(************** 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[ 41048, 1261]*) (*NotebookOutlinePosition[ 42163, 1297]*) (* CellTagsIndexPosition[ 42119, 1293]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Documents Using Palettes", "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["Document Structure", "Section"], Cell[TextData[{ "This notebook will guide you through making a typeset document in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Open a new notebook with File\[Rule]New or \ \[ControlKey]\[LeftModified]n\[RightModified]. First we'll give a title to \ the document. In the new notebook select Format\[Rule]Style\[Rule]Title or \ type \[AltKey]\[LeftModified]1\[RightModified]. Then type \"My Document \ Using Palettes\". To center the title, select Format\[Rule]Text Allignment\ \[Rule]Align Center or type \[AltKey]\[LeftModified]r\[RightModified]ac. Now \ save your document as mydocpal.nb." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " notebooks are separated into sections with ", StyleBox["Sections", FontSlant->"Italic"], ", ", StyleBox["Subsections", FontSlant->"Italic"], " and ", StyleBox["Subsubsections", FontSlant->"Italic"], ". You can make a Section by selecting Format\[Rule]Style\[Rule]Section or \ pressing \[AltKey]\[LeftModified]4\[RightModified] and then typing the name \ of the section. By default, Section cells are indicated with a Filled Square \ Cell ", StyleBox["Dingbat", FontSlant->"Italic"], ". (Cell Dingbat's are the symbol in the upper left corner of the cell. \ This cell has a Light Bulb Dingbat.) By default, Subsection cells have a \ Filled Small Square Dingbat; Subsubsections have an Empty Small Square \ Dingbat." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell["\<\ In 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["Text, Inline Formulas and Display Formulas", "Section"], Cell[TextData[ "To write text in a notebook first indicate that the next cell should be a \ text cell and then begin typing. You can choose a text cell in several ways: \ select Format\[Rule]Style\[Rule]Text from the menu bar, select Text from the \ pull-down menu in the toolbar or for Windows, press \[AltKey]\[LeftModified]7\ \[RightModified]."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell["This is a text cell.", "Text"], Cell["\<\ Text cells can be left, center, right or full justified. You can \ select these options through the toolbar or Format pull-down menu on the menu \ bar. The text in the hint cells is full justified.\ \>", "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell["Centered text.", "Text", TextAlignment->Center, TextJustification->0], Cell["Right justified text.", "Text", TextAlignment->Right, TextJustification->0], Cell[TextData[{ "You can mix text and mathematical formulas with ", StyleBox["inline formulas", FontSlant->"Italic"], ". To make an inline formula in a text cell, press \[ControlKey]\ \[LeftModified]9\[RightModified], type the formula, and then press \ \[ControlKey]\[LeftModified]0\[RightModified]. When you press \[ControlKey]\ \[LeftModified]9\[RightModified], a highlighted box will appear. Type the \ formula in this box as you would an input. When you press \[ControlKey]\ \[LeftModified]0\[RightModified], the formula will become unhighlighted and \ the cursor will move the the right of the formula. Type the formula in the \ following text cell with:\n\ \[ControlKey]\[LeftModified]9\[RightModified]sin(x+y)=sin\[SpaceIndicator]x\ \[SpaceIndicator]sin\[SpaceIndicator]y+cos\[SpaceIndicator]x\[SpaceIndicator]\ cos\[SpaceIndicator]y\[ControlKey]\[LeftModified]0\[RightModified]\n(The \ \[SpaceIndicator] character indicates a space.)" }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "The addition formula for for sines is ", Cell[BoxData[ \(TraditionalForm\`sin(x + y) = sin\ x\ sin\ y + cos\ x\ cos\ y\)]], "." }], "Text"], Cell[TextData[{ "Note that if you type a single character, ", StyleBox["Mathematica", FontSlant->"Italic"], " assumes it is a variable and writes it in ", StyleBox["italics", FontSlant->"Italic"], ". If you type two or more characters together, ", StyleBox["Mathematica", FontSlant->"Italic"], " assumes it is a function name or a word and writes it in plain face font. \ The spacing in the formula is automatically adjusted to make it look good. \ Don't over-use spaces; use them sparingly. Below is the expression typed \ without an inline formula. Note how ", StyleBox["Mathematica", FontSlant->"Italic"], " uses formatting and spacing to increase readability of formulas.\nThe \ addition formula for for sines is sin(x+y)=sin x sin y+cos x cos y." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "To make a cell that contains only an inline formula and no surrounding \ text, First make an empty text cell and then start the formula with \ \[ControlKey]\[LeftModified]9\[RightModified]. Pressing \[AltKey]\ \[LeftModified]7\[RightModified] \ \[ControlKey]\[LeftModified]9\[RightModified] and then starting the formula \ will not work. You'll be in regular text mode.\n\[AltKey]\[LeftModified]7\ \[RightModified] \[SpaceKey] ", Cell[BoxData[ FormBox[ FrameBox[ StyleBox["BACKSPACE", FontSize->6], BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " \[ControlKey]\[LeftModified]9\[RightModified]Log\[SpaceIndicator]z=Log|z|+\ i\[SpaceIndicator]Arg\[SpaceIndicator]z\[ControlKey]\[LeftModified]0\ \[RightModified]" }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`Log\ z = Log | z | \(+i\)\ Arg\ z\)]]], "Text"], Cell[TextData[{ "To center the contents of a cell, select Format\[Rule]Text \ Alignment\[Rule]Align Center, click the Center Justify Selection button in \ the toolbar, or type \[AltKey]\[LeftModified]r\[RightModified]ac.\n\[AltKey]\ \[LeftModified]7\[RightModified] \[SpaceKey] ", Cell[BoxData[ FormBox[ FrameBox[ StyleBox["BACKSPACE", FontSize->6], BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " \[ControlKey]\[LeftModified]9\[RightModified]f(x)=x+sin\[SpaceIndicator]x-\ cos(exp\[SpaceIndicator]x)\[ControlKey]\[LeftModified]0\[RightModified] \ \[AltKey]\[LeftModified]r\[RightModified] a c" }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`f(x) = x + sin\ x - cos(exp\ x)\)]]], "Text", TextAlignment->Center], Cell[TextData[{ "If you want to type a formula with no surrounding text, it is best to use \ a ", StyleBox["Display Formula", FontSlant->"Italic"], " cell. Select Format\[Rule]Style\[Rule]DisplayFormula from the menu, \ choose DisplayFormula from the toolbar or press \[AltKey]\[LeftModified]0\ \[RightModified] and type DisplayFormula in the pop-up window. Then type the \ formula as you would an input." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(g \((x, y)\) = tan \((y/x)\)\)], "DisplayFormula"], Cell[TextData[ "The second time you press \[AltKey]\[LeftModified]0\[RightModified], \ DisplayFormula will be shown as the default. You can press \[ReturnKey] to \ accept this. It is common to center Display Formulas."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(sec\ x = 1/cos\ x\)], "DisplayFormula", TextAlignment->Center, TextJustification->0] }, Closed]], Cell[CellGroupData[{ Cell["Using BasicInput.nb", "Section"], Cell[TextData[{ "If the BasicInput palette is not open, open it with File\[Rule]Palettes\ \[Rule]BasicInput. You can see which windows are currently open and switch \ between windows by clicking on Window in the menu bar. In this section we \ will be using BasicInput to write mathematical expressions in inline formulas \ and display formulas. The BasicInput palette contains ", StyleBox["buttons", FontSlant->"Italic"], " that give you two dimensional typset expressions." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[CellGroupData[{ Cell["Subscripts, Superscripts and the Top and Bottom Positions", "Subsection"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " x \[TabKey] y \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " x \[TabKey] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " y \[TabKey] z \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " (x+y) \[TabKey] z \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left], Cell[BoxData[ \(x\^y + x\^\(y\^z\) + \((x + y)\)\^z\)], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\_\[Square]\)\)]], " x \[TabKey] n \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\+\[Square]\)\)]], " x \[TabKey] _ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\&\[Square]\)\)]], " x \[TabKey] ^ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\[FilledSquare]\&_\)]], " x \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\&^\)\)]], " x \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(x\_n + x\+_ + x\&^ + x\&_ + x\&^\)], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[FilledSquare]\&_\)]], " x+y+z \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\+\[Square]\)\)]], " x+y+z \[TabKey] _ \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\(x + y + z\)\&_ + \(x + y + z\)\+_\)], "DisplayFormula"] }, Closed]], Cell[CellGroupData[{ Cell["Fractions and Square Roots", "Subsection"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " x \[TabKey] y \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] ", Cell[BoxData[ \(TraditionalForm\`\(\@\[FilledSquare]\%\[Square]\)\)]], " 5 \[TabKey] 3 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(x\/y + \@5\%3 + \@2\)], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " x \[TabKey] y \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " x \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + y \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " x \[TabKey] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\@\(x\/y\) + \@\(\@x + y\) + \@x\/2\)], "DisplayFormula"] }, Closed]], Cell[CellGroupData[{ Cell["Greek Letters, Built-in Constants and Mathematical Symbols", "Subsection"], Cell[TextData[ "\[ControlKey]\[LeftModified]9\[RightModified]sin(\[Theta] + \[Phi])=sin\ \[SpaceIndicator]\[Theta]\[SpaceIndicator]sin\[SpaceIndicator]\[Phi]+cos\ \[SpaceIndicator]\[Theta]\[SpaceIndicator]cos\[SpaceIndicator]\[Phi]\ \[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[{ Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " \[ExponentialE] \[TabKey] \[ImaginaryI] \[Pi] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = - 1" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\[ExponentialE]\^\(\[ImaginaryI]\ \[Pi]\) = \(-1\)\)], "DisplayFormula"], Cell[TextData[{ "\[CapitalGamma] ( ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " 1 \[TabKey] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] ) = \ ", Cell[BoxData[ \(TraditionalForm\`\@\[FilledSquare]\)]], " \[Pi] \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\[CapitalGamma] \((1\/2)\) = \@\[Pi]\)], "DisplayFormula"], Cell[TextData[{ "sin(45\[Degree])= ", 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[ \(sin \((45 \[Degree])\) = 1\/\@2\)], "DisplayFormula"], Cell[TextData[{ "\[ControlKey]\[LeftModified]9\[RightModified] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " \[Infinity] \[TabKey] \[Infinity] \[ControlKey]\[LeftModified]0\ \[RightModified] and \[ControlKey]\[LeftModified]9\[RightModified] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " 1 \[TabKey] \[Infinity] \[ControlKey]\[LeftModified]0\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Infinity]\/\[Infinity]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`1\^\[Infinity]\)]], " are indeterminate forms." }], "Text"], Cell[TextData[{ "\[Union] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\_\[Square]\)\)]], " S \[TabKey] k = S" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\(\[Union]\ S\_k\) = S\)], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\+\[Square]\)\)]], " lim \[TabKey] n \[Rule] \[Infinity] \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " ( 1 + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " 1 \[TabKey] n \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] ) \ \[TabKey] n \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = \ \[ExponentialE]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(lim\+\(n \[Rule] \[Infinity]\)\((1 + 1\/n)\)\^n = \[ExponentialE]\)], "DisplayFormula"], Cell[TextData[{ "Note that when you type a limit in an inline formula, the under position \ of ", Cell[BoxData[ \(TraditionalForm\`z \[Rule] 0\)]], " is moved to the subscript position." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "The residue of ", Cell[BoxData[ \(TraditionalForm\`1\/\(sin\ z\)\)]], " at ", Cell[BoxData[ \(TraditionalForm\`z = 0\)]], " is ", Cell[BoxData[ \(TraditionalForm\`lim\+\(z \[Rule] 0\)\((z\/\(sin\ z\))\) = 1\)]], "." }], "Text"], Cell["Hunt and peck.", "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(x \[LessEqual] y \[And] z \[NotEqual] 2\)], "DisplayFormula"] }, Closed]], Cell[CellGroupData[{ Cell["Integrals, Sums, Products and Matrices", "Subsection"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm \`\[Integral]\[FilledSquare] \[DifferentialD]\[Square]\)]], " ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " \[ExponentialE] \[TabKey] \[Xi] \[TabKey] \[Xi]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\[Integral]\(\[ExponentialE]\^\[Xi]\) \[DifferentialD]\[Xi]\)], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm \`\(\[Integral]\_\[Square]\%\[Square]\)\[FilledSquare] \[DifferentialD]\[Square]\)]], "a \[TabKey] b \[TabKey] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " sin \[TabKey] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ (x) \[TabKey] x" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\[Integral]\_a\%b\(\( sin\^2\) \((x)\)\) \[DifferentialD]x\)], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm \`\(\(\[Sum]\[InvisibleSpace]\)\+\(\[Square]\( = \[Square]\)\)\%\[Square]\) \[FilledSquare]\)]], " n \[TabKey] 1 \[TabKey] \[Infinity] \[TabKey] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " 1 \[TabKey] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " n \[TabKey] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] = ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " \[Pi] \[TabKey] 2 \[TabKey] 6 \[ControlKey]\[LeftModified]\[SpaceKey]\ \[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\[Sum]\+\(n = 1\)\%\[Infinity] 1\/n\^2 = \[Pi]\^2\/6\)], "DisplayFormula"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " moves the top and bottom positions to superscript and subscript when you \ type the sum in an inline formula." }], "Text", CellDingbat->"\[LightBulb]"], Cell[TextData[{ "The Riemann zeta function of 2 is ", Cell[BoxData[ \(TraditionalForm \`\[Sum]\+\(n = 1\)\%\[Infinity] 1\/n\^2 = \[Pi]\^2\/6\)]], "." }], "Text", TextAlignment->Left, TextJustification->0], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm \`\(\(\[Product]\[InvisibleSpace]\)\+\(\[Square]\( = \[Square]\)\)\%\[Square]\) \[FilledSquare]\)]], " n \[TabKey] 1 \[TabKey] \[Infinity] \[TabKey] ( 1 + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " 1 \[TabKey] ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\^\[Square]\)\)]], " n \[TabKey] 2 \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] \ \[ControlKey]\[LeftModified]\[SpaceKey]\[RightModified] ) = ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\/\[Square]\)\)]], " sinh\[SpaceIndicator]\[Pi] \[TabKey] \[Pi] \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(\[Product]\+\(n = 1\)\%\[Infinity]\((1 + 1\/n\^2)\) = \(sinh\ \[Pi]\)\/\[Pi]\)], "DisplayFormula"], 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[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {"a", "b"}, {"c", "d"} }], ")"}], RowBox[{"(", GridBox[{ {"x"}, {"y"} }], ")"}]}], "=", RowBox[{"(", GridBox[{ {"u"}, {"v"} }], ")"}]}]], "DisplayFormula"], Cell[TextData[{ Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"\[Square]", "\[Square]"}, {"\[Square]", "\[Square]"} }], ")"}], TraditionalForm]]], " a \[TabKey] b \[ControlKey]\[LeftModified],\[RightModified] c \[TabKey] x \ \[TabKey] y \[TabKey] z \[ControlKey]\[LeftModified]\[ReturnKey]\ \[RightModified] 1 \[TabKey] 2 \[TabKey] 3 \[ControlKey]\[LeftModified]\ \[SpaceKey]\[RightModified]" }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ RowBox[{"(", GridBox[{ {"a", "b", "c"}, {"x", "y", "z"}, {"1", "2", "3"} }], ")"}]], "DisplayFormula"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Editing Text and Using Output in Formulas", "Section"], Cell[TextData[ "You can copy a cell by selecting the surrounding right bracket and then \ selecting Edit\[Rule]Copy or pressing \[ControlKey]\[LeftModified]c\ \[RightModified]. If you click between cells, a horizontal line will appear. \ You can paste the cell at that position with Edit\[Rule]Paste or \ \[ControlKey]\[LeftModified]v\[RightModified]."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[ "You can copy text by highlighting the text and then clicking Edit\[Rule]Copy \ or pressing \[ControlKey]\[LeftModified]c\[RightModified]. Click the cursor \ at a position in a text cell or between cells and paste with Edit\[Rule]Paste \ or \[ControlKey]\[LeftModified]v\[RightModified]."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(Expand[\((x + y)\)\^5]\)], "Input"], Cell["\<\ Copy the contents of the above output and paste it into a display \ formula to get the right side of the formula below.\ \>", "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(TraditionalForm \`\((x + y)\)\^5 = x\^5 + 5\ x\^4\ y + 10\ x\^3\ y\^2 + 10\ x\^2\ y\^3 + 5\ x\ y\^4 + y\^5\)], "DisplayFormula"], Cell[TextData[{ "By default, ", StyleBox["Mathematica", FontSlant->"Italic"], " inputs are in ", StyleBox["StandardForm", FontSlant->"Italic"], ". This is a precise, two-dimensional form that has nifty bells and \ whistles, like radicals, fractions and superscripts. In earlier versions of \ ", StyleBox["Mathematica", FontSlant->"Italic"], " one had to input expressions in ", StyleBox["InputForm", FontSlant->"Italic"], ", a one-dimensional form that uses only ordinary keyboard characters. ", StyleBox["Mathematica", FontSlant->"Italic"], " now lets you use either form for input. Write out the first input below \ in your notebook. Then copy and paste the input to make a duplicate. Select \ the second input cell and then select Cell\[Rule]Convert To\[Rule]InputForm \ to get the second input. (When you open a ", StyleBox["Mathematica", FontSlant->"Italic"], " 2.0 notebook, you will be given the option of converting the inputs and \ ouputs to StandardForm.)" }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(\(\[Pi]\ \[ExponentialE]\^\(\[ImaginaryI]\ \[Omega]\ x\)\)\/\(x \@\( x\^2 + 1\)\)\)], "Input"], Cell[TextData["(Pi*E^(I*\[Omega]*x))/(x*Sqrt[x^2 + 1])"], "Input"], Cell[TextData[{ "By default ", StyleBox["Mathematica", FontSlant->"Italic"], " outputs are shown in StandardForm. StandardForm is handy because ", StyleBox["Mathematica", FontSlant->"Italic"], " will take it as input. You can copy from any StandardForm output and \ paste it into an input." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "Text-based interfaces show outputs in OutputForm, a one-dimensional form \ that uses only ordinary keyboard characters. You can make the output be \ displayed in OutputForm with the ", StyleBox["OutputForm[]", FontWeight->"Bold"], " function." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(\(\[Pi]\ \[ExponentialE]\^\(\[ImaginaryI]\ \[Omega]\ x\)\)\/\(x \@\( x\^2 + 1\)\) + f[\[Omega]] Sin[x]\)], "Input"], Cell[BoxData[ \(\(\[Pi]\ \[ExponentialE]\^\(\[ImaginaryI]\ \[Omega]\ x\)\)\/\(x \@\( x\^2 + 1\)\) + f[\[Omega]] Sin[x] // OutputForm\)], "Input"], Cell[TextData[{ "You can also tell ", StyleBox["Mathematica", FontSlant->"Italic"], " to show the output in TraditionalForm. This tries to show the expression \ in traditional mathematical notation. There is good news and bad news \ concerning TraditionalForm. The good news is that TraditionalForm \ expressions look like the mathematical expressions you are used to writing \ and seeing in books. You can paste them into inline formulas and display \ formulas. The bad new is that TraditionalForm expressions are not in general \ suitable for ", StyleBox["Mathematica", FontSlant->"Italic"], " inputs. This is because traditional mathematical notation is not precise \ like StandardForm. You can always convert a StandardForm expression into \ TraditionalForm, but it may not be possible to uniquely convert \ TraditionalForm to StandardForm. You can display a ", StyleBox["Mathematica", FontSlant->"Italic"], " output in TraditionalForm with the ", StyleBox["TraditionalForm[]", FontWeight->"Bold"], " function." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(\(\[Pi]\ \[ExponentialE]\^\(\[ImaginaryI]\ \[Omega]\ x\)\)\/\(x \@\( x\^2 + 1\)\) + f[\[Omega]] Sin[x] // TraditionalForm\)], "Input"], Cell["\<\ Evaluate the following inputs to see why TraditionalForm is \ ambiguous.\ \>", "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(a \((b + c)\) // TraditionalForm\)], "Input"], Cell[BoxData[ \(a[b + c] // TraditionalForm\)], "Input"], Cell[BoxData[ \({{n}, {m}} // TraditionalForm\)], "Input"], Cell[BoxData[ \(Binomial[n, m] // TraditionalForm\)], "Input"], Cell[TextData[{ "In most cases, ", StyleBox["Mathematica", FontSlant->"Italic"], " is able to decipher a TraditionalForm expression given as input, but it \ is better to use TraditionalForm only for displaying expressions and use \ StandardForm for input. Below, we solve a differential equation and display \ the answer in TraditionalForm." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(DSolve[ \(\(y'\)'\)[x] + \(1\/x\) \(y'\)[x] + \((1 - 1\/x\^2)\) y[x] == 0, y[x], x]\)], "Input"], Cell[BoxData[ \(PowerExpand[%] // TraditionalForm\)], "Input"], Cell["\<\ Copy a portion of the above output and paste it into an inline \ formula to produce cell below.\ \>", "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "The solution of the differential equation is ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{\(J\_1\), \((x)\), " ", SubscriptBox[ TagBox["c", C], "1"]}], "+", RowBox[{\(\(Y\_1\)(x)\), " ", SubscriptBox[ TagBox["c", C], "2"]}]}], TraditionalForm]]], "." }], "Text"], Cell[TextData[ "By default, inline formulas are displayed in TraditionalForm and display \ formulas are displayed in StandardForm. The display formulas will look \ closer to what you are used to seeing in books if you display them in \ TraditionalForm and center justify the cell. Copy the first three Display \ Formula cells from below and paste them into this section in your notebook. \ (Note that you can shift-click and control-click to modify your selection \ just as you can in other Windows applications.) Select all the Display \ Formula cells, center justify them and then select Cell\[Rule]Display As\ \[Rule]TraditionalForm, (or use the keyboard shortcut). Note that you get a \ better looking font and spiffier formatting with TraditionalForm."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ \(\[Integral]\_a\%b\(\( sin\^2\) \((x)\)\) \[DifferentialD]x\)], "DisplayFormula", TextAlignment->Left, TextJustification->0], Cell[BoxData[ \(\[Product]\+\(n = 1\)\%\[Infinity]\((1 + 1\/n\^2)\) = \(sinh\ \[Pi]\)\/\[Pi]\)], "DisplayFormula", TextAlignment->Left, TextJustification->0], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {"a", "b"}, {"c", "d"} }], ")"}], RowBox[{"(", GridBox[{ {"x"}, {"y"} }], ")"}]}], "=", RowBox[{"(", GridBox[{ {"u"}, {"v"} }], ")"}]}]], "DisplayFormula", TextAlignment->Left, TextJustification->0], Cell[BoxData[ \(TraditionalForm \`\[Integral]\_a\%b\(\( sin\^2\)(x)\) \[DifferentialD]x\)], "DisplayFormula", TextAlignment->Center, TextJustification->0], Cell[BoxData[ \(TraditionalForm \`\[Product]\+\(n = 1\)\%\[Infinity]\((1 + 1\/n\^2)\) = \(sinh\ \[Pi]\)\/\[Pi]\)], "DisplayFormula", TextAlignment->Center, TextJustification->0], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {"a", "b"}, {"c", "d"} }], ")"}], RowBox[{"(", GridBox[{ {"x"}, {"y"} }], ")"}]}], "=", RowBox[{"(", GridBox[{ {"u"}, {"v"} }], ")"}]}], TraditionalForm]], "DisplayFormula", TextAlignment->Center, TextJustification->0] }, Closed]], Cell[CellGroupData[{ Cell["Using BasicTypesetting.nb", "Section"], Cell[TextData[ "Select File\[Rule]Palettes\[Rule]BasicTypesetting to open the \ BasicTypesetting palette. This palette contains most of the mathematical \ symbols and other features that you will need to write papers. For the \ Display Formulas in this section, center the text in the cell and display it \ in TraditionalForm."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "\[ScriptCapitalL]\t\tBasicTypesetting.nb, first block, last row.\n\ \[Congruent]\t\tBasicTypesetting.nb, fifth block, second row.\n", Cell[BoxData[ \(TraditionalForm \`\(\[Integral]\_\[Square]\%\[Square]\)\[FilledSquare] \[DifferentialD]\[Square]\)]], "\tBasicInput.nb.\n\[Infinity]\t\tBasicTypesetting.nb, first block, sixth \ row.\n\[ExponentialE]\t\tBasicTypesetting.nb, first block, sixth row." }], "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[ "\[DoubleStruckCapitalZ], \[DoubleStruckCapitalR] and \[DoubleStruckCapitalC] \ are double struck letters. They are in BasicTypesetting.nb, first block, \ last row.\n\[Element] is in the fifth block, fifth row."], "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[TextData[{ Cell[BoxData[ FormBox[ FrameBox["\[FilledSquare]", BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " is in BasicTypesetting.nb, fourth block.\n\[Element] is in the fifth \ block, fifth row." }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[ FrameBox[ \(\[Integral]\_\(- \[Infinity]\)\%\[Infinity]\( \[ExponentialE]\^\(\[ImaginaryI]\ \[Omega]\ x\)\/\(x\^2 + 1\)\) \[DifferentialD]x = \[Pi]\ \[ExponentialE]\^\(-\(| \[Omega] | \)\)\ \ \ \ for\ \[Omega] \[Element] \[DoubleStruckCapitalR]\), BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]], "DisplayFormula", TextAlignment->Center, TextJustification->0], Cell[TextData[ "\[DifferentialD] and \[PartialD] are in the first block. There is no need \ for a space between \[DifferentialD] or \[PartialD] and the letter following \ it."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "The chain rule is ", 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\)]], "." }], "Text"], Cell[TextData[{ "\[CapitalDelta]\tfirst block, fourth row.\n\[Congruent]\tfifth block, \ second row.\n\[Del]\tfirst block, fifth row.\n\[CenterDot]\tfifth block, \ first row.\n\[Phi]\tfirst block, third row.\n\ \[CapitalDelta]\[SpaceIndicator]u \[Congruent] \[Del] \[CenterDot] ( \[Del]\ \[SpaceIndicator]u )\n\[CapitalDelta]\[SpaceIndicator]\[Phi] = ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\_\[Square]\)\)]], " \[Phi] \[TabKey] x\[SpaceIndicator]x + ", Cell[BoxData[ \(TraditionalForm\`\(\[FilledSquare]\_\[Square]\)\)]], " \[Phi] \[TabKey] y\[SpaceIndicator]y" }], "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]\_\(x\ x\) + \[Phi]\_\(y\ y\)\)]], "." }], "Text"], Cell[TextData[{ Cell[BoxData[ FormBox[ RowBox[{"{", GridBox[{ {"\[Square]"}, {"\[Square]"} }]}], TraditionalForm]]], " \tthird block." }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ FormBox[ RowBox[{\(H(x)\), "=", RowBox[{"{", GridBox[{ {\(1\ \ \ \ for\ x > 0, \)}, {\(0\ \ \ \ for\ x < 0. \)} }]}]}], TraditionalForm]], "DisplayFormula", TextAlignment->Center, TextJustification->0], Cell[TextData[ "Start with matrices. Add rows with \[ControlKey]\[LeftModified]\[ReturnKey]\ \[RightModified]; add columns with \[ControlKey]\[LeftModified],\ \[RightModified]. The various ellipses are in the sixth block."], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], 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, TextJustification->0], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[ClockwiseContourIntegral]\)]], "\tfifth block, first row, last column." }], "Text", CellDingbat->"\[LightBulb]"], Cell[BoxData[ \(TraditionalForm \`\(1\/\(2 \[Pi]\ \[ImaginaryI]\)\) \(\[ClockwiseContourIntegral]\(1\/\(sin\ z\)\) \[DifferentialD]z\) = 1 \)], "DisplayFormula", TextAlignment->Center, TextJustification->0] }, Closed]], Cell[CellGroupData[{ Cell["Alignment", "Section"], Cell[CellGroupData[{ Cell["A Sequence of Centered Equations in One Cell", "Subsection"], Cell[TextData[{ "To make a sequence of centered equations in one cell, type ", Cell[BoxData[ FormBox[GridBox[{ {"\[Square]"}, {"\[Square]"} }], TraditionalForm]]], ", (third block in BasicTypesetting.nb), and put an equation in each row. \ You can add rows with \ \[ControlKey]\[LeftModified]\[ReturnKey]\[RightModified]. For the text \ below, use copy and paste to reduce typing." }], "Text", CellDingbat->"\[LightBulb]", TextAlignment->Left, TextJustification->1], Cell[BoxData[ FormBox[GridBox[{ { \(\[ScriptCapitalL][t\^\[Nu]] = \[Integral]\_0\%\[Infinity]\( t\^\[Nu]\) \(\[ExponentialE]\^\(\(-s\)\ t\)\) \[DifferentialD]t, \ \ \ \ \[ForAll] \ Re(\[Nu]) > \(-1\)\)}, { \(\[ScriptCapitalL][t\^\[Nu]] = \[Integral]\_0\%\[Infinity]\(\((x\/s)\)\^\[Nu]\) \(\[ExponentialE]\^\(-x\)\) \(1\/s\) \[DifferentialD]x, \ \ \ \ \[ForAll] \ Im(s) = 0\)}, { \(\[ScriptCapitalL][t\^\[Nu]] = \(1\/s\^\(\[Nu] + 1\)\) \(\[Integral]\_0\%\[Infinity]\( x\^\[Nu]\) \(\[ExponentialE]\^\(-x\)\) \[DifferentialD]x\)\)}, { \(\[ScriptCapitalL][t\^\[Nu]] = \(\[CapitalGamma](\[Nu] + 1)\)\/s\^\(\[Nu] + 1\)\)} }], TraditionalForm]], "DisplayFormula", TextAlignment->Center, TextJustification->0] }, Closed]] }, Closed]] }, Open ]] }, FrontEndVersion->"5.2 for Microsoft Windows", ScreenRectangle->{{0, 1680}, {0, 963}}, WindowToolbars->{"RulerBar", "EditBar"}, CellGrouping->Automatic, WindowSize->{772, 476}, WindowMargins->{{2, Automatic}, {Automatic, 2}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "Magnification"->1}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, CharacterEncoding->"XAutomaticEncoding", Magnification->1.5, StyleDefinitions -> "Default.nb" ] (******************************************************************* Cached data follows. 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