ y)\) + \(p\_x\) \((t\ x, t\ y)\) t\ x + \(p\_y\) \((t\ x, t\ y)\) t\ y)\) \[DifferentialD]t\)}, { \( = \[Integral]\_0\%1\(\[DifferentialD]\/\[DifferentialD]t\) \((p \((t\ x, t\ y)\) t)\) \[DifferentialD]t\)}, {\( = \((p \((t\ x, t\ y)\) t)\) |\_0\%1\)}, {\(\( = p \((x, y)\)\), \)} }, ColumnAlignments->{"="}], TextForm]], "DisplayFormula"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Importing Graphics", "Section"], Cell[TextData[{ "Select ", StyleBox["File\[Rule]Open", FontWeight->"Bold"], ". Change the ", StyleBox["Files of Type", FontWeight->"Bold"], " field to ", StyleBox["Encapsulated Postscript", FontWeight->"Bold"], ". (This will make it easier to find the file for which we are looking.) \ Open the file ", StyleBox["figure.eps", FontWeight->"Bold"], ". ", StyleBox["Mathematica", FontSlant->"Italic"], " will open a new notebook that contains one cell. This cell contains the \ figure. Highlight the cell by clicking on the right bracket. Copy the cell \ with ", StyleBox["Edit\[Rule]Copy", FontWeight->"Bold"], " or ", StyleBox["\[ControlKey]\[LeftModified]c\[RightModified]", FontWeight->"Bold"], ". Paste the figure below this cell by clicking the cursor between this \ cell and the cell below to create a horizontal line and then selecting ", StyleBox["Edit\[Rule]Paste", FontWeight->"Bold"], " or ", StyleBox["\[ControlKey]\[LeftModified]v\[RightModified]", FontWeight->"Bold"], "." }], "Text", CellDingbat->"\[LightBulb]", TextJustification->1] }, Closed]], Cell[CellGroupData[{ Cell["Bells and Whistles", "Section"], Cell[TextData[{ "Put a different cell Dingbat on this cell using ", StyleBox["Format\[Rule]Cell Dingbat", FontWeight->"Bold"], ". (You have to select the cell by clicking on the cell bracket first.) \ Put a thin horizontal line above this cell using ", StyleBox["Format\[Rule]Horizontal Lines", FontWeight->"Bold"], ". Change the text justification with ", StyleBox["Format\[Rule]Text Justification\[Rule]Full Justification", FontWeight->"Bold"], ". 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