(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 459697, 10143] NotebookOptionsPosition[ 433550, 9371] NotebookOutlinePosition[ 437085, 9470] CellTagsIndexPosition[ 436353, 9450] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Physicist's Introduction to ", StyleBox["Mathematica ", FontSlant->"Italic"], "6 " }], "Title", CellChangeTimes->{{3.394579470096292*^9, 3.3945794805215673`*^9}, { 3.395926278610983*^9, 3.3959262787251673`*^9}}, FontColor->RGBColor[0, 0, 1]], Cell[TextData[StyleBox["Third Edition 2007", FontSlant->"Italic"]], "Subtitle", CellChangeTimes->{{3.394579519605548*^9, 3.3945795336356897`*^9}, { 3.394579849753665*^9, 3.3945798497607594`*^9}}], Cell["PHYSICS 200", "Subtitle", CellChangeTimes->{{3.394579873314529*^9, 3.3945798826114264`*^9}}], Cell[CellGroupData[{ Cell["Nicholas Wheeler", "Author", CellChangeTimes->{{3.39457972270331*^9, 3.3945797314311037`*^9}}], Cell["REED COLLEGE", "Institution", CellChangeTimes->{{3.3945797341591387`*^9, 3.39457973632885*^9}, { 3.394579793724296*^9, 3.3945797937303047`*^9}}] }, Open ]], Cell["", "Text", CellChangeTimes->{{3.394580016736314*^9, 3.394580026314102*^9}}], Cell["", "Text", CellChangeTimes->{{3.394580016736314*^9, 3.394580026561102*^9}}], Cell[TextData[{ "NOTE: The first editionof this material, written during the summer of 2000, \ was designed in the presumption that ", StyleBox["Mathematica ", FontSlant->"Italic"], "4 would be running on", StyleBox[" ", FontSlant->"Italic"], "Macintosh OS 9. By the summer of 2006 ", StyleBox["Mathematica", FontSlant->"Italic"], " had acquired new capabilities, and OS X had become commonplace. My 2nd \ edition, intended to take into account those developments, was written in the \ presumption that ", StyleBox["Mathematica", FontSlant->"Italic"], " 5.2 would be running on OS X version 10.4 or a comparable system." }], "Text", CellChangeTimes->{{3.394580016736314*^9, 3.394580050806147*^9}, { 3.3945801422986927`*^9, 3.394580206674231*^9}, {3.3945802628593817`*^9, 3.3945803180189543`*^9}, {3.394580349560506*^9, 3.3945803986598263`*^9}, { 3.394580731027203*^9, 3.39458079244934*^9}, {3.394580857178791*^9, 3.3945809323363867`*^9}}], Cell[TextData[{ "Now ", StyleBox["Mathematica", FontSlant->"Italic"], " 6 has appeared, which has new capabilities, but has been stripped of many \ of the features most characteristic of ", StyleBox["Mathematica", FontSlant->"Italic"], " 5.2. The differences are so great that notebooks written in 5.2 typically \ will not run (or at least will not run smoothly) on 6. I have been obliged to \ start once again, from scratch." }], "Text", CellChangeTimes->{{3.394580016736314*^9, 3.394580050806147*^9}, { 3.3945801422986927`*^9, 3.394580206674231*^9}, {3.3945802628593817`*^9, 3.3945803180189543`*^9}, {3.394580349560506*^9, 3.3945803986598263`*^9}, { 3.394580731027203*^9, 3.39458079244934*^9}, {3.394580857178791*^9, 3.394580970284161*^9}, {3.394581007871481*^9, 3.3945810487235413`*^9}, { 3.3945810787391033`*^9, 3.394581108663926*^9}, {3.3945811403194036`*^9, 3.394581224282379*^9}, {3.394581262007915*^9, 3.3945812620209723`*^9}}], Cell["", "Text", CellChangeTimes->{{3.394581262223153*^9, 3.3945812622287416`*^9}}], Cell["", "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Laboratory 0", FontColor->RGBColor[1, 0, 0]]], "Subtitle", CellChangeTimes->{{3.394581250479834*^9, 3.394581255896365*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "Why Bother to Learn ", StyleBox["Mathematica", FontSlant->"Italic"], "?" }], "Section"], Cell[TextData[{ "Until a few years ago my own response to that question would have been \ \"Why indeed? I became a physicist in order to learn some things about how \ Nature works, not things about v.6 of some proprietary \ software\[Ellipsis]described in a book thicker and heavier than any of my \ physics books!\" But the fact of the matter is that we probe Nature not with \ our bare hands, but with tools\[LongDash]man-made contrivances, whether we \ call them principles, theorems, analytical techniques or multi-channel \ analyzers. So the short answer is: Because ", StyleBox["Mathematica", FontSlant->"Italic"], " is a wonderful new tool\[LongDash]sharper and more broadly useful than \ most others that spring to mind, and remarkably easy to use." }], "Text", CellChangeTimes->{ 3.3945884823832006`*^9, {3.394588515776514*^9, 3.394588515794959*^9}}], Cell[TextData[{ StyleBox["\n\t", FontFamily->"AGaramond"], StyleBox["Mathematica", FontSlant->"Italic"], ", first released in June 1988, is a creation of Stephen Wolfram (born in \ 1959). It provides an almost exhaustive compendium of mathematical data and \ information, and a computing engine of such immeasurably broad potential that \ few can claim mastery of all its parts\[Ellipsis]which is why ", StyleBox["The Mathematica Book ", FontSlant->"Italic"], "is so thick, and why so much supplemental material (books, downloadable \ software) treating this or that special area of application have come into \ being. Let us therefore accept at the outset that our present objective must \ be a limited one\[LongDash]to gain a working familiarity with the elementary \ first principles of ", StyleBox["Mathematica", FontSlant->"Italic"], ", and some rough sense of its potential. Refined procedures we agree to \ reserve for the day when the work at hand ", StyleBox["requires", FontSlant->"Italic"], " that we move beyond the basics, and lends urgency to the effort." }], "Text", CellChangeTimes->{ 3.3945884823832006`*^9, 3.394588515776514*^9, {3.3945885828408012`*^9, 3.394588588714109*^9}, {3.394588639698522*^9, 3.3945886996770477`*^9}}], Cell[TextData[{ StyleBox["\n\t", FontFamily->"AGaramond"], "It will very soon become apparent to you that ", StyleBox["Mathematica", FontSlant->"Italic"], " is so powerful\[LongDash]and so easy to control\[LongDash]that it opens a \ door to quick-and-easy ", StyleBox["mathematical experimentation", FontColor->RGBColor[0, 0, 1]], " that until now has stood shut even to the greatest minds\[LongDash]a door \ to an entirely new and much more improvisatory way of thinking about and \ doing pure & applied mathematics. You will find yourself in position to do \ things that formerly you would not even have dreamed of doing (certainly not \ of doing casually, without a lot of labor-intensive special-purpose \ programming), and that the formulation/testing of conjectures has come to \ occupy a central position in your mathematical life. " }], "Text", CellChangeTimes->{ 3.3945884823832006`*^9, 3.394588515776514*^9, {3.3945885828408012`*^9, 3.394588588714109*^9}, {3.394588639698522*^9, 3.394588699659889*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Getting Started\[Ellipsis]and Stopped", "Section", CellChangeTimes->{3.3957840092322397`*^9}, TextAlignment->Left, TextJustification->1.], Cell[TextData[{ "I begin with a cautionary word: It is inevitable that you will from time to \ time (and especially in the beginning) steer ", StyleBox["Mathematica", FontSlant->"Italic"], " off the road, and have to ", StyleBox["Restart", FontWeight->"Bold"], ". To avoid catastrophy" }], "Text", CellChangeTimes->{3.395784009232904*^9}, TextAlignment->Left, TextJustification->1.], Cell[TextData[StyleBox["Be sure that you have Saved open documents running \ in other applications.", FontSize->16, FontColor->RGBColor[1, 0, 0]]], "Text", CellChangeTimes->{{3.394591008989142*^9, 3.39459104500974*^9}, 3.3957840092335873`*^9}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " comes in two large and semi-autonomous packages:" }], "Text", CellChangeTimes->{{3.3945913058299847`*^9, 3.394591305843693*^9}, 3.39578400923419*^9}, TextAlignment->Left, TextJustification->1.], Cell["", "Text", CellChangeTimes->{3.3957840092371693`*^9}], Cell[CellGroupData[{ Cell[TextData[StyleBox["\[Bullet] the computing engine itself, called the \ \"kernel\";", "Item3Paragraph"]], "Item1Paragraph", CellChangeTimes->{{3.394588975210185*^9, 3.394588976921069*^9}, { 3.394591286865964*^9, 3.3945912868821497`*^9}, 3.39578400924193*^9}, TextAlignment->Left, TextJustification->1.], Cell[TextData[StyleBox["", "Item3Paragraph"]], "Item1Paragraph", CellChangeTimes->{3.395784009243037*^9}], Cell[TextData[{ "\[Bullet] the \"front end\", which mediates the flow of information between \ you and the kernel (or perhaps several kernels, running simultaneously on \ several computers). The front end manages screen display, graphics, access to \ the Documentation Center (which in ", StyleBox["Mathematica", FontSlant->"Italic"], " 6 replaces the \"Browser,\" and is where one goes for assistance) and much \ else, and can perform certain tasks independently of the kernel; it was \ originally conceived and designed not by Wolfram himself, but by Theodore \ Gray. 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To turn on the kernel and (more to the \ point) to ", StyleBox["establish communication between the front end and the kernel", FontColor->RGBColor[0, 0, 1]], " the traditional procedure is to type ", StyleBox["2-2", "Input"], " and hit ENTER:" }], "Text", CellChangeTimes->{{3.3945896767550173`*^9, 3.39458967814644*^9}, 3.3945913405277653`*^9, 3.39578400924625*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"2", "-", "2"}]], "Input", CellChangeTimes->{{3.39458939848449*^9, 3.394589398891244*^9}, 3.395784009247507*^9}], Cell[BoxData["0"], "Output", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{3.394589408007695*^9, 3.395778015890663*^9, 3.395784009248708*^9}], Cell[TextData[{ "NOTE: The traditional procedure is to type ", StyleBox["2+2", "Input"], ". 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CellChangeTimes->{{3.394720980160801*^9, 3.3947209875101337`*^9}, 3.3957840096555347`*^9, {3.396739516714301*^9, 3.396739522090391*^9}}, FontColor->RGBColor[1, 0, 0]], Cell["\t", "Text", CellChangeTimes->{{3.394721057358857*^9, 3.3947210573717937`*^9}, 3.3957840096565104`*^9}], Cell[TextData[{ "Not infrequently you will want, for one reason or another, to ", "terminate a calculation. Maybe you've realized you have asked ", StyleBox["Mathematica", FontSlant->"Italic"], " to do the wrong thing, or the calculation has run so long that you suspect \ (unfortunately, ", StyleBox["Mathematica", FontSlant->"Italic"], " returns no progress reports) something may be wrong with your command, or \ ", StyleBox["Mathematica", FontSlant->"Italic"], " reports back that it has been caught up in an endless loop. In such cases \ the first thing to try is" }], "Text", CellChangeTimes->{3.394721057358857*^9, 3.395784009658017*^9}], Cell[TextData[{ "\t\[CloverLeaf]", StyleBox[".", "Input"], " ", StyleBox["Simple abort", FontColor->RGBColor[1, 0, 0]], ": hold down \[CloverLeaf] and press period\[Ellipsis]and wait." }], "Text", CellChangeTimes->{3.395784009658687*^9}], Cell[TextData[{ "Equivalently, you might select ", StyleBox["Abort Evaluation", FontWeight->"Bold"], " from the front end's ", StyleBox["Evaluation", FontWeight->"Bold"], " menu.The kernel has to \"back up,\" so the wait is roughly proportional to \ how deep you were into the calculation, but eventually (after perhaps several \ seconds or minutes) an ", StyleBox["Out[#]=Aborted ", "Output"], "should appear. " }], "Text", CellChangeTimes->{ 3.395784009668829*^9, {3.3980858645955*^9, 3.39808587276661*^9}}], Cell[TextData[{ "\tBut ", StyleBox["Mathematica", FontSlant->"Italic"], ", once started, reveals a single-minded reluctance to quit, and after a \ long wait you may conclude that the simple technique just described is not \ going to work. Or perhaps you are simply tired of waiting. Try" }], "Text", CellChangeTimes->{3.395784009669757*^9}], Cell[TextData[StyleBox[" Evaluation > Quit Kernel", FontWeight->"Bold"]], "Text", CellChangeTimes->{{3.395785570259762*^9, 3.395785611799075*^9}}], Cell["or", "Text", CellChangeTimes->{{3.395785630774227*^9, 3.395785630888204*^9}}], Cell[TextData[{ "\t\[CloverLeaf]", StyleBox["q", "Input"], " ", StyleBox["Simple quit ", FontColor->RGBColor[1, 0, 0]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": you will be asked if you want to ", StyleBox["Save", FontWeight->"Bold"], " your work, " }], "Text", CellChangeTimes->{3.3957840096719627`*^9}], Cell[TextData[{ "then both the front end and the kernel will shut down, and you will have to \ ", StyleBox["Restart ", FontWeight->"Bold"], "the application. ", "If that is ineffective, try hitting" }], "Text", CellChangeTimes->{3.395784009672772*^9}], Cell[TextData[{ "\t\[CloverLeaf]\[OptionKey]\[EscapeKey] ", StyleBox["Hard dump of the kernel", FontColor->RGBColor[1, 0, 0]], ". ", StyleBox["Save", FontWeight->"Bold"], " your work, ", StyleBox["Quit", FontWeight->"Bold"], " ", StyleBox["Mathematica", FontSlant->"Italic"], ", ", StyleBox["Restart", FontWeight->"Bold"], "." }], "Text", CellChangeTimes->{3.395784009677306*^9}], Cell[TextData[{ "Finally, you can ", StyleBox["turn off the computer ", FontColor->RGBColor[1, 0, 0]], "(a \"forced quit\" may be necessary) or, in dire cases, ", StyleBox["unplug the computer", FontColor->RGBColor[1, 0, 0]], "\[Ellipsis]but will lose any unsaved open documents. It is in anticipation \ of such an event (or other misfortune) that you should be careful to " }], "Text", CellChangeTimes->{ 3.3957840096783133`*^9, {3.395785689320642*^9, 3.3957857094115973`*^9}}], Cell[TextData[{ StyleBox["Save your notebook at frequent intervals", FontSize->18, FontColor->RGBColor[1, 0, 0]], StyleBox[".", FontSize->18], " " }], "Text", CellChangeTimes->{3.395784009797346*^9}, TextAlignment->Center, TextJustification->0], Cell[TextData[{ StyleBox["SUGGESTION", FontWeight->"Bold"], ": WRITE THOSE ALTERNATIVE TERMINATION METHODS DOWN ON A SLIP OF PAPER. For \ when you most need them you will not be able to access this notebook (or any \ other source) where they are described." }], "Text", CellChangeTimes->{{3.394721328763859*^9, 3.3947214098388987`*^9}, 3.395784009798369*^9, {3.395835302715201*^9, 3.3958353046331797`*^9}}, FontColor->RGBColor[0, 0, 1]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Notebooks", "Section", CellChangeTimes->{{3.394721483033993*^9, 3.3947214851053247`*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " documents are called \"notebooks,\" and wear the suffix ", StyleBox[".nb ", FontWeight->"Bold"], "Open the ", StyleBox["File", FontWeight->"Bold"], " menu, select ", StyleBox["New", FontWeight->"Bold"], " (alternatively: hit \[CloverLeaf]", StyleBox["n", "Input"], "), and you have created a new notebook. Use ", StyleBox["File > Save As\[Ellipsis]", FontWeight->"Bold"], " (alternatively: \[ShiftKey]\[CloverLeaf]", StyleBox["s", "Input"], ") to name and save the notebook. " }], "Text"], Cell[TextData[{ "\tNotebooks can be rendered in various \"styles\"\[LongDash]designs \ intended for different uses. ", StyleBox["Mathematica", FontSlant->"Italic"], " 6 is shipped with 17 canned designs: open ", StyleBox["Format > Stylesheet ", FontWeight->"Bold"], "to see the list and sublists. Try them, one after the other, to see what \ they do to this text, which I have written (and prefer to have read) in ", StyleBox["Book > Textbook", FontWeight->"Bold"], " style. " }], "Text", CellChangeTimes->{{3.394721579409309*^9, 3.394721580269803*^9}, { 3.394721631446026*^9, 3.394721653313335*^9}, {3.394721933975503*^9, 3.394722018445116*^9}, {3.395835359201804*^9, 3.395835371329782*^9}}], Cell[TextData[{ "\tDifferent canned styles come equipped with different sets of options\ \[LongDash]few in some cases, numerous in others. Open ", StyleBox["Window", FontWeight->"Bold"], ", note the control options placed thus at your disposal, and activate ", StyleBox["Show Toolbar", FontWeight->"Bold"], ". Select the ", StyleBox["Default ", FontWeight->"Bold"], "style, and open the ", StyleBox["ToolBar", FontWeight->"Bold"], " menu: it shows only a few options. Now return to ", StyleBox["Textbook Style", FontWeight->"Bold"], ": it shows dozens of options\[Ellipsis]which is one (but only one) of the \ reasons I have elected to work in that style." }], "Text", CellChangeTimes->{{3.394722170372025*^9, 3.394722223821724*^9}, { 3.394722270909728*^9, 3.394722307482848*^9}, {3.3947223997304792`*^9, 3.3947224008634243`*^9}, {3.39472246601089*^9, 3.394722499673676*^9}, { 3.394722530973023*^9, 3.394722569362176*^9}, {3.394722602110221*^9, 3.394722631944882*^9}, 3.39472268956629*^9, {3.394722808959923*^9, 3.394722817264742*^9}, 3.39472323410818*^9}], Cell[TextData[{ "\tUnder ", StyleBox["Format", FontWeight->"Bold"], " you find ", StyleBox["Edit Stylesheet", FontWeight->"Bold"], ", and someday you may have occasion to do just that. But for the moment we \ have already in hand all the resources we will need. My general advice:" }], "Text", CellChangeTimes->{{3.394722826781066*^9, 3.394722866268916*^9}, 3.3947228981927023`*^9, {3.394723283977133*^9, 3.394723283986878*^9}}], Cell["", "Text"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["\[Bullet] Mathematica", FontSlant->"Italic"], " is intolerant of typos\[LongDash]all capitalization, every brace and \ bracket (whether round, curly or square), every bit of punctuation must be \ exactly right\[LongDash]so ", StyleBox["work with the magnification (adjustable at the bottom of the page) \ big enough", FontColor->RGBColor[0, 0, 1]], " that you can clearly distinguish ", StyleBox[".", "Input"], " from ", StyleBox[",", "Input"], " etc." }], "Item1Paragraph", CellChangeTimes->{{3.3947229203946657`*^9, 3.394723134594233*^9}, { 3.394723288160347*^9, 3.394723288296936*^9}}, TextAlignment->Left, TextJustification->1.], Cell["", "Item1Paragraph"], Cell[TextData[{ StyleBox["\[Bullet] ", "Code"], StyleBox["Show the", FontColor->RGBColor[0, 0, 1]], StyleBox[" Toolbar", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "; it is a great aid to the insertion of section titles, explanatory text, \ etc." }], "Item1Paragraph", CellChangeTimes->{{3.394723169770825*^9, 3.3947232621294823`*^9}, { 3.39472329345754*^9, 3.394723293588152*^9}}], Cell["", "Item1Paragraph"], Cell[TextData[{ "\[Bullet] Make the page large, yet small enough to ", StyleBox["leave room on the screen for an input pallet or two", FontColor->RGBColor[0, 0, 1]], "." }], "Item1Paragraph", CellChangeTimes->{{3.394723308426923*^9, 3.394723348051628*^9}, { 3.39472339322703*^9, 3.394723393365368*^9}}], Cell["", "Item1Paragraph"], Cell[TextData[{ "\[Bullet] At the beginning of each work session your first command will \ cause ", StyleBox["Mathematica", FontSlant->"Italic"], " to attempt automatically to open the Kernel, but if the command is \ complicated that attempt may take long time, or even fail. ", StyleBox["Always start with a simple command, like the classic evaluation of \ ", FontColor->RGBColor[0, 0, 1]], StyleBox["2-2", "Input", FontColor->RGBColor[0, 0, 1]], "." }], "Item1Paragraph", CellChangeTimes->{{3.394723404329403*^9, 3.394723404585609*^9}, { 3.3947236822328053`*^9, 3.394723772921163*^9}}, TextAlignment->Left, TextJustification->1.] }, Open ]], Cell["", "Text", CellChangeTimes->{{3.396017937194881*^9, 3.39601793733853*^9}}], Cell[TextData[{ "For access to a lot of useful information about this broad topic and the \ topic addressed below, go to ", StyleBox["Documentation Center", FontWeight->"Bold"], " and search for ", StyleBox["tutorial/InputAndOutputInNotebooksOverview", FontColor->RGBColor[0, 0, 1]], "." }], "Text", CellChangeTimes->{{3.3960179441728287`*^9, 3.396018039143424*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Input Techniques &Tips", "Section", CellChangeTimes->{{3.39472384400985*^9, 3.394723879851776*^9}, { 3.396659941900584*^9, 3.39665994797968*^9}, {3.3966600482438*^9, 3.396660058710927*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " assigns distinct and non-interchangeable responsibilities to ( ), [ ] and \ { }. 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But first a\n" }], "Text"], Cell[TextData[{ StyleBox["TIP", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ": The correct way to type ", StyleBox["(stuff)", "Input"], " is not to type ", StyleBox["(", "Input"], " then ", StyleBox["stuff", "Input"], " then ", StyleBox[")", "Input"], " but " }], "Text", CellChangeTimes->{{3.394723908588951*^9, 3.394723955725506*^9}}], Cell[TextData[{ StyleBox["( ) then the ", FontColor->RGBColor[0, 0, 1]], StyleBox["stepleft", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[" key \[LeftArrow] then ", FontColor->RGBColor[0, 0, 1]], StyleBox["stuff", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[" and finally the ", FontColor->RGBColor[0, 0, 1]], StyleBox["stepright", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[" key \[RightArrow]", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[TextData[{ "That way, having typed a ", StyleBox["(", "Input"], ", you will avoid both the danger of forgetting or misplacing the ", StyleBox[")", "Input"], ", and will avoid also the distraction of ", StyleBox["Mathematica", FontSlant->"Italic"], "'s ", StyleBox["signal", FontColor->RGBColor[1, 0, 1]], " that it has detected an unclosed parenthetic. 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Returning to our recent example: to evaluate ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{" ", "0"}], RowBox[{" ", "\[Infinity]"}]], RowBox[{"x", " ", SuperscriptBox["e", RowBox[{"-", SuperscriptBox["x", "3"]}]], StyleBox["dx", FontSlant->"Italic"]}]}], TraditionalForm]]], " one might use the ", StyleBox["BasicMathInput", FontWeight->"Bold"], " palette (of which more in a minute) to construct the command " }], "Text", CellChangeTimes->{{3.394724709282152*^9, 3.3947247287107687`*^9}, { 3.3958718319649677`*^9, 3.395871837224243*^9}, {3.395871885467689*^9, 3.3958720096998987`*^9}, {3.395872043951157*^9, 3.395872046709063*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[{"x", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", SuperscriptBox["x", "3"]}]], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input"], Cell[BoxData[ RowBox[{ FractionBox["1", "3"], " ", RowBox[{"Gamma", "[", FractionBox["2", "3"], "]"}]}]], "Output", CellChangeTimes->{3.394724764514414*^9}] }, Open ]], Cell["\<\ which, as you see, functions exactly like its telegraphic counterpart. The \ standard collection serves most needs, but can readily be expanded by the \ user who has specialized requirements. \ \>", "Text", CellChangeTimes->{{3.395872103165753*^9, 3.39587212030284*^9}}], Cell[TextData[{ "The ", StyleBox["Palettes", FontWeight->"Bold"], " menu leads you to a selection of six pallets listed above the line (I will \ have nothing to say about the advanced options below the line, or the \ procedure you can use to construct palettes that serve your specialized \ needs). Open each, to get a rough sense of the lay of the land. The ", StyleBox["AlgebraicManipulation", FontWeight->"Bold"], " palette provides quick access to common commands we will soon commit to \ memory, so is of relatively little use. Of especially high utility is the ", StyleBox["BasicMathInput", FontWeight->"Bold"], " palette, which you will often want to have available in some handy \ position on your computer screen. Also of very frequent use are the resources \ of the ", StyleBox["SpecialCharacters ", FontWeight->"Bold"], "palette, which is seen to be really a collection of twelve palettes: ", StyleBox["Palettes > SpecialCharacters", FontWeight->"Bold"], " and ", StyleBox["Insert > SpecialCharacter... ", FontWeight->"Bold"], "serve equally well to get you there." }], "Text", CellChangeTimes->{{3.3947249651384163`*^9, 3.3947252390079412`*^9}, { 3.394725269057184*^9, 3.39472533559262*^9}, {3.3947253683321257`*^9, 3.3947254714669952`*^9}, {3.395763913671471*^9, 3.3957640084341183`*^9}, 3.3957640429706993`*^9, {3.395872136971569*^9, 3.3958722551023903`*^9}, { 3.395872301333708*^9, 3.395872398011807*^9}, {3.3958724434374733`*^9, 3.395872444604208*^9}, {3.395872503147379*^9, 3.3958725361887283`*^9}}], Cell["", "Text", CellChangeTimes->{{3.395874506512013*^9, 3.395874506523726*^9}}], Cell["", "Text"], Cell[TextData[{ "Concerning the ", StyleBox["BasicMathInput", FontWeight->"Bold"], ", a ", StyleBox["CAUTIONARY WARNING", FontSize->18, FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is in order, for ", StyleBox["Mathematica", FontSlant->"Italic"], " 6 has in this connection developed an ", StyleBox["unfortunate quirk", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Suppose we are working in \"Textbook\" style, and (because we went ", StyleBox["Window > ", FontWeight->"Bold"], "\[Checkmark]", StyleBox[" Show Toolbar", FontWeight->"Bold"], " at the beginning of this work session) have the \"Toolbar\" showing (which \ is always a good idea). Suppose, moreover, that\[LongDash]having placed \ ourselves in the ", StyleBox["Input", "Input"], " mode\[LongDash]we propose to use the ", StyleBox["BasicMathInput", FontWeight->"Bold"], " to write" }], "Text", CellChangeTimes->{{3.395872571117893*^9, 3.395872621940997*^9}, { 3.3958726644278097`*^9, 3.395872747555105*^9}, 3.3958728111842537`*^9, { 3.395872842633339*^9, 3.395872850608891*^9}, {3.395872890930279*^9, 3.395873028531869*^9}, {3.3958730894531937`*^9, 3.395873093845118*^9}, { 3.3958731950149183`*^9, 3.395873222724663*^9}, {3.395873310739025*^9, 3.3958734355711327`*^9}, {3.395873499744812*^9, 3.395873529091711*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"\[Integral]", RowBox[{"\[Placeholder]", RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{{3.3958730425261307`*^9, 3.395873059165308*^9}}], Cell["\<\ We are astounded to discover that the symbol actually created by the \ \"integrate\" button looks like this\ \>", "Text", CellChangeTimes->{{3.395873573715946*^9, 3.3958736184933434`*^9}}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"\[Integral]", RowBox[{"\[Placeholder]", RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}], FontColor->GrayLevel[0.5]]], "Title", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "and that ", StyleBox["Mathematica", FontSlant->"Italic"], " has flipped spontaneously into \"Title\" mode. To create the symbol we \ intended, and to get on with writing out intended command, we have to return \ to the Toolbar and\[LongDash]by hand\[LongDash]flip back into ", StyleBox["Input", "Input"], " mode. It turns out that this disease is present only when the ", StyleBox["BasicMathInput ", FontWeight->"Bold"], "palette is being used to creat the ", StyleBox["first", FontSlant->"Italic"], " symbol of a command: no problem arises if the palette is used to create ", StyleBox["subsequent", FontSlant->"Italic"], " symbols. We can use that circumstant to construct a ", StyleBox["WORKAROUND", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ": To create (say)" }], "Text", CellChangeTimes->{{3.395873677078683*^9, 3.395873715421816*^9}, { 3.39587390968891*^9, 3.395874261478868*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"\[Integral]", RowBox[{"\[Placeholder]", RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}], FontColor->GrayLevel[0.5]]], "Input"], Cell["first type (say)", "Text", CellChangeTimes->{{3.395874346863606*^9, 3.395874347174514*^9}, { 3.395874414729616*^9, 3.3958744240721197`*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"q", RowBox[{"\[Integral]", RowBox[{"\[Placeholder]", RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}]}], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{{3.395874357728698*^9, 3.395874363963039*^9}}], Cell[TextData[{ "and then ", StyleBox["erase", FontSlant->"Italic"], " the ", StyleBox["q", "Input"], ". Alternatively (and just as quickly) one can avoid the problem altogether \ by ", StyleBox["using the keyboard", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" (in the manner discussed below) to create 2-dimensional symbols", FontWeight->"Bold"], ". For example, one has only to type \[EscapeKey]intt", "\[EscapeKey] to create" }], "Text", CellChangeTimes->{{3.3958743725446663`*^9, 3.3958743788313017`*^9}, { 3.395874444824616*^9, 3.3958744693689404`*^9}, 3.3958879169972057`*^9, { 3.395887969390656*^9, 3.395888065673304*^9}, {3.3958881059530897`*^9, 3.395888153849815*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"\[Integral]", RowBox[{"\[Placeholder]", RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{{3.3958881646913967`*^9, 3.395888170885013*^9}}], Cell["", "Text", CellChangeTimes->{{3.3958745217413397`*^9, 3.39587452181069*^9}}], Cell["", "Text"], Cell[TextData[{ "What distinguishes the \[SelectionPlaceholder] boxes from the \ \[Placeholder] boxes that are evident on the ", StyleBox["BasicMathInput ", FontWeight->"Bold"], "palette? The answer is made obvious by example. If you were to enter " }], "Text", CellChangeTimes->{{3.394726817533639*^9, 3.3947268865937967`*^9}, { 3.394726996787691*^9, 3.394727024179656*^9}, {3.3958366406228933`*^9, 3.395836677542235*^9}, {3.395836732150011*^9, 3.3958367487039022`*^9}, { 3.3958745786272593`*^9, 3.3958746101157837`*^9}, {3.395874965639903*^9, 3.395875002833149*^9}}], Cell[BoxData[ StyleBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"Sin", "[", "x", "]"}]}], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{{3.395875012826663*^9, 3.395875026020825*^9}}], Cell[TextData[{ "as ", StyleBox["Input", "Input"], ", then to ", StyleBox["Select", FontWeight->"Bold"], " that expression and to hit the ", Cell[BoxData[ FormBox[ RowBox[{"\[Integral]", RowBox[{"\[SelectionPlaceholder]", RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}], TraditionalForm]]], " button, the expression would go inside the ", "\[SelectionPlaceholder], producing" }], "Text", CellChangeTimes->{{3.39587503670361*^9, 3.395875160244492*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"\[Integral]", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"Sin", "[", "x", "]"}]}], ")"}], RowBox[{"\[DifferentialD]", "\[Placeholder]"}]}]}], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{3.395875176548049*^9}], Cell[TextData[{ "Now place the cursor on \[Placeholder], type ", StyleBox["x", "Input"], " and get" }], "Text", CellChangeTimes->{{3.3958751977217197`*^9, 3.395875242620777*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Integral]", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"Sin", "[", "x", "]"}]}], ")"}], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input", CellChangeTimes->{3.3958752551370163`*^9}], Cell[BoxData[ RowBox[{ FractionBox[ SuperscriptBox["x", "3"], "3"], "-", RowBox[{"Cos", "[", "x", "]"}]}]], "Output", CellChangeTimes->{3.395875258900085*^9}] }, Open ]], Cell[TextData[{ "Similarly, we might type and ", StyleBox["Select", FontWeight->"Bold"], " ", Cell[BoxData[ FormBox[ SuperscriptBox["\[SelectionPlaceholder]", "\[Placeholder]"], TraditionalForm]]], " button, on the other hand, gives" }], "Text", CellChangeTimes->{{3.395875279106031*^9, 3.395875331062756*^9}, { 3.395875404198682*^9, 3.3958754401525993`*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"1", "+", SqrtBox[ RowBox[{"1", "+", FractionBox[ RowBox[{"a", "+", "x"}], "b"]}]]}], "Output", FontColor->GrayLevel[0.5]]], "Input"], Cell[TextData[{ "and then hit the ", Cell[BoxData[ FormBox[ SuperscriptBox["\[SelectionPlaceholder]", "\[Placeholder]"], TraditionalForm]]], " button to obtain" }], "Text", CellChangeTimes->{{3.395875462817815*^9, 3.395875486304757*^9}}], Cell[BoxData[ StyleBox[ SuperscriptBox[ RowBox[{"(", StyleBox[ RowBox[{"1", "+", SqrtBox[ RowBox[{"1", "+", FractionBox[ RowBox[{"a", "+", "x"}], "b"]}]]}], "Output", FontColor->GrayLevel[0.5]], ")"}], "\[Placeholder]"], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{3.39587550377383*^9}], Cell["\<\ which, after entering a 3 into the \[Placeholder] becomes\ \>", "Text", CellChangeTimes->{{3.395875533523404*^9, 3.395875559521576*^9}}], Cell[BoxData[ StyleBox[ SuperscriptBox[ RowBox[{"(", StyleBox[ RowBox[{"1", "+", SqrtBox[ RowBox[{"1", "+", FractionBox[ RowBox[{"a", "+", "x"}], "b"]}]]}], "Output", FontColor->GrayLevel[0.5]], ")"}], "3"], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{{3.395875569319414*^9, 3.395875571274006*^9}}], Cell[TextData[{ "Our final example makes clear the fact that in some contexts \ \[SelectionPlaceholder] distinguishes the box into which the next keystroke \ will be inserted (", StyleBox["Mathematica", FontSlant->"Italic"], " manuals often call \[SelectionPlaceholder] the \"SelectionPlaceholder,\" \ and \[Placeholder] simply \"a Placeholder\"). We have interest in a 5\[Cross] \ 7 matrix, so go ", StyleBox["Insert > Table/Matrix > New", FontWeight->"Bold"], " and, by selection the appropriate options, create" }], "Text", CellChangeTimes->{{3.3958757583539877`*^9, 3.3958757636520042`*^9}, { 3.39587580483677*^9, 3.395875861982582*^9}, {3.395875908276903*^9, 3.395876142874856*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"} }], "\[NoBreak]", ")"}], "Output"]}]], "Input", CellChangeTimes->{3.395876158272172*^9}], Cell[TextData[{ "Placing the cursor on \[Placeholder] the in the upper left corner, we type \ ", StyleBox["a", "Input"], "\[TabKey]", StyleBox["b", "Input"], "\[TabKey]", StyleBox["c", "Input"], "\[DownArrow]", StyleBox["d", "Input"], "\[DownArrow]", StyleBox["e", "Input"], "\[DownArrow]", StyleBox["f", "Input"], "\[TabKey]", StyleBox["g", "Input"], "\[TabKey]", StyleBox["h", "Input"], "\[UpArrow]", StyleBox["i", "Input"], "\[TabKey]", StyleBox["j ", "Input"], "to create" }], "Text", CellChangeTimes->{{3.3958761770080137`*^9, 3.395876374030846*^9}, { 3.39587649268349*^9, 3.395876540887269*^9}, {3.395876578268907*^9, 3.39587658143497*^9}, 3.395876617571093*^9}], Cell[BoxData[ StyleBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"a", "b", "c", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "d", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "e", "\[Placeholder]", "i", "j", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "f", "g", "h", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"} }], "\[NoBreak]", ")"}], "Output", FontColor->GrayLevel[0.5]]], "Input", CellChangeTimes->{{3.395876391847283*^9, 3.395876470011964*^9}}], Cell["\<\ This illustrates how (very commonly) \[TabKey] and (less commonly) \ \[DownArrow], \[UpArrow], \[LeftArrow] and \[RightArrow] are used to adjust \ the location of the box \[SelectionPlaceholder] that will receive the next \ keystroke.\ \>", "Text", CellChangeTimes->{{3.395877525869815*^9, 3.395877690811957*^9}}], Cell["", "Text", CellChangeTimes->{{3.395877978705565*^9, 3.395877978716895*^9}}], Cell["", "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Creating 2-Dimensional Commands & Special Symbols at \ the Keyboard", FontColor->RGBColor[1, 0, 0]]], "Subsection", CellChangeTimes->{{3.395878027862287*^9, 3.395878055878998*^9}, 3.395890683795794*^9}], Cell[TextData[{ "\tPalette buttons are a great aid to speed and legibility. But they \ require use of the mouse, and in some situations their repetitive use can \ become tedious (though deft use of ", StyleBox["Cut/Copy/Paste", FontWeight->"Bold"], " often permits accelerated escape from the tedium). It is useful to know \ that the action of palette buttons can often be achieved directly from the \ keyboard. Open", StyleBox[" Palettes > SpecialCharacters", FontWeight->"Bold"], ", then open (say) ", StyleBox["Technical Symbols", FontWeight->"Bold"], ". Click on (say) ", "\[ExponentialE]", " and see a \"double struck e.\" ", StyleBox["Mathematica", FontSlant->"Italic"], " considers \"e\" to be simply a letter, and uses the \"double struck e\" \ to denote the base of the natural logarithms, with numerical value " }], "Text", CellChangeTimes->{{3.394730011616481*^9, 3.394730070961762*^9}, 3.394730265314146*^9, {3.394743281351359*^9, 3.394743380532983*^9}, { 3.394743422260159*^9, 3.394743487295187*^9}, {3.395878122809132*^9, 3.395878122816884*^9}, 3.3958906837965117`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "\[ExponentialE]", "]"}]], "Input", CellChangeTimes->{{3.394743493242663*^9, 3.394743496377014*^9}, 3.395890683797583*^9}], Cell[BoxData["2.718281828459045`"], "Output", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{3.394743502603353*^9, 3.3958906837986927`*^9}] }, Open ]], Cell[TextData[{ "The palette informs you, if you click on the letter \"e\", that you can \ produce \[ExponentialE] at the point identified by the blinking cursor either \ (1) by selecting \[ExponentialE] on the palette and hitting the", StyleBox[" Insert ", FontColor->RGBColor[0, 0, 1]], StyleBox["button, or (2) by typing ", FontColor->GrayLevel[0]], "\[EscapeKey]", StyleBox["ee", FontColor->GrayLevel[0]], "\[EscapeKey]. Similarly ", StyleBox[" ", FontColor->GrayLevel[0]] }], "Text", CellChangeTimes->{{3.3947435223287697`*^9, 3.394743635223667*^9}, { 3.394743671692487*^9, 3.394743705849512*^9}, {3.3947440616927834`*^9, 3.394744089901079*^9}, {3.395878139523705*^9, 3.395878140259574*^9}, { 3.395878172683687*^9, 3.395878209659083*^9}, 3.395890683805622*^9}], Cell[CellGroupData[{ Cell["\[HBar] can be produced by \[EscapeKey]hb\[EscapeKey]", "Item1Paragraph", CellChangeTimes->{{3.3947437219072943`*^9, 3.3947437448416862`*^9}, { 3.3947437761717577`*^9, 3.394743776181695*^9}, 3.395890683810205*^9}], Cell["\[Infinity] can be produced by \[EscapeKey]inf\[EscapeKey]", \ "Item1Paragraph", CellChangeTimes->{{3.3947437810495567`*^9, 3.394743822543239*^9}, 3.3958906838109293`*^9}], Cell[TextData[{ StyleBox["\[ImaginaryI]", "Input"], StyleBox[" can be produced by ", "Text"], "\[EscapeKey]", StyleBox["ii", "Text"], "\[EscapeKey]" }], "Item1Paragraph", CellChangeTimes->{{3.3947438320099*^9, 3.394743891288959*^9}, 3.3958906838240833`*^9}] }, Open ]], Cell[TextData[{ StyleBox["Etc", FontSlant->"Italic"], ". Not all of the special characters can be produced in this way, but most \ of the most commonly encountered ones can be, and the palettes tell you which \ can (and how), which can't. Notice in this connection that the" }], "Text", CellChangeTimes->{{3.394728290882221*^9, 3.3947282983796988`*^9}, { 3.394743946804285*^9, 3.3947440145390863`*^9}, {3.394744118726935*^9, 3.394744171264182*^9}, {3.3958782429646387`*^9, 3.395878264507114*^9}, { 3.3958783491570883`*^9, 3.39587834960398*^9}, 3.3958906838250427`*^9}], Cell[TextData[{ " \[Pi] produced by \[EscapeKey]p\[EscapeKey], else by the ", StyleBox["Greek Letters", FontWeight->"Bold"], " palette" }], "Text", CellChangeTimes->{{3.395878364833696*^9, 3.395878425738799*^9}, 3.395890683825592*^9}], Cell["\<\ functions simultaneously as a letter and as a mathematical constant:\ \>", "Text", CellChangeTimes->{{3.395878441958021*^9, 3.395878444338779*^9}, 3.395890683826082*^9}], Cell[BoxData[ RowBox[{"N", "[", "\[Pi]", "]"}]], "Input", CellChangeTimes->{{3.39474435194862*^9, 3.394744360756934*^9}, 3.395890683827136*^9}], Cell["\<\ On the other hand, the letter \"i\" is always just a letter: the square root \ of minus one is always double struck: \ \>", "Text", CellChangeTimes->{{3.394744468586183*^9, 3.394744559197508*^9}, { 3.395878477281129*^9, 3.395878494086487*^9}, 3.395890683828031*^9}], Cell[CellGroupData[{ Cell[BoxData[ SqrtBox[ RowBox[{"-", "1"}]]], "Input", CellChangeTimes->{{3.39474457932794*^9, 3.394744579599021*^9}, 3.39589068382903*^9}], Cell[BoxData["\[ImaginaryI]"], "Output", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{3.394744580845439*^9, 3.3958906838300743`*^9}] }, Open ]], Cell[TextData[{ "Relatedly, \"capital I\"\[LongDash]when it occurs as stand-alone ", StyleBox["input", "Input"], "\[LongDash]is a \"Protected Symbol,\" which is always interpreted to mean a \ complex number:" }], "Text", CellChangeTimes->{{3.394744620094555*^9, 3.3947447029441633`*^9}, { 3.39475505941558*^9, 3.3947550847269993`*^9}, {3.39475514390318*^9, 3.394755163843885*^9}, {3.3947551999453163`*^9, 3.394755207640321*^9}, { 3.395878508335896*^9, 3.395878584481371*^9}, 3.3958906838308992`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "I", "]"}]], "Input", CellChangeTimes->{{3.394744491101329*^9, 3.394744494168064*^9}, 3.395890683831883*^9}], Cell[BoxData[ RowBox[{"0.`", "\[InvisibleSpace]", "+", RowBox[{"1.`", " ", "\[ImaginaryI]"}]}]], "Output", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{3.394744495409768*^9, 3.3958906838333893`*^9}] }, Open ]], Cell[TextData[{ "Similarly protected are ", StyleBox["C", "Input"], ",", StyleBox[" E", "Input"], " and ", StyleBox["N", "Input"], "." }], "Text", CellChangeTimes->{{3.394755227503088*^9, 3.394755247646103*^9}, { 3.394755410764512*^9, 3.394755410779714*^9}, 3.395890683834646*^9}], Cell["", "Text", CellChangeTimes->{{3.394755412724399*^9, 3.3947554127353487`*^9}, 3.3958906838352137`*^9}], Cell["\<\ Here is a short list of keyboard commands that produce important mathematical \ symbols:\ \>", "Text", CellChangeTimes->{{3.395879727843967*^9, 3.395879759017645*^9}, 3.3958906838357*^9}], 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In either ", StyleBox["Mathematica", FontSlant->"Italic"], " expects you to write ", StyleBox["==", "Input"], ". 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", FontColor->RGBColor[0, 0, 1]], StyleBox["For this purpose ", FontColor->GrayLevel[0]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->GrayLevel[0]], StyleBox[" provides the command ", FontColor->GrayLevel[0]], StyleBox["Clear", "Input", FontColor->GrayLevel[0]], StyleBox[".", FontColor->GrayLevel[0]] }], "Text", CellChangeTimes->{ 3.394762825468993*^9, {3.394762945713656*^9, 3.394762957743438*^9}, { 3.394763009838211*^9, 3.3947630540421553`*^9}, 3.394763981557497*^9, { 3.394766320900345*^9, 3.394766345513104*^9}, {3.3947955026046886`*^9, 3.394795617765551*^9}, {3.394795649197989*^9, 3.394795683366171*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "Clear"}]], "Input", CellChangeTimes->{{3.394763259131871*^9, 3.394763260451*^9}}], Cell[BoxData[ RowBox[{ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"Clear\\\", \\\"[\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"symbol\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"symbol\ \\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\ \[Ellipsis]\\\", \\\"TR\\\"]}], \\\"]\\\"}]\\) clears values and definitions \ for the \\!\\(\\*SubscriptBox[StyleBox[\\\"symbol\\\", \\\"TI\\\"], StyleBox[\ \\\"i\\\", \\\"TI\\\"]]\\). \\n\\!\\(\\*RowBox[{\\\"Clear\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"\\\\\\\"\\\\!\\\\(\\\\*StyleBox[\\\\\\\"form\\\\\\\",\\\\\ \\\"TI\\\\\\\"]\\\\_1\\\\)\\\\\\\"\\\", ShowStringCharacters->True], \ \\\",\\\", StyleBox[\\\"\\\\\\\"\\\\!\\\\(\\\\*StyleBox[\\\\\\\"form\\\\\\\",\ \\\\\\\"TI\\\\\\\"]\\\\_2\\\\)\\\\\\\"\\\", ShowStringCharacters->True], \ \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"]\\\"}]\\) clears \ values and definitions for all symbols whose names match any of the string \ patterns \\!\\(\\*SubscriptBox[StyleBox[\\\"form\\\", \\\"TI\\\"], \ StyleBox[\\\"i\\\", \\\"TI\\\"]]\\). \"\>", "MSG"], " ", ButtonBox[ StyleBox["\[RightSkeleton]", "SR"], Active->True, BaseStyle->"Link", ButtonData->"paclet:ref/Clear"]}]], "Print", "PrintUsage", CellChangeTimes->{3.394763263467609*^9}, CellTags->"Info3394738062-2405879"] }, Open ]], Cell["To see how this works, command", "Text", CellChangeTimes->{{3.394766382948803*^9, 3.394766389568693*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "g", "]"}]], "Input", CellChangeTimes->{{3.394763104255145*^9, 3.394763107427248*^9}}], Cell[TextData[{ "and see that ", StyleBox["g", "Input"], " is now once again just a letter in the alphabet:" }], "Text", CellChangeTimes->{{3.39476642019278*^9, 3.394766468334495*^9}}], Cell[CellGroupData[{ Cell[BoxData["g"], "Input", CellChangeTimes->{3.3947631211952887`*^9}], Cell[BoxData["g"], "Output", CellChangeTimes->{3.394763122226521*^9}] }, Open ]], Cell["It is, in particular, no longer the name of a graph:", "Text", CellChangeTimes->{{3.394766476497957*^9, 3.394766499153908*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", "g", "]"}]], "Input", CellChangeTimes->{{3.394763131791226*^9, 3.394763138708922*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Show", "::", "\<\"gtype\"\>"}], ":", " ", "\<\"\\!\\(Symbol\\) is not a type of graphics. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/Show/gtype\\\", \ ButtonNote -> \\\"Show::gtype\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.394763139999075*^9}], Cell[BoxData[ RowBox[{"Show", "[", "g", "]"}]], "Output", CellChangeTimes->{3.394763140230462*^9}] }, Open ]], Cell["", "Text", CellChangeTimes->{{3.394766517251514*^9, 3.3947665172663116`*^9}}], Cell[TextData[{ "What about the removal of the function ", StyleBox["f[x]", "Input"], "? The command" }], "Text", CellChangeTimes->{{3.394766529864873*^9, 3.394766576857808*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "f"}]], "Input", CellChangeTimes->{{3.394765020515209*^9, 3.3947650226774597`*^9}}], Cell[CellGroupData[{ Cell["Global`f", "Print", "PrintUsage", CellChangeTimes->{3.394765026517373*^9}, CellTags->"Info3394739824-6564964"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ { RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", SuperscriptBox["x", "17"]}]}, {" "}, { RowBox[{ RowBox[{"f", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ RowBox[{"u", " ", SuperscriptBox["x", "3"]}], "+", RowBox[{"v", " ", SuperscriptBox["y", "3"]}], "+", "w"}]}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{"Columns" -> {{ Scaled[0.999]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}], Definition["f"], Editable->False]], "Print", CellChangeTimes->{3.394765026808124*^9}, CellTags->"Info3394739824-6564964"] }, Open ]] }, Open ]], Cell[TextData[{ "reminds us that we have in fact\[LongDash]carelessly\[LongDash]taken ", StyleBox["f", "Input"], " to be the name of two distinct functions. The command" }], "Text", CellChangeTimes->{{3.3947665940464087`*^9, 3.394766622652916*^9}, { 3.394766716624579*^9, 3.394766719084063*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "f", "]"}]], "Input", CellChangeTimes->{{3.394763476228554*^9, 3.394763481857666*^9}}], Cell[TextData[{ "simultaneously expunges ALL the meanings we have previously associated with \ the letter ", StyleBox["f", "Input"], ", as we now demonstrate:" }], "Text", CellChangeTimes->{{3.394766743229732*^9, 3.394766838183556*^9}, { 3.3947957580816517`*^9, 3.394795758324264*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"f", "[", "x", "]"}], "\[IndentingNewLine]", RowBox[{"f", "[", RowBox[{"x", ",", "y"}], "]"}]}], "Input", CellChangeTimes->{{3.394763513277622*^9, 3.3947635136717157`*^9}}], Cell[BoxData[ RowBox[{"f", "[", "x", "]"}]], "Output", CellChangeTimes->{3.3947635151601877`*^9}], Cell[BoxData[ RowBox[{"f", "[", RowBox[{"x", ",", "y"}], "]"}]], "Output", CellChangeTimes->{3.394763515173325*^9}] }, Open ]], Cell[TextData[{ "It is to avoid this difficulty that one must be careful to ", StyleBox["assign distinct names to all functions", FontVariations->{"Underline"->True}], ". In the present instance we might more wisely have written (say)" }], "Text", CellChangeTimes->{{3.394795778082514*^9, 3.3947958345043383`*^9}, { 3.394795873815778*^9, 3.394795910305291*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"f1", "[", "x_", "]"}], ":=", SuperscriptBox["x", "17"]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f2", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ RowBox[{"u", " ", SuperscriptBox["x", "3"]}], "+", RowBox[{"v", " ", SuperscriptBox["y", "3"]}], "+", "w"}]}]}], "Input", CellChangeTimes->{{3.394795920886179*^9, 3.394795992199338*^9}}], Cell["We check those definitions", "Text", CellChangeTimes->{{3.3947960344887333`*^9, 3.394796041498651*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"f1", "[", "x", "]"}], "\[IndentingNewLine]", RowBox[{"f2", "[", RowBox[{"x", ",", "y"}], "]"}]}], "Input", CellChangeTimes->{{3.394796065600071*^9, 3.394796082839573*^9}}], Cell[BoxData[ SuperscriptBox["x", "17"]], "Output", CellChangeTimes->{3.394796086221792*^9}], Cell[BoxData[ RowBox[{"w", "+", RowBox[{"u", " ", SuperscriptBox["x", "3"]}], "+", RowBox[{"v", " ", SuperscriptBox["y", "3"]}]}]], "Output", CellChangeTimes->{3.394796086318076*^9}] }, Open ]], Cell["and verify that", "Text", CellChangeTimes->{{3.394796108043486*^9, 3.39479611357941*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "f1", "]"}]], "Input", CellChangeTimes->{{3.394796118933939*^9, 3.394796124960417*^9}}], Cell["expunges the former, but not the latter:", "Text", CellChangeTimes->{{3.394796134659852*^9, 3.3947961444198637`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"f1", "[", "x", "]"}], "\[IndentingNewLine]", RowBox[{"f2", "[", RowBox[{"x", ",", "y"}], "]"}]}], "Input", CellChangeTimes->{{3.394796065600071*^9, 3.394796082839573*^9}}], Cell[BoxData[ RowBox[{"f1", "[", "x", "]"}]], "Output", CellChangeTimes->{3.394796166296135*^9}], Cell[BoxData[ RowBox[{"w", "+", RowBox[{"u", " ", SuperscriptBox["x", "3"]}], "+", RowBox[{"v", " ", SuperscriptBox["y", "3"]}]}]], "Output", CellChangeTimes->{3.394796166399377*^9}] }, Open ]], Cell[TextData[{ StyleBox["TIP", FontColor->RGBColor[1, 0, 0]], StyleBox[": One should be careful to ", FontWeight->"Plain"], StyleBox["clear assignments/definitions when you are finished with them", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox[". This frees up memory, and helps avoid distracting surprises and \ confusion. But you will sometimes forget, so\[Ellipsis]", FontWeight->"Plain"] }], "Text", CellChangeTimes->{3.3947964739248543`*^9}, FontWeight->"Bold"], Cell[TextData[{ StyleBox["TIP", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ": It is a good idea to make ", StyleBox["Clear[", "Input"], StyleBox["the symbols you plan to use", "Input", FontSlant->"Italic"], StyleBox["]", "Input"], " your first command when, in the midst of a work session, you start a fresh \ computation." }], "Text", CellChangeTimes->{{3.3947964812569923`*^9, 3.394796484688569*^9}, { 3.394796759758543*^9, 3.394796841401969*^9}}], Cell["\<\ We will have no immediate need of this more comprehensive command:\ \>", "Text", CellChangeTimes->{{3.3947968821400337`*^9, 3.394796911870767*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "ClearAll"}]], "Input", CellChangeTimes->{{3.3947963456832247`*^9, 3.3947963515867977`*^9}}], Cell[BoxData[ RowBox[{ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"ClearAll\\\", \\\"[\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"symb\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"symb\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"]\\\"}]\\) clears all values, definitions, attributes, \ messages and defaults associated with symbols. \ \\n\\!\\(\\*RowBox[{\\\"ClearAll\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"\\\\\\\"\\\\!\\\\(\\\\*StyleBox[\\\\\\\"form\\\\\\\",\\\\\ \\\"TI\\\\\\\"]\\\\_1\\\\)\\\\\\\"\\\", ShowStringCharacters->True], \ \\\",\\\", StyleBox[\\\"\\\\\\\"\\\\!\\\\(\\\\*StyleBox[\\\\\\\"form\\\\\\\",\ \\\\\\\"TI\\\\\\\"]\\\\_2\\\\)\\\\\\\"\\\", ShowStringCharacters->True], \ \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"]\\\"}]\\) clears \ all symbols whose names textually match any of the \ \\!\\(\\*SubscriptBox[StyleBox[\\\"form\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \ \\\"TI\\\"]]\\). \"\>", "MSG"], " ", ButtonBox[ StyleBox["\[RightSkeleton]", "SR"], Active->True, BaseStyle->"Link", ButtonData->"paclet:ref/ClearAll"]}]], "Print", "PrintUsage", CellChangeTimes->{3.3947963595971537`*^9}, CellTags->"Info3394771153-4685404"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["How to Clear a Subscripted Variable", FontColor->RGBColor[0, 0, 1]]], "Subsubsection", CellChangeTimes->{{3.3959222721372557`*^9, 3.3959222822939873`*^9}, { 3.39674003990418*^9, 3.396740048700333*^9}}], Cell["Suppose you have had occasion to define", "Text", CellChangeTimes->{{3.3947974664669847`*^9, 3.394797466475914*^9}, { 3.3959222998175287`*^9, 3.395922308302979*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ SubscriptBox["a", "3"], "=", "SomeExpression"}]], "Input", CellChangeTimes->{{3.395922316282895*^9, 3.395922344701715*^9}}], Cell[BoxData["SomeExpression"], "Output", CellChangeTimes->{3.3967402308152018`*^9}] }, Open ]], Cell[TextData[{ "and want now to clear ", Cell[BoxData[ SubscriptBox["a", "3"]], CellChangeTimes->{{3.395922316282895*^9, 3.395922344701715*^9}}], ". The command" }], "Text", CellChangeTimes->{{3.395922354172758*^9, 3.395922404433103*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Clear", "[", SubscriptBox["a", "3"], "]"}]], "Input", CellChangeTimes->{{3.395922414707202*^9, 3.395922420150168*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "::", "\<\"ssym\"\>"}], RowBox[{ ":", " "}], "\<\"\\!\\(a\\_3\\) is not a symbol or a string. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/Clear/ssym\\\", \ ButtonNote -> \\\"Clear::ssym\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.3959224297921343`*^9, 3.395922946195819*^9}] }, Open ]], Cell["did not work. Nor does it work to command", "Text", CellChangeTimes->{{3.395922407557123*^9, 3.395922446017338*^9}, { 3.395922761044621*^9, 3.395922798655869*^9}, {3.395922887829625*^9, 3.395922895561619*^9}, 3.395923077405677*^9}], Cell[BoxData[ RowBox[{"Clear", "[", "a", "]"}]], "Input", CellChangeTimes->{{3.395922901528296*^9, 3.395922905988083*^9}}], Cell["for we still have", "Text", CellChangeTimes->{{3.395923097899159*^9, 3.3959231005627537`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ SubscriptBox["a", "3"]], "Input", CellChangeTimes->{{3.395922915340185*^9, 3.395922927232656*^9}}], Cell[BoxData["SomeExpression"], "Output", CellChangeTimes->{{3.395922916573523*^9, 3.395922956944254*^9}}] }, Open ]], Cell[TextData[{ "How to proceed? ", StyleBox["Vacate the definition", FontSlant->"Italic"], " by defining ", Cell[BoxData[ SubscriptBox["a", "3"]], CellChangeTimes->{{3.395922316282895*^9, 3.395922344701715*^9}}], " to be \"nothing,\" this way:" }], "Text"], Cell[BoxData[ RowBox[{ SubscriptBox["a", "3"], "=."}]], "Input", CellChangeTimes->{{3.3959228170777683`*^9, 3.395922817627245*^9}}], Cell["Test the result:", "Text", CellChangeTimes->{{3.3959228320055037`*^9, 3.395922835446644*^9}}], Cell[CellGroupData[{ Cell[BoxData[ SubscriptBox["a", "3"]], "Input"], Cell[BoxData[ SubscriptBox["a", "3"]], "Output", CellChangeTimes->{3.395923010812722*^9}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Sources of Information", "Section", CellChangeTimes->{{3.394797482817168*^9, 3.394797498902595*^9}}], Cell[CellGroupData[{ Cell[TextData[StyleBox["Hardcopy Materials", FontColor->RGBColor[1, 0, 0]]], "Subsection", CellChangeTimes->{{3.394797519687331*^9, 3.394797525247477*^9}}], Cell[TextData[{ "Earlier versions of ", StyleBox["Mathematica", FontSlant->"Italic"], " shipped with hardcopy editions of " }], "Text", CellChangeTimes->{{3.394798509117401*^9, 3.394798522613658*^9}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["\[Bullet] ", "Code"], StyleBox["The ", FontColor->RGBColor[0, 0, 1]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" Book", FontColor->RGBColor[0, 0, 1]], StyleBox[", which provided definitive descriptions of every feature of the \ software, but was much too fat to carry around. Chapter I ", FontColor->GrayLevel[0]], StyleBox["\"A Practical Introduction to ", FontColor->RGBColor[0, 0, 1]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\"", FontColor->RGBColor[0, 0, 1]], StyleBox[" ran to 228 pages, and provided a valuable survey of the basics, \ with many examples. 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" }], "Item1Paragraph", CellChangeTimes->{{3.3948003596676617`*^9, 3.3948004938019238`*^9}}] }, Open ]], Cell[TextData[{ "\[LineSeparator]The release of v.6 has rendered those books obsolete, but \ not entirely, and has actually increased their value, for with the release of \ v.6 Wolfram seems to have elected to discontinue the preparation/distribution \ of such volumes: all such information must now be sought electronically, by \ consulting resources accessed ", StyleBox["via", FontSlant->"Italic"], " the ", StyleBox["Help", FontWeight->"Bold"], " menu. " }], "Text", CellChangeTimes->{{3.394800528878998*^9, 3.394800646445311*^9}, { 3.394800679806973*^9, 3.3948007149674*^9}, {3.394800870534418*^9, 3.394801009270389*^9}, {3.395923269492755*^9, 3.395923292966135*^9}}], Cell[TextData[{ "A great many books by authors not associated with Wolfram are available in \ the market place\[LongDash]visit ", Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"WolframBooks\"\>", True-> StyleBox["\<\"WolframBooks\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://store.wolfram.com/catalog/books/author.html"], None}, ButtonNote->"http://store.wolfram.com/catalog/books/author.html"], Annotation[#, "http://store.wolfram.com/catalog/books/author.html", "Hyperlink"]& ]], CellChangeTimes->{3.395764508230997*^9}], " \[LongDash]but most of those are similarly obsolete. Of those, some are \ addressed to students, others to experts; some provide tutorial overviews, \ others threat specialized topics (differential equations, graphics, \ statistics, ", StyleBox["etc", FontSlant->"Italic"], ".)." }], "Text", CellChangeTimes->{{3.394801407120575*^9, 3.394801424783676*^9}, { 3.394801455633752*^9, 3.3948015411239853`*^9}, 3.395764359240102*^9, { 3.3957645217037287`*^9, 3.395764535101459*^9}}], Cell["", "Text", CellChangeTimes->{{3.3957651352535763`*^9, 3.395765135257669*^9}}], Cell[TextData[{ StyleBox["REMARK", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ": To insert the link into that sentence, I used a resouce you can read \ about if you command" }], "Text", CellChangeTimes->{{3.395764588852191*^9, 3.3957646923745213`*^9}, { 3.395923387600307*^9, 3.3959234074716883`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "Hyperlink"}]], "Input", CellChangeTimes->{{3.395764700602132*^9, 3.395764703487236*^9}}], Cell[BoxData[ RowBox[{ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"Hyperlink\\\", \\\"[\\\", \ StyleBox[\\\"uri\\\", \\\"TI\\\"], \\\"]\\\"}]\\) represents a hyperlink that \ jumps to the specified URI when clicked. \ \\n\\!\\(\\*RowBox[{\\\"Hyperlink\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"label\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"uri\\\", \ \\\"TI\\\"]}], \\\"]\\\"}]\\) represents a hyperlink to be displayed as \ \\!\\(\\*StyleBox[\\\"label\\\", \\\"TI\\\"]\\). \"\>", "MSG"], " ", ButtonBox[ StyleBox["\[RightSkeleton]", "SR"], Active->True, BaseStyle->"Link", ButtonData->"paclet:ref/Hyperlink"]}]], "Print", "PrintUsage", CellChangeTimes->{3.395764710624609*^9}, CellTags->"Info3395739510-6287617"] }, Open ]], Cell[TextData[{ "and follow the ", StyleBox["\[RightSkeleton]", FontColor->RGBColor[0, 0, 1]], ". 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", FontColor->GrayLevel[0]], "Note carefully that, while it might be most natural to type \"WolframBooks,\ \" the command will not function unless you type \"WolframBooks", StyleBox["\",", "Input", FontColor->RGBColor[1, 0, 0]] }], "Text", CellChangeTimes->{{3.3959235976231194`*^9, 3.39592363954047*^9}, { 3.3959236834995613`*^9, 3.395923695773629*^9}}], Cell["", "Text", CellChangeTimes->{{3.395765143940773*^9, 3.39576514398647*^9}}], Cell[TextData[{ StyleBox["The ", FontColor->RGBColor[0, 0, 1]], StyleBox["Mathematica", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" Journal", FontColor->RGBColor[0, 0, 1]], " appears monthly, reads much like ", StyleBox["American Journal of Physics", FontSlant->"Italic"], " or ", StyleBox["Mathematical Monthly", FontSlant->"Italic"], " (so is, for the most part, readily accessible to students), and is \ available in the ÌÇÐÄÊÓÆµ Library." }], "Text", CellChangeTimes->{{3.3948015917506943`*^9, 3.394801693708486*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Built-in Sources", FontColor->RGBColor[1, 0, 0]]], "Subsection", CellChangeTimes->{{3.394797950519897*^9, 3.3947979573411694`*^9}}], Cell[TextData[{ "The primary source of information about v.6 is provided now by ", StyleBox["Help > Documentation Center", FontWeight->"Bold"], ", but it is like a Chinese box\[LongDash]arrays of links to arrays of links \ to arrays of links\[Ellipsis] I cannot possibly present a map or those \ resources, urge you to spend some time exploring on your own to try to gain a \ vague sense of the lay of the land. 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Suppose, for example, that we had computed\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "0"}], "\[Infinity]"], FractionBox[ SuperscriptBox["x", "j"], SuperscriptBox[ RowBox[{"(", RowBox[{"j", "+", "u"}], ")"}], "\[Nu]"]]}]], "Input"], Cell[BoxData[ RowBox[{"LerchPhi", "[", RowBox[{"x", ",", "\[Nu]", ",", "u"}], "]"}]], "Output", CellChangeTimes->{3.394798053668703*^9}] }, Open ]], Cell["\<\ and find ourselves wondering \"What in the world is a 'LerchPhi function'?\" \ We might enter\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "LerchPhi"}]], "Input"], Cell[BoxData[ RowBox[{ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"LerchPhi\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"z\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"s\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"a\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) \ gives the Lerch transcendent \\!\\(\\*RowBox[{StyleBox[\\\"\[CapitalPhi]\\\", \ \\\"TR\\\"], RowBox[{\\\"(\\\", 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But\ \[LongDash]backing up to our starting point\[LongDash]if in \ \>", "Text"], Cell[BoxData[ RowBox[{"LerchPhi", "[", RowBox[{"x", ",", "\[Nu]", ",", "u"}], "]"}]], "Output"], Cell[TextData[{ "we ", StyleBox["Select", FontWeight->"Bold"], " the output (select only the ", StyleBox["LerchPhi", "Output"], "; leave out the ", StyleBox["[x,\[Nu],u]", "Output"], ") and then open ", StyleBox["Help > Find Selected Function\[Ellipsis] ", FontWeight->"Bold"], "we are instantly led to a notebook that provides a detailed description of \ the \"Lerch transcendent\" and of its relation to (among others) the Riemann \ zeta and polylog functions. " }], "Text", CellChangeTimes->{{3.394804969423312*^9, 3.394804978371689*^9}, 3.394805011898033*^9}], Cell[TextData[{ "Under TUTORIALS (near the bottom of the page), open and explore the link to \ the very valuable ", StyleBox["Special Functions", FontColor->RGBColor[0, 0, 1]], " notebook." }], "Text", CellChangeTimes->{{3.394805868388329*^9, 3.39480587377155*^9}, { 3.395923935802503*^9, 3.39592394991999*^9}}], Cell["", "Text", CellChangeTimes->{{3.39480587709713*^9, 3.394805932115736*^9}, { 3.39592396812307*^9, 3.395923979591449*^9}}], Cell[TextData[{ "Distinct from ", StyleBox["Information", "Input"], " is ", StyleBox["Options", "Input"], ". 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Again, ", StyleBox["ask ", FontVariations->{"Underline"->True}], StyleBox["Mathematica", FontSlant->"Italic", FontVariations->{"Underline"->True}], ". Which, for example, about the ", StyleBox["AlignmentPoint", "Input"], " option has this to say:" }], "Text", CellChangeTimes->{{3.3959240562775*^9, 3.395924140482459*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Information", "[", "AlignmentPoint", "]"}]], "Input", CellChangeTimes->{{3.395924192080106*^9, 3.39592420280667*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox["\<\"AlignmentPoint is an option which specifies how objects \ should by default be aligned when they appear in Inset.\"\>", "MSG"], " ", ButtonBox[ StyleBox["\[RightSkeleton]", "SR"], Active->True, BaseStyle->"Link", ButtonData->"paclet:ref/AlignmentPoint"]}]], "Print", "PrintUsage", CellChangeTimes->{3.39592420841778*^9}, CellTags->"Info3395899007-4752452"], Cell[BoxData[ InterpretationBox[GridBox[{ { RowBox[{ RowBox[{"Attributes", "[", "AlignmentPoint", "]"}], "=", RowBox[{"{", "Protected", "}"}]}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}], Definition["AlignmentPoint"], Editable->False]], "Print", CellChangeTimes->{3.395924208505515*^9}, CellTags->"Info3395899007-4752452"] }, Open ]] }, Open ]], Cell[TextData[{ "Here as always, if you follow the ", StyleBox["\[RightSkeleton]", FontColor->RGBColor[0, 0, 1]], " you will be led to detailed discussion and examples." }], "Text", CellChangeTimes->{{3.3959241856367826`*^9, 3.3959241868268843`*^9}, { 3.395924244221796*^9, 3.3959242795889587`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Your Own \"My Tricks\" Notebook", FontColor->RGBColor[1, 0, 0]]], "Subsection", CellChangeTimes->{{3.394806345215577*^9, 3.394806359927826*^9}}], Cell[TextData[{ "I mention finally an undocumentable resource which will in time become the \ most valuable of all. Experience is problem-solving, in this sphere as in all \ others. When ", StyleBox["Mathematica", FontSlant->"Italic"], " has presented difficulties which you have finally overcome (it will, and \ you will), ", StyleBox["take the time to record your success in a dedicated notebook", FontColor->RGBColor[0, 0, 1]], ". You will then never again have to solve that particular problem, and can \ use your former success as a ", StyleBox["Copy/Paste ", FontWeight->"Bold"], "template. For your" }], "Text"], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"Mathematica", " ", "power"}], "=", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"t", "=", "today"}], "tomorrow"], RowBox[{"Problems", " ", "successfully", " ", "solved"}]}]}], FontColor->GrayLevel[0.500008]]], "Input", CellChangeTimes->{{3.3948064391555653`*^9, 3.394806441029306*^9}}], Cell["\<\ And don't be too proud to save also\[LongDash]perhaps in a separate notebook \ of \"Stolen Tricks\"\[LongDash]a record of the ideas developed by others \ that seem to you interesting, or potentially useful. Quite a number of those \ will be encountered as we proceed.\ \>", "Text", CellChangeTimes->{{3.3948065146808023`*^9, 3.3948065201457653`*^9}}], Cell[TextData[{ "\tSometimes your \"tricks\" will consist of programs that run a dozen or \ more lines (", StyleBox["Mathematica", FontSlant->"Italic"], " programs are seldom ", StyleBox["very", FontSlant->"Italic"], " long; that heavy work was done by the designers of the software), but more \ often they will consist of felicitous selections from among available \ options. The value of your Tricks Notebooks will be much increased if you ", StyleBox["include explanatory text and references", FontColor->RGBColor[0, 0, 1]], "\[LongDash]easy if you open ", StyleBox["Window > Show Toolbar", FontWeight->"Bold"], ". 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