(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 16776, 541]*) (*NotebookOutlinePosition[ 46826, 1634]*) (* CellTagsIndexPosition[ 46782, 1630]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Math 245", FontSlant->"Italic"], " ", StyleBox["\[FilledSmallCircle]", FontSlant->"Plain"], " 9 September 1999" }], "Subsubtitle", CellMargins->{{22, 62}, {Inherited, Inherited}}, TextAlignment->Center, TextJustification->0], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " Introduction\[LongDash]Part 3" }], "Subtitle", CellMargins->{{-1.1875, -33.1875}, {Inherited, Inherited}}], Cell[TextData[StyleBox["Your name(s):\n\n", FontWeight->"Bold"]], "ExampleSection", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell["What else can Mathematica do?", "Section", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "Already you have seen some examples of numerical, symbolic, and graphical \ work with ", StyleBox["Mathematica", FontSlant->"Italic"], ". Here are a few more. Try to predict the output before evaluating each \ input cell" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell["Simplifying expressions", "Subsection", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["\<\ Mathematica has only a limited number of rules automatically applied to \ expressions you evaluate. For example:\ \>", "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(Log[2\ Exp[5]]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "You can undoubtedly see another, possibly simpler form for this. (Of \ course simplicity is in the eye of the beholder.) Ofen you can something \ more closely resemblying the \"simple\" form you expected by using the ", StyleBox["Simplify", FontFamily->"Courier"], " function:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(Simplify[Log[2\ Exp[5]]]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["Here's another one:", "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(Sqrt[\((x^2\ - \ 9)\)/\((x - 3)\)]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "To simplify the output, we could use one of the following methods:\n\ \[FilledSmallCircle] Edit the original input cell so as to apply ", StyleBox["Simplify", FontFamily->"Courier"], ".\n \[FilledSmallCircle] Copy the input cell to a new one and apply ", StyleBox["Simplify", FontFamily->"Courier"], " in the new one.\n \[FilledSmallCircle] In the original or a copied input \ cell, assign the value to a name, for example: ", StyleBox["quantity = Sqrt[(x^2 - 9)/(x-3)]", FontFamily->"Courier"], ". Then evaluate ", StyleBox["Simplify[quantity]", FontFamily->"Courier"], ".\n \[FilledSmallCircle] Apply ", StyleBox["Simplify", FontFamily->"Courier"], " to the ", StyleBox["preceding-result", FontWeight->"Bold", FontSlant->"Italic"], " variable ", StyleBox["%", FontFamily->"Courier"], ", which holds the output of the most recently evaluated input cell:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(Simplify[%]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "The preceding-result variable (", StyleBox["%", FontFamily->"Courier"], ") can be used in any expression and not just for ", StyleBox["Simplify", FontFamily->"Courier"], ". For example:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(25\/3\ 9\/100\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(%\ + \ 1\/4\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}] }, Closed]], Cell[CellGroupData[{ Cell["Lists", "Subsection", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "Several objects may be grouped together into a ", StyleBox["list", FontWeight->"Bold", FontSlant->"Italic"], ", which is denoted with braces. For example:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \({15\/30, \ \[Pi], \ "\", \ Expand[\((a\ + \ b)\)\^3]}\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}] }, Closed]], Cell[CellGroupData[{ Cell["Vectors", "Subsection", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "A list consisting of several number represents a ", StyleBox["vector", FontWeight->"Bold"], ". The operations of adding two vectors and multiplying a vector be a \ scalar (that is, a number) are done so:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \({1, \ 2}\ + \ {5, \ \(-8\)}\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(4\ {1, \ 2}\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["\<\ Individual entries in a list can be extracted by indexing, as follows:\ \>", "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell[BoxData[{ \(\(vec\ = \ {4, \ 8};\)\), "\n", \(vec[\([2]\)]\)}], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "For indexing, you may prefer to type \[EscapeKey]", StyleBox["[[", FontFamily->"Courier"], "\[EscapeKey] and \[EscapeKey]", StyleBox["]]", FontFamily->"Courier"], "\[EscapeKey] to get more distinctive double brackets:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(vec\[LeftDoubleBracket]2\[RightDoubleBracket]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Equations and solving (optional for now)", "Subsection", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["\<\ If you're running out of time today, you may skip this subsection for now. \ But come back to it at a later date.\ \>", "BoxedText", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ StyleBox["\[WarningSign]", FontSize->20, FontColor->RGBColor[1, 0, 0]], " Equations are formed with ", StyleBox["two", FontSlant->"Italic"], " equal signs!" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(2\ + \ 2\ == \ 4\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(x\ \((x\ + \ x)\)\ == \ 2\ x\^2\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "To solve an equation, use the ", StyleBox["Solve", FontFamily->"Courier"], " function:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(Solve[3 x\ - \ 7\ == \ 89\/5, \ x]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "Surprised at the output? It does not directly give you the solution, but \ rather a ", StyleBox["replacement rule", FontWeight->"Bold", FontSlant->"Italic"], " for the solve variable. (Moreover, the rule is in the form of a \ brace-enclosed list; more about that later.)" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "To convert such a replacement rule into an actual value, use the form ", StyleBox["expr /. rule", FontFamily->"Courier"], "." }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(x\ /. %\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "Better yet, anticipate having to do this and assign the replacement rule \ result of the ", StyleBox["Solve", FontFamily->"Courier"], " to a name: " }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(mysoln\ = \ Solve[3 x\ - \ 7\ == \ 89\/5, \ x]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(x\ /. \ mysoln\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "There still one nasty thing about the answer\[LongDash]it's a list, albeit \ with a single entry. And that's because the result of ", StyleBox["Solve", FontFamily->"Courier"], " was a one-entry list, and that entry is itself a list. To get rid of the \ outer list braces, you can index or apply in this case the equivalent \ function ", StyleBox["First", FontFamily->"Courier"], ":" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[{ \(mysoln\ = \ First[Solve[3 x\ - \ 7\ == \ 89\/5, \ x]]\), "\n", \(x\ /. \ mysoln\)}], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["\<\ To solve several equations simultaneously, put them into a list:\ \>", "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(Solve[{2\ x\ - \ 3\ y\ == \ 7, \ 5\ x\ + \ 6\ y\ == \ 4}, \ {x, \ y}]\)], "Input", CellMargins->{{17.625, 73}, {Inherited, Inherited}}] }, Closed]], Cell[CellGroupData[{ Cell["Numerical values", "Subsection", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "As you have already seen, ", StyleBox["Mathematica", FontSlant->"Italic"], " can work with exact rational and irrational quantities. When you want to \ convert such an exact quantity, say one involving ", Cell[BoxData[ \(TraditionalForm\`\@2\)]], ", into its numerical equivalent, use the function ", StyleBox["N", FontFamily->"Courier"], "." }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \({\@2, \ N[\@2]}\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "By default, ", StyleBox["Mathematica", FontSlant->"Italic"], " displays only 6 significant digits, but you can ask for more if you start \ with exact numbers:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(N[\@2, \ 40]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "If, though, your input is a floating-point (approximate) number including \ a decimal point, then ", StyleBox["Mathematica", FontSlant->"Italic"], " will only give meaningful results to machine precision:" }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(N[\@2.0]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "High precision arithmetic is possible with ", StyleBox["Mathematica:", FontSlant->"Italic"] }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ \(N[\[Pi], \ 100]\)], "Input", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "Unfortunately, ", StyleBox["Mathematica ", FontSlant->"Italic"], "precision is a complicated subject, and that's all we'll say about it \ here." }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Creating notebooks", "Section", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ StyleBox["To create a new notebook", FontWeight->"Bold", FontSlant->"Italic"], ", from the ", StyleBox["File", FontFamily->"Helvetica"], " menu you would select ", StyleBox["New", FontFamily->"Helvetica"], ". The new, blank notebook that opens will be untitled; you will give it a \ name when you first save the notebook." }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ StyleBox["Try it now:", Background->GrayLevel[0.900008]], " Create a new notebook. In it type some input cell and evaluate that \ cell. At the top of the notebook, create a text cell and type your name(s) \ there. " }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["\<\ If you create a new notebook, it will doubtless look plainer than this one. \ Tthis one has had a distinctive \"style sheet\" applied to format the entire \ notebook in order to make it more attractive (I hope) and to more readily \ distinguish input and output cells from others.\ \>", "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "You may have several notebooks open at once in a ", StyleBox["Mathematica", FontSlant->"Italic"], " session. To select the one in which you want to work, just click \ anywhere in its window." }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}] }, 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!)" }], "BoxedText", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell["What's next?", "Section", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "Congratulations! You have completed this brief introduction to ", StyleBox["Mathematica.", FontSlant->"Italic"], " \nNow you're ready to start using ", StyleBox["Mathematica", FontSlant->"Italic"], " to learn topics in this course. If you have time today, go next to the \ notebook ", StyleBox["Flatland.nb", FontFamily->"Courier"], ". Otherwise,\" clean up\" as indicated below and work on that notebook \ next time." }], "Text", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}] }, Closed]], Cell["Cleaning up", "Section", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell[TextData[{ "When you are finished at your ", StyleBox["Mathematica", FontSlant->"Italic"], " session for today, please:\n \[FilledSmallCircle] Save all notebooks \ (such as this one) that you want to save to your diskette (or copy them to \ your diskette from the ", StyleBox["User Item", FontFamily->"Courier"], "s folder on ", StyleBox["Math HD", FontFamily->"Courier"], " where you originally put them).\n \[FilledSmallCircle] Close all open \ notebooks.\n \[FilledSmallCircle] Exit (quit) ", StyleBox["Mathematica", FontSlant->"Italic"], " from the ", StyleBox["File", FontFamily->"Helvetica"], " menu." }], "BoxedText", CellMargins->{{17.625, Inherited}, {Inherited, Inherited}}], Cell["Copyright \[Copyright] 1999 by Murray Eisenberg", "Copyright", CellMargins->{{17.625, 62}, {Inherited, Inherited}}, TextAlignment->Center, TextJustification->0] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 723}}, ScreenStyleEnvironment->"Working", WindowToolbars->{}, CellGrouping->Manual, WindowSize->{687, 517}, WindowMargins->{{Automatic, 99}, {Automatic, 69}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, Magnification->1, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of all cells in \ a given style. 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