(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' 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[ 25166, 943]*) (*NotebookOutlinePosition[ 55209, 2035]*) (* CellTagsIndexPosition[ 55165, 2031]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Math 421", FontSlant->"Italic"], " ", StyleBox["\[FilledSmallCircle]", FontSlant->"Plain"], " September 2004" }], "Subsubtitle", TextAlignment->Center, TextJustification->0], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " Introduction\[LongDash]Part 2" }], "Subtitle"], Cell["Type your name(s) into the cell below.", "BoxedText"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Your name(s):\n\n", FontWeight->"Bold"]], "ExampleSection"], Cell["\<\ The sections and subsections in this notebook (and in most others you will \ use in the course) are in closed groups, to give an outline view. Open each \ group when you are ready.\ \>", "BoxedText"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Mathematical notation in ", StyleBox["Mathematica", FontSlant->"Italic"], " " }], "Section"], Cell[CellGroupData[{ Cell["Names of objects", "Subsection"], Cell[TextData[{ StyleBox["All of ", FontWeight->"Bold"], StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic"], StyleBox["'s built-in names begin with upper-case letters", FontWeight->"Bold"], " (or for some special names, with ", StyleBox["$", FontFamily->"Courier"], "). Unlike in most traditional elementary mathematical notation, names may \ consist of multiple letters. In fact, most built-in function names are \ entire words or unspaced phrases. For example:" }], "Text"], Cell[BoxData[ \(Limit[\(z\^2 - \ 9\)\/\(z\ - \ 3\), \ z\ \[Rule] \ 3]\)], "Input"], Cell[BoxData[ \(FactorInteger[5625]\)], "Input"], Cell["\<\ A handful of the most common elementary transcendental functions keep their \ usual abbreviations\[LongDash]but with initial upper-case letters of \ course:\ \>", "Text"], Cell[BoxData[ \(ArcTan[Sin[\[Pi]\/2]]\)], "Input"] }, Closed]], Cell[TextData[{ "Names that ", StyleBox["you", FontWeight->"Bold", FontSlant->"Italic"], " invent should ordinarily begin with a lower-case letter." }], "Text", CellFrame->True, TextAlignment->Center, FontWeight->"Bold", Background->GrayLevel[0.833326]], Cell["Try the following and be sure you understand the output:", "Text"], Cell[BoxData[{ \(arcTan\ = \ Pi/4\), "\[IndentingNewLine]", \(arcTan[1]\), "\[IndentingNewLine]", \(ArcTan[1]\)}], "Input"], Cell[TextData[{ "Since names may consist of more than a single letter, be especially \ careful when entering something like the ", StyleBox["Mathematica", FontSlant->"Italic"], " version of a symbolic expression ", Cell[BoxData[ \(TraditionalForm\`a\ + \ b\ \[ImaginaryI]\)]], ": be sure to put a space between the symbol that's multiplying ", Cell[BoxData[ \(TraditionalForm\`\[ImaginaryI]\)]], ". Try the following and be sure you understand what happened." }], "Text"], Cell[BoxData[{ \(a\ = \ 2; \ b\ = \ v;\ \), "\[IndentingNewLine]", \(a\ + \ bI\), "\[IndentingNewLine]", \(a\ + \ b\ I\)}], "Input"], Cell[TextData[{ "When the first factor in a product is an actual number, you do ", StyleBox["not", FontSlant->"Italic"], " need any intervening space. Examine the following input cell carefully\ \[LongDash]run your cursor along from character to character to observe there \ is ", StyleBox["no", FontSlant->"Italic"], " space between the ", StyleBox["3", FontFamily->"Courier"], " and the ", StyleBox["I", FontFamily->"Courier"], ". Then evaluate the cell." }], "Text"], Cell[BoxData[ \(2\ + \ 3 I\)], "Input"], Cell[CellGroupData[{ Cell["Exponents, fractions, and square-roots", "Subsection"], Cell["\<\ If you are running out of time today, you could omit this subsection for now \ and go through it at another time.\ \>", "BoxedText"], Cell[TextData[{ StyleBox["To enter a superscript", FontWeight->"Bold", FontSlant->"Italic"], StyleBox[" ,", FontWeight->"Bold", FontSlant->"Italic"], " you may use the character ", StyleBox["^", FontFamily->"Courier"], " inline. For example, type ", StyleBox["x^2", FontFamily->"Courier"], " for the square of ", StyleBox["x", FontFamily->"Courier"], ". To get raised exponents, use the ", StyleBox["\[ControlKey]", Magnification->1.5], StyleBox[" ", FontFamily->"Times", Magnification->1.5], StyleBox["^", FontFamily->"Courier"], " key combination, type the exponent, and use the mouse or cursor keys to \ move to the right beyond the exponent.\nSimilarly, ", StyleBox["to enter a fraction,", FontWeight->"Bold", FontSlant->"Italic"], " you may use the / character inline. For example: ", StyleBox["2/3", FontFamily->"Courier"], " To get a multi-line built-up fraction, use the ", StyleBox["\[ControlKey] ", Magnification->1.5], StyleBox["/", FontFamily->"Courier"], " key combination.\n", StyleBox["To get a square root", FontWeight->"Bold", FontSlant->"Italic"], ", you may use the ", StyleBox["Sqrt", FontFamily->"Courier"], " function inline. For example: ", StyleBox["Sqrt[2]", FontFamily->"Courier"], " To get a traditional square-root symbol, use the ", StyleBox["\[ControlKey]", Magnification->1.5], " ", StyleBox["2", FontFamily->"Courier"], " key combination.\nTo leave superscript, fraction , or square root mode \ and return to normal typing on the line, type ", StyleBox["\[ControlKey]\[SpaceKey]", Magnification->1.5], ". Or, use the right-cursor key." }], "Text"], Cell[TextData[{ StyleBox["Try it now:", Background->GrayLevel[0.900008]], " In new input cells, enter the ", StyleBox["Mathematica", FontSlant->"Italic"], " equivalent of the traditional mathematical notation\n", Cell[BoxData[ \(TraditionalForm\`\@\(\(z\^\(\(2\)\(\ \)\) - \ 9\)\/\(z - \ 3\)\)\ + \ \ 6\)]], " first inline and then as a multi-line display." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Common math constants", "Subsection"], Cell[TextData[{ StyleBox["To enter common the math constants", FontWeight->"Bold", FontSlant->"Italic"], " traditionally denoted ", Cell[BoxData[ \(TraditionalForm\`e\)]], ", \[Pi], ", Cell[BoxData[ \(TraditionalForm\`i\)]], " (that is, ", Cell[BoxData[ \(TraditionalForm\`\@\(-1\)\)]], "), and ", Cell[BoxData[ \(TraditionalForm\`\[Infinity]\)]], ", you may type ", StyleBox["E", FontFamily->"Courier"], ", ", StyleBox["Pi", FontFamily->"Courier"], ", ", StyleBox["I", FontFamily->"Courier"], ", and ", StyleBox["Infinity", FontFamily->"Courier"], ", respectively. To get their more traditionally-appearing forms \ \[ExponentialE], \[Pi], and \[ImaginaryI], and ", Cell[BoxData[ \(TraditionalForm\`\[Infinity]\)]], ", use paired ", StyleBox["\[EscapeKey]", Magnification->1.5], " (Escape) key sequences. For example, you would type \[Pi] as ", StyleBox["\[EscapeKey]", Magnification->1.5], StyleBox["p", FontFamily->"Courier"], StyleBox["\[EscapeKey]", Magnification->1.5], ". (Pressing ", StyleBox["\[EscapeKey]", Magnification->1.5], " will cause the glyph ", StyleBox["\[AliasIndicator]", FontFamily->"Courier"], " to appear temporarily in the cell.) ", StyleBox["Try these:", Background->GrayLevel[0.900008]] }], "Text"], Cell[TextData[{ "(1) In a new input cell type the ", StyleBox["Mathematica", FontSlant->"Italic"], " expression traditionally appearing as the following; then evaluate it.\n\t\ ", Cell[BoxData[ FormBox[ StyleBox[\(\[ImaginaryI]\^\(\(\ \)\(2\)\)\), Magnification->1.5], TraditionalForm]], Magnification->1.5] }], "Text"], Cell[TextData[{ "(2) In a new input cell type the ", StyleBox["Mathematica", FontSlant->"Italic"], " expression traditionally appearing as the following; then evaluate it.\n\t\ ", Cell[BoxData[ FormBox[ StyleBox[\(\[ExponentialE]\^\(2 \[Pi]\ \[ImaginaryI]\)\), Magnification->1.5], TraditionalForm]]] }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Equality and ordering", "Subsection"], Cell[TextData[{ "Equality is denoted by ", StyleBox["two", FontWeight->"Bold", FontSlant->"Italic"], " equal signs. ", StyleBox["Evaluate the following two cells now.", Background->GrayLevel[0.900008]] }], "Text"], Cell[BoxData[ \(2\ \[Equal] \ 1\ + \ 1\)], "Input"], Cell[BoxData[ \(3\ \[Equal] \ 5\ - \ 1\)], "Input"], Cell[TextData[{ "Try typing a similar equality between numbers yourself now. Create a new \ cell below this one; in it type the expression saying that 3 equal 6 divided \ by 2. ", StyleBox["Do it now.", Background->GrayLevel[0.900008]] }], "Text"], Cell[TextData[{ "Did you notice what happened as you typed the two equal signs in a row? \ As soon as you typed the next character (either 3 or a space), the form of \ the two equal signs changed to a stylized pair of narrower equal signs. That \ happened because ", StyleBox["Mathematica", FontSlant->"Italic"], " understands certain sequences of keystrokes to be abbreviations." }], "Text"], Cell[TextData[{ "How do you think less-than-or-equal is typed? Try it: Create a new cell \ below this one and in it type an expression that results in ", StyleBox["2 \[LessEqual] 3", FontFamily->"Courier"], ". Then evaluate the cell." }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Constants and functions", "Section"], Cell[CellGroupData[{ Cell["Clearing", "Subsection"], Cell[TextData[{ "Before introducing a new a name for a constant or a function, it's a good \ idea to ", StyleBox["clear", FontWeight->"Bold"], " any values it may previously have been given:" }], "Text"], Cell[BoxData[ \(Clear[a2bc, \ myNumber]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Assigning constants", "Subsection"], Cell[TextData[{ "To assign a constant value to a name, use the form ", StyleBox["name = expr", FontFamily->"Courier"], " with an equals sign, like this:" }], "Text"], Cell[BoxData[ \(myNumber\ = \ a2bc + 5 I\)], "Input"], Cell["\<\ The output from that input was not especially interesting, and this is often \ the case when you assign a value to a symbol. The resulting output can be \ supressed.\ \>", "Text"], Cell[TextData[{ StyleBox["To suppress the result from evaluating an expression,", FontWeight->"Bold", FontSlant->"Italic"], " terminate the expression with a semicolon." }], "Text", CellFrame->True, TextAlignment->Center, TextJustification->0, FontWeight->"Bold", Background->GrayLevel[0.833326]], Cell["Try this and compare what happens with what happened above:", "Text"], Cell[BoxData[ \(\(myNumber\ = \ a2bc\ + 5 I\ ;\)\)], "Input"], Cell["\<\ Once assigned a value, the name can of course be used in subsequent \ expressions:\ \>", "Text"], Cell[BoxData[ \(myNumber/2\)], "Input"], Cell[BoxData[ \(\(a2bc\ = \ 7;\)\)], "Input"], Cell[BoxData[ \(myNumber/2\)], "Input"], Cell[TextData[{ "Notice that the value of ", StyleBox["myNumber", FontFamily->"Courier"], " did not change, even though you just assigned the new value ", StyleBox["7", FontFamily->"Courier"], " to ", StyleBox["a2bc", FontFamily->"Courier"], " and had originally set ", StyleBox["myNumber = a2bc+5", FontFamily->"Courier"], "." }], "Text"], Cell[TextData[{ "Recall that equality is denoted by two equal signs, not one. What happens \ if you mistakenly use only a single equal sign? ", StyleBox["Try it now:", Background->GrayLevel[0.900008]] }], "Text"], Cell[BoxData[ \(2\ = \ 1\ + \ 1\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Multiplication", "Subsection"], Cell[TextData[{ "Since ", StyleBox["Mathematica", FontSlant->"Italic"], "\[LongDash]like many other programming languages but unlike conventional \ school mathematics\[LongDash]allows multi-character names such as ", StyleBox["myNumber", FontFamily->"Courier"], " and ", StyleBox["a2bc", FontFamily->"Courier"], ", simply juxtaposing two letters does ", StyleBox["not", FontSlant->"Italic"], " indicate multiplication:" }], "Text"], Cell[BoxData[{ \(a\ = \ 2\ + \ 3 I; \ b\ = \ 4\ + \ 5 I;\), "\[IndentingNewLine]", \(ab\)}], "Input"], Cell[BoxData[{ \(a\ b\), "\[IndentingNewLine]", \(a*b\), "\[IndentingNewLine]", \(a\ \[Times]\ b\)}], "Input"], Cell[TextData[{ "The multiplication sign \[Times] in the product expression a \[Times] b \ was typed as ", StyleBox["\[EscapeKey]", Magnification->1.5], StyleBox["*", FontFamily->"Courier"], StyleBox["\[EscapeKey]", Magnification->1.5] }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Working with functions", "Subsection"], Cell[TextData[{ StyleBox["\[WarningSign]", FontSize->18, Background->RGBColor[1, 1, 0]], " As you have already seen, ", StyleBox["the arguments of a ", Background->RGBColor[1, 1, 0]], StyleBox["Mathematica", FontSlant->"Italic", Background->RGBColor[1, 1, 0]], StyleBox[" function are enclosed in square brackets", Background->RGBColor[1, 1, 0]], " and ", StyleBox["not", FontSlant->"Italic"], " in parentheses. For example:" }], "Text"], Cell[BoxData[{ \(Re[3\ + \ 4 I]\), "\[IndentingNewLine]", \(Im[3\ + \ 4 I]\)}], "Input"], Cell[BoxData[ \(Norm[3\ + \ 4 I]\)], "Input"], Cell[BoxData[ \(Conjugate[3\ + \ 4 I]\)], "Input"], Cell[BoxData[{ \(\(z\ = \ 3\ + \ 4 I;\)\), "\[IndentingNewLine]", \(z\ Conjugate[z]\)}], "Input"], Cell[TextData[{ "Parentheses are used in ", StyleBox["Mathematica", FontSlant->"Italic"], " to group expressions. ", StyleBox["Try this:", Background->GrayLevel[0.900008]], " Explain the output from the expression in the following cell:" }], "Text"], Cell[BoxData[ \(Norm \((3\ + \ 4 I)\)\)], "Input"], Cell["\<\ If a function has several arguments, they are separated with commas. For \ example:\ \>", "Text"], Cell[BoxData[ \(Log[2, \ 32]\)], "Input"], Cell[TextData[{ StyleBox["To define a function", FontWeight->"Bold", FontSlant->"Italic"], " of a single argument in ", StyleBox["Mathematica", FontSlant->"Italic"], ", use the form\n\t", StyleBox["fname[var_] := expr\n", FontFamily->"Courier"], "where the expression ", StyleBox["expr", FontFamily->"Courier"], " will typically involve the symbol ", StyleBox["var", FontFamily->"Courier"], ". Be sure to append the underscore (", StyleBox["\[ShiftKey]", Magnification->1.5], " ", StyleBox["-", FontFamily->"Courier"], " ) to the argument name ", StyleBox["var", FontFamily->"Courier"], ". And be sure to use colon equal (", StyleBox[" :=", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " ), not just equal. For example:" }], "Text"], Cell[BoxData[ \(\(curve[t_]\ := \ ParametricPlot[{Cos[\[Theta]], \ \ Sin[\[Theta]]}, \ {\[Theta], \ 0, \ t}, \ AspectRatio\ \[Rule] \ Automatic];\)\)], "Input"], Cell[BoxData[ \(curve[\[Pi]/2]\)], "Input"], Cell[BoxData[ \(Table[curve[\(\[Pi]\/2\) k], \ {k, \ 1, \ 4}]\)], "Input"], Cell[TextData[{ "Do the obvious thing to define a function of several arguments. For \ example, for a function of two arguments:\n\t", StyleBox["fname[var1_, var2_] := expr", FontFamily->"Courier"], "\n", StyleBox["Try this:", Background->GrayLevel[0.900008]], " Define a function of two arguments\[LongDash]which in use will be ", StyleBox["complex", FontVariations->{"Underline"->True}], " numbers\[LongDash]that calculates the distance between them. For \ example, if the arguments are given the values ", Cell[BoxData[ \(TraditionalForm\`7\ + \ \(\(10\) \(\[ImaginaryI]\)\(\ \)\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`4\ + \ 6 \[ImaginaryI]\)]], ", then the result of evaluating your function should be 5. (", StyleBox["Hint:", FontSlant->"Italic"], " Use the norm function ", StyleBox["Norm", FontFamily->"Courier"], ".)" }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Getting built-in help (important!)", "Section"], Cell[TextData[{ "Perhaps this section is the most important in this tutorial: it tells how \ to get help from ", StyleBox["Mathematica", FontSlant->"Italic"], " itself. There are two basic ways\[LongDash]evaluating an information \ expression and using the help browser. " }], "Text"], Cell[CellGroupData[{ Cell["Information", "Subsection"], Cell["\<\ To get a brief summary of the syntax and meaning of a built-in object, \ evaluate a cell with an information expression like the following:\ \>", "Text"], Cell[BoxData[ \(\(?Integrate\)\)], "Input"], Cell[TextData[{ StyleBox["Try it now:", Background->GrayLevel[0.900008]], " Use the information you obtained about ", StyleBox["Integrate", FontFamily->"Courier"], " to figure out how to calculate with ", StyleBox["Mathematica", FontSlant->"Italic"], " an indefinite integral (antiderivative) of ", StyleBox["x", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`Exp(\(-\ \(x\^2\/2\)\))\)]], ".\n", StyleBox["\[WarningSign]", FontColor->RGBColor[1, 0, 0], Magnification->2], " Recall that arguments to ", StyleBox["Mathematica", FontSlant->"Italic"], " functions are enclosed in square brackets, not parentheses!" }], "Text"], Cell["Here's another information request:", "Text"], Cell[BoxData[ \(\(?Plot\)\)], "Input"], Cell[TextData[{ "The ", StyleBox["derivative", FontWeight->"Bold", FontSlant->"Italic"], " of a function may be denoted by a prime, for example:" }], "Text"], Cell[BoxData[ \(\(Cos'\)[z]\)], "Input"], Cell[BoxData[{ \(Clear[f]\), "\n", \(f[z_]\ := \ 0.75 Cos[2 z]\ Exp[\(-\(z\/10\)\)]\), "\n", \(\(f'\)[z]\)}], "Input"], Cell[TextData[{ StyleBox["Try this:", Background->GrayLevel[0.900008]], " Guided by the information message you obtained about ", StyleBox["Plot", FontFamily->"Courier"], ", on the same axes plot the graphs of both ", StyleBox["f[x]", FontFamily->"Courier"], " and ", StyleBox["f'[x]", FontFamily->"Courier"], " over the interval from ", StyleBox["-2\[Pi]", FontFamily->"Courier"], " to ", StyleBox["2\[Pi].", FontFamily->"Courier"], StyleBox[" (Save lots of typing: copy and paste!)", FontFamily->"Times"] }], "Text"], Cell[TextData[{ "Asking for information about a name that ", StyleBox["you", FontSlant->"Italic"], " have defined will display its definition:" }], "Text"], Cell[BoxData[ \(\(?f\)\)], "Input"], Cell["\<\ If you know just part of the name of an object, you can use wild cards in the \ information request. For example:\ \>", "Text"], Cell[BoxData[ \(\(?Int*\)\)], "Input"], Cell[TextData[{ StyleBox["Try it now:", Background->GrayLevel[0.900008]], " Find out what objects have names ", StyleBox["beginning", FontSlant->"Italic"], " with ", StyleBox["Complex", FontFamily->"Courier"], "." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "The help browser (", StyleBox["very", FontSlant->"Italic"], " important!)" }], "Subsection"], Cell[TextData[{ "The ", StyleBox["Help Browser", FontWeight->"Bold"], " provides (nearly) complete documentation about ", StyleBox["Mathematica. ", FontSlant->"Italic"], "In fact, the Help Browser contains the entire text of Stephen Wolfram's \ 1,688-page definitive reference, \"The ", StyleBox["Mathematica", FontSlant->"Italic"], " Book\", 5th ed." }], "Text"], Cell[TextData[{ StyleBox["To open the Help Browser", FontWeight->"Bold", FontSlant->"Italic"], ", from the ", StyleBox["Help", FontFamily->"Helvetica"], " menu select ", StyleBox["Help Browser", FontFamily->"Helvetica"], ". Then navigate to find the topic you want. It's fairly intuitive how to \ do this. But if you need help on how to use the Help Browser, ask a human: \ it's much easier for someone to show you than to describe how in words." }], "Text"], Cell[TextData[{ StyleBox["Try it now:", Background->GrayLevel[0.900008]], " Use the Help Browser to find out about the built-in function ", StyleBox["Solve", FontFamily->"Courier"], "." }], "Text"], Cell["\<\ Many Help Browser entries include at the end a section that looks like the \ following:\ \>", "Text"], Cell[CellGroupData[{ Cell["Further examples", "ExampleSection"], Cell["(examples would go here)", "Text"], Cell["\<\ Such a section is just a specially formatted close group of cells. To see \ the further examples, click on the little triangle to open the group and see \ the examples.\ \>", "Text"], Cell[TextData[{ StyleBox["Try it now:", Background->GrayLevel[0.900008]], " Open the group of further examples in the Help Browser help about ", StyleBox["Solve", FontFamily->"Courier"], "." }], "Text"], Cell[TextData[{ "Another way to open the Help Browser for help about a built-in object ", StyleBox["name", FontFamily->"Courier"], " is to follow the ", StyleBox["More...", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], " hyperlink you see whenever you use the ", StyleBox["?name", FontFamily->"Courier"], " form of information request. ", StyleBox["Try it now:", Background->GrayLevel[0.900008]], " Evaluate the following cell, then click on the ", StyleBox["More...", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], " hyperlink at the end of the resulting information." }], "Text"], Cell[BoxData[ \(\(?N\)\)], "Input"] }, Closed]] }, Closed]] }, Closed]], Cell[TextData[{ "Before proceeding, print a copy of this notebook\[LongDash]one copy for \ each of you if you are working with a partner\[LongDash]to keep for \ reference. (Do ", StyleBox["not", FontSlant->"Italic"], " hand it in!) Be sure you typed your name(s) at the top so you can \ identify which printouts are yours." }], "BoxedText"], Cell[CellGroupData[{ Cell["What's next?", "Section"], Cell[TextData[{ "If you have time at this lab session\[LongDash]you \ should!\[LongDash]continue this introduction by opening the notebook ", StyleBox["Intro3.nb", FontFamily->"Courier"], ". Otherwise, \"clean up\" as indicated below." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Cleaning up", "Section"], Cell[TextData[{ "When you are finished at your ", StyleBox["Mathematica", FontSlant->"Italic"], " session for today, please:\n \[FilledSmallCircle] Save whatever notebooks \ (such as this one) that you want.\n \[FilledSmallCircle] Close all open \ notebooks.\n \[FilledSmallCircle] Exit (quit) ", StyleBox["Mathematica", FontSlant->"Italic"], " from the ", StyleBox["File", FontFamily->"Helvetica"], " menu.\n \[FilledSmallCircle] Log out." }], "BoxedText"], Cell["Copyright \[Copyright] 2004 by Murray Eisenberg. 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Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PageHeaderLines->{True, True}, PrintingOptions->{"FirstPageHeader"->False, "FacingPages"->True}, CellFrameLabelMargins->6, StyleMenuListing->None] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], ShowCellBracket->False, CellMargins->{{0, 0}, {0, 0}}, PageBreakBelow->False, LineSpacing->{1, 0}, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, FontSize->34, FontColor->GrayLevel[1], Background->RGBColor[0.571389, 0.19675, 0.570504]], Cell[StyleData["Title", "Presentation"], CellMargins->{{0, 0}, {0, 0}}, LineSpacing->{1, 0}, FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{0, 0}, {0, 0}}, FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{0, 0}, {0, 0}}, FontSize->24, FontTracking->"Plain", Background->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], ShowCellBracket->False, CellMargins->{{0, 0}, {0, 0}}, PageBreakBelow->False, LineSpacing->{1, 3}, ParagraphIndent->-96, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->18, FontColor->GrayLevel[1], Background->RGBColor[0.2, 0.700008, 0.700008]], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{0, 0}, {0, 0}}, LineSpacing->{1, 6}, ParagraphIndent->-157, FontSize->30], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{0, 0}, {0, 0}}, ParagraphIndent->-78, FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{0, 0}, {0, 0}}, ParagraphIndent->-85, FontSize->16, Background->GrayLevel[0.6]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], ShowCellBracket->False, CellMargins->{{10, 4}, {30, 10}}, PageBreakBelow->False, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{8, 10}, {40, 20}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {12, 8}}, FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{9, 10}, {50, 10}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellFrame->{{6, 0}, {0, 1}}, CellDingbat->None, CellMargins->{{12, Inherited}, {4, 24}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, CellFrameMargins->6, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[0.571389, 0.19675, 0.570504]], Cell[StyleData["Section", "Presentation"], CellMargins->{{10, 10}, {8, 32}}, LineSpacing->{1, 2}, FontSize->24, FontTracking->"Condensed"], Cell[StyleData["Section", "Condensed"], CellMargins->{{8, Inherited}, {2, 12}}, FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{9, 0}, {2, 50}}, FontSize->14, FontTracking->"Plain", FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellMargins->{{12, Inherited}, {8, 20}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->13, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{11, 10}, {8, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{8, Inherited}, {2, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {4, 40}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{25, Inherited}, {8, 12}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, CounterIncrements->"Subsubsection", FontFamily->"Times", FontSize->13, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{29, 10}, {8, 26}}, 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]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {5, 5}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 12}, CounterIncrements->"Text", FontFamily->"Times"], Cell[StyleData["Text", "Presentation"], CellMargins->{{13, 10}, {8, 8}}, LineSpacing->{1, 5}, ParagraphSpacing->{0, 12}], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, LineSpacing->{1, 1}, ParagraphSpacing->{0, 4}], Cell[StyleData["Text", "Printout"], CellMargins->{{9, 0}, {4, 4}}, ParagraphSpacing->{0, 6}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {5, 5}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 6}, CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{13, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {2, 2}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{9, 0}, {4, 4}}, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output to the \ kernel. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellFrame->{{3, 0}, {0, 0}}, CellMargins->{{52, 10}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{5, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontWeight->"Bold", Background->RGBColor[1, 0.700008, 0.4]], Cell[StyleData["Input", "Presentation"], CellMargins->{{62, Inherited}, {10, 10}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {4, 4}}], Cell[StyleData["Input", "Printout"], CellMargins->{{44, 0}, {6, 6}}, Background->GrayLevel[0.8]] }, Closed]], Cell[StyleData["InlineInput"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontWeight->"Bold"], 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, FormatType->InputForm, CounterIncrements->"Output", Background->RGBColor[1, 0.900008, 0.900008]], Cell[StyleData["Output", "Presentation"], CellMargins->{{62, Inherited}, {12, 5}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Condensed"], CellMargins->{{40, Inherited}, {4, 1}}], Cell[StyleData["Output", "Printout"], CellMargins->{{44, 0}, {6, 2}}, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{62, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Message", "Presentation"], CellMargins->{{74, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], 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, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{74, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], 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->{{74, Inherited}, {Inherited, Inherited}}], 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]] }, Closed]], Cell[CellGroupData[{ Cell["Unique Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["BoxedText"], CellFrame->True, CellMargins->{{12, 10}, {5, 5}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 12}, CounterIncrements->"Text", FontFamily->"Times", FontWeight->"Bold", FontColor->RGBColor[0.571389, 0.19675, 0.570504], Background->GrayLevel[0.849989]], Cell[StyleData["BoxedText", "Presentation"], CellMargins->{{13, 10}, {8, 8}}, LineSpacing->{1, 5}, ParagraphSpacing->{0, 12}, FontSize->15], Cell[StyleData["BodyText", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, LineSpacing->{1, 1}, ParagraphSpacing->{0, 4}], Cell[StyleData["BodyText", "Printout"], CellMargins->{{9, 0}, {4, 4}}, ParagraphSpacing->{0, 6}, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ExampleSection"], ShowCellBracket->False, ShowGroupOpenCloseIcon->True, CellMargins->{{11, 4}, {0, 10}}, CellGroupingRules->{"SectionGrouping", 70}, CellFrameMargins->12, FontSize->13, FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 0.4]], Cell[StyleData["ExampleSection", "Printout"], CellMargins->{{3, 0}, {0, 10}}, PageBreakBelow->False, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Author"], ShowCellBracket->False, CellMargins->{{10, 4}, {2, 10}}, FontSize->16, FontSlant->"Italic"], Cell[StyleData["Author", "Presentation"], CellMargins->{{12, 10}, {2, 12}}, LineSpacing->{1, 5}, ParagraphSpacing->{0, 12}, FontSize->20], 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->{{12, 10}, {50, 2}}, LineSpacing->{1, 5}, FontSize->12], 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}], 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"], CellMargins->{{62, Inherited}, {5, 12}}, LineSpacing->{1, 0}], Cell[StyleData["Definition", "Condensed"], CellMargins->{{40, 10}, {1, 4}}], Cell[StyleData["Definition", "Printout"], CellMargins->{{44, 0}, {2, 6}}, 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"], CellMargins->{{62, Inherited}, {5, 12}}, LineSpacing->{1, 0}], Cell[StyleData["Theorem", "Condensed"], CellMargins->{{40, 10}, {1, 4}}], Cell[StyleData["Theorem", "Printout"], CellMargins->{{44, 0}, {2, 6}}, 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], CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[0.571389, 0.19675, 0.570504]], Cell[StyleData["ExerciseMain", "Presentation"], CellMargins->{{18, 10}, {8, 32}}, 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, CounterIncrements->"Subsubsection", FontFamily->"Times", FontSize->13, FontWeight->"Bold", FontColor->RGBColor[0.571389, 0.19675, 0.570504]], Cell[StyleData["Exercise", "Presentation"], CellMargins->{{33, 10}, {8, 26}}, LineSpacing->{1, 0}, FontSize->18], 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}}, FontSize->11, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ExerciseText"], CellMargins->{{62, 10}, {5, 5}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 8}, CounterIncrements->"ExcersiceText", FontFamily->"Times"], Cell[StyleData["ExerciseText", "Presentation"], CellMargins->{{74, 10}, {8, 8}}, LineSpacing->{1, 5}, ParagraphSpacing->{0, 12}], Cell[StyleData["ExerciseText", "Condensed"], CellMargins->{{52, 10}, {2, 2}}, LineSpacing->{1, 1}, ParagraphSpacing->{0, 4}], Cell[StyleData["ExerciseText", "Printout"], CellMargins->{{54, 0}, {4, 4}}, ParagraphSpacing->{0, 6}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{62, 10}, {2, 10}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], CellMargins->{{74, 10}, {2, 10}}, FontSize->10], Cell[StyleData["DisplayFormula", "Condensed"], CellMargins->{{52, 10}, {2, 10}}, FontSize->10], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{54, 10}, {2, 10}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{62, 10}, {2, 10}}, DefaultFormatType->DefaultInputFormatType, AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->False, ZeroWidthTimes->True], Cell[StyleData["ChemicalFormula", "Presentation"], CellMargins->{{74, 10}, {2, 10}}, FontSize->10], 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}}, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{13, 30}, {Inherited, 4}}, FontSize->9.5], 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]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, etc. They \ automatically give the cell a FrameLabel containing a reference to a \ particular counter, and also increment that counter.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellMargins->{{62, 10}, {Inherited, Inherited}}, CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->DefaultInputFormatType, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False], Cell[StyleData["NumberedEquation", "Presentation"], CellMargins->{{74, 10}, {Inherited, Inherited}}], Cell[StyleData["NumberedEquation", "Condensed"], CellMargins->{{52, 10}, {Inherited, Inherited}}], Cell[StyleData["NumberedEquation", "Printout"], CellMargins->{{54, 0}, {Inherited, Inherited}}] }, Closed]], 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"]], 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"]], Cell[StyleData["NumberedTable", "Condensed"]], Cell[StyleData["NumberedTable", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], 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"] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. 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If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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