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-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "diagram" -1 265 1 {CSTYLE "" -1 -1 "" 0 0 239 239 239 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "dblnorm.mws" -1 266 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 2 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Item" 0 267 1 {CSTYLE " " -1 -1 "Lucida Sans" 1 12 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 6 -1 3 0 0 0 0 0 -1 0 }{PSTYLE "rdiagram" -1 268 1 {CSTYLE "" -1 -1 "" 0 0 239 239 239 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "texcomment" -1 269 1 {CSTYLE "" -1 -1 "" 0 0 128 128 128 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "paragraph" -1 270 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 3 "" 0 "Raison d'Maple" {TEXT -1 14 "Raison d'Ma ple" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 26 " Four Properties of Maple \+ " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 428 " Here we intend to provide you with just enough information about the Maple language to give a h eadstart at using it productively in the problem solving process. The particular version of Maple that we are using as we describe it is Ma ple V, Release 4, running either in Windows 3.1 on DOS or Windows 95 . You may be using an earlier release on a different platform, but mo st of what is in this document is still relevant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 " Maple has at least four \+ properties which make it very useful in problem solving. " }{TEXT 277 9 "\nDeutsch:" }{TEXT -1 2 " \n" }{TEXT 278 158 "Vier Eigenschafte n von Maple\nDieses Worksheet gibt ihnen gen\374gend Information \374b er die Maple-Sprache um sie produktiv im Probleml\366sungsprozess zu \+ verwenden. " }}{PARA 0 "" 0 "" {TEXT 270 35 "It is an immediate mode \+ language: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 222 "That means that you can type in commands and execute them, just like in the lang uages Basic and Logo. A Maple command is simply a string of characte rs ending in a semicolon ';' or colon ':'. For example, the comma nd" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " 2+5, factor(x^2+5*x +6),expa nd((x+y)^2);" }}}{EXCHG {PARA 0 "" 0 "factor" {TEXT -1 125 " tells Map le to do a sequence of three things: add 2 and 5, factor the quadrat ic, and expand the binomial. The strings " }{TEXT 269 6 "factor" } {TEXT -1 6 " and " }{TEXT 269 6 "expand" }{TEXT -1 454 " are called M aple 'words'. These are names of procedures which have been defined f or performing the action (sometimes) suggested by the name on the stuf f enclosed in parentheses just after the word. That stuff is usually called the 'input' of the word. The result of performing the proced ure on the input is naturally called the 'output' of the word. If the command is terminated with a semicolon (colon), the output is display ed (not displayed). \n" }{TEXT 279 8 "Deutsch:" }}{PARA 0 "" 0 "" {TEXT 312 15 "Maple ist eine " }{TEXT 313 24 "immediate mode language: " }{TEXT 314 1041 "\nDas bedeutet Sie k\366nnen Befehle eintippen, und sofort ausf\374hren. Ein Maple-Befehl ist ein einfache Reihe von Vari ablen, Schriftzeichen und Buchstaben an deren Ende ein Semikolon \";\" oder ein Doppelpunkt steht \":\" Zum Beispiel der Befehl ............ .sagt Maple eine Reihe von drei Dingen zu tun: zwei mit f\374nf zu add ieren, den Term in Faktoren zu zerlegen, die binomische Formel auszumu ltiplizieren. Die Befehle \"factor\" und \"expand\" sind sog. Maple-\" W\366rter\". Hinter diesen Maple-W\366rtern verbergen sich Prozeduren, die mathematische Berechnungen durchf\374hren f\374r die das Maple-\" Wort\" steht ( expand = ausmultiplizieren usw.). Maple f\374hrt den Be fehl auf das aus, was in Klammern hinter den Maple-\"Wort\"/ Maple-Bef ehl steht. Das nennt man den sog. \"Input\". F\374hrt man eine Prozedu r auf einen bestimmten \"Input\" aus, erh\344lt man den zugeh\366rigen \"Output\" (d.h. man erh\344lt ein Ergebnis oder die Best\344tigung e ines Befehls). Steht am Ende eines Befehls ein Semikolon (Doppelpunkt) , wird der Output in blauer Schrift angezeigt (nicht angezeigt). \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 270 45 "It \+ is a symbolic and graphical manipulator: " }{TEXT -1 1 " " }}{PARA 0 " " 0 "" {TEXT -1 538 "That means that it is built to work with algebrai c expressions and draw pictures. There is a large vocabulary of Mapl e words, such as factor, simplify, and expand which are used to 'symbo lically manipulate' expressions in the manner you are used to doing \+ with pencil and paper. There are also a number of plotting words, whi ch are used to draw graphs of functions of one or two variables, cur ves and surfaces. These drawings can be animated (ie displayed in seq uence) to study change. Two of the plotting words most often used, \+ " }{TEXT 269 4 "plot" }{TEXT -1 7 " and " }{TEXT 269 6 "plot3d" } {TEXT -1 187 ", are part of the regular Maple vocabulary. The rest, a nd there are several, are found in the the plots package, a sort of \+ specialized vocabulary of words which is loaded separately. \n" } {TEXT 280 10 "Deutsch: " }}{PARA 0 "" 0 "" {TEXT 281 821 "Es benutzt \+ Grafik und Symbole:\nDas Bedeutet, Maple ist konzipiert, mit algebrais chen Ausdr\374cken zu arbeiten, und Schaubilder/Graphen zu malen. Es g ibt einen gro\337en Wortschatz an Maple-W\366rtern, z.B \"factor\", \" simplify\", und \"expand\" die dazu dienen symbolische Ausdr\374cke (w ie Terme, Funktionen und Variablen) zu verarbeiten und zu berechnen. \+ Es gibt auch eine Anzahl von \"plotting-Befehlen\", die dazu dienen Fu nktionen mit ein oder zwei Variablen, Kurven und Oberfl\344chen zu zei chnen. Diese Zeichnungen k\366nnen animiert werden, um Ver\344nderunge n zu beobachten. Die zwei am h\344ufigsten verwendeten plot-Befehle si nd \"plot\" und \"plot3d\", geh\366ren zu dem regul\344ren Maple-Worts chatz. Der Rest, und das ist einiges, findet man in sog. \"Packages\", die seperat zum Gebrauch geladen werden k\366nnen (z.B with(plots), w ith(geom3d) usw.)." }}{PARA 0 "" 0 "" {TEXT 270 31 "It is an extensib le language. " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 558 "What th is means is that you can define additional words and add them to the v ocabulary. Initially, there will be little need to do this, except to define functions. The existing vocabulary is large enough to carry \+ out the solution to many problems. After awhile, it becomes very usef ul to be able to add new words to the vocabulary. If you develop so me words to work on a specialized class of problems, these can be put into a package of words for easy access between worksheets. Maple co mes equipped with several such packages already, including " }{TEXT 261 5 "plots" }{TEXT -1 198 ", a package of drawing words, linalg - a very useful package of vector and matrix manipulation words, comb inat - a package of words from combinatorics, and networks - a graph theory package.\n" }{TEXT 282 355 "Deutsch:\nEs ist eine erweiterbare Sprache.\nDas bedeutet, Sie k\366nnen zum Maple-Wortschatz eigene \"W \366rter\"(Befehle) und Prozeduren hinzuf\374gen. \nMan kann in Maple \+ eigene Befehle entwickeln um ein bestimmtes Problemfeld abzudecken, so g. Packages. Maple besitzt bereits eine Anzahl dieser Packages, z.B. p lots: eine Befehlssammlung zur grafischen Darstellung. " }{TEXT -1 1 " \n" }}{PARA 0 "" 0 "" {TEXT 270 51 "It comes with a worksheet environm ent -- see below." }}{PARA 0 "" 0 "" {TEXT -1 228 "We want to learn to use Maple to solve problems. In order make good use of the language \+ for this purpose, we need to become familiar with the worksheet enviro nnment, get to know the language, and foster our experimental urges.\n " }{TEXT 283 263 "Deutsch:\nMan arbeitet mit \"Worksheets\" - siehe un ten:\nWir wollen lernen mit Maple Probleme zu l\366sen. Um mit Maple \+ (mathematische) Probleme zu l\366sen, m\374ssen wir uns vertraut mache n mit den M\366glichkeiten eines Maple-Worksheets (mws) und die Maple- Sprache lernen. " }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 48 " The Works heet: A handy place to solve problems" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 548 "When you click on the Maple Icon in Windows, an untitled worksheet opens up. Think of it as a clean sheet of paper. Typicall y, after awhile, the worksheet will contain a record of the work done \+ to date on the problem or problems you have been working on. Very oft en, you might be in a problem-solving team working on the problems. T he worksheet can be given a name and saved onto a disk for later worki ng or for handing in. The worksheet file consists of a number of cell s of three different types: Input cells, Output cells, and Text cells .\n" }{TEXT 284 624 "Deutsch\nDas Worksheet: Ein guter Ort um Probleme zu l\366sen.\nWenn Sie das Maple-Icon in Windows aufrufen, \366ffnet \+ sich ein unbenanntes Worksheet. Stellen Sie es sich als ein blankes Bl att Papier vor. Auf einem Worksheet kann man seine mathematischen Prob leme l\366sen, dokumentieren, veranschaulichen und erarbeiten. Man kan n auch in Gruppen an einem Worksheet arbeiten. Jedem Worksheet kann m an einen Namen geben, und f\374r den sp\344teren Gebrauch auf Diskette oder Festplatte abspeichern. Ein Worksheet besteht aus drei verschied enen Zellentypen, die man bearbeiten kann: den Input-Zellen, den Outpu t-Zellen, und den Text-Zellen. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 270 13 "Input Cells: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 70 " These are started with a righ t angle bracket '>'. Here are a couple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "An " }{TEXT 269 11 "input cell " }{TEXT -1 440 " is the pl ace where you put the 'commands' or 'statements' you want Maple to exe cute. The cell can contain one or more statements, each ending with a semicolon. The nice thing about these cells in a worksheet is that th ey can be modified and reexecuted over and over again. This enables y ou to correct typing mistakes with relative ease. For example, suppos e I wanted Maple to calculate '3*(4+5*3)*(7+6);' but left out a par enthesis. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "3*(4+5*3)*(7+6 ;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 285 603 "Deutsch:\nInput-Z ellen (Eingabe-Zellen):\nInput-Zellen beginnen mit einer rechteckigen \+ Klammer \">\". Hier sind ein Paar.\nIn eine Input-Zelle schreibt man M aple-Befehle und Statements, die Maple ausf\374hren soll. Eine Zelle k ann aus einem oder mehreren Statements bestehen, die jeweils mit einem Semikolon enden. Das sch\366ne an diesen Eingabe-Zellen ist, da\337 s ie immer wieder ver\344ndert und wieder ausgef\374hrt werden k\366nnen . Das erm\366glicht ihnen Tippfehler relativ einfach zu korrigieren. I ch m\366chte zum Beispiel das Maple den Term '3*(4+5*3)*(7+6); f\374r \+ mich ausrechnet, ich habe aber eine Klammer vergessen. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 228 " An error message is generated which ma y help you find your mistake. So you can make a change in that input cell and reexecute it. Use the mouse to put the cursor at the spot where the error occurs and make the correction " }}{PARA 0 "" 0 "" {TEXT -1 182 "You can also use this ability to change and reexecute in put cells to change the numbers in whatever problem you have worked o ut a solution to and see how the solution is affected.\n" }{TEXT 286 391 "Deutsch:\nEine Fehlermeldung wird ausgegeben, die ihnen hilft ihr en Fehler zu finden. Sie k\366nnen ihren Fehler in der Eingabe-Zelle k orrigieren, und sie erneut ausf\374hren. Benutzen Sie die Maus um den \+ Cursor an die Fehlerstellen zu setzen, und korrigieren Sie den Fehler. So k\366nne Sie Zahlen, Variablen und Terme in der Eingabe-Zellen ver \344ndern, und sehen wie es sich auf die L\366sung auswirkt. " } {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 270 13 "Output Cells:" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 50 "Almost every input cell, when \+ executed, gives an " }{TEXT 259 11 "output cell" }{TEXT -1 205 " cont aining the results of the calculations. It is appended to the input c ell which produced it. For example, let's add 3 to the 23rd and 4 to \+ the 12th -- then let's factor the result into prime factors." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " s := 3^23 + 4^12;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " ifactor(s);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }{TEXT 287 8 "Deutsch:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 288 329 "Output-Zellen:\nWenn eine Input-Zelle ausgef\374hrt wird, bekommt man eine sog. Output-Zelle (in blauer Schrift) die das Ergebnis der R echnung beinh\344lt. Die Output-Zelle h\344ngt von der Input-Zelle ab, die sie ausgegeben hat. Zum Beispiel, lass uns 3 hoch 23 mit 4 hoch 1 2 addieren -- und danach die Faktoren in Primfaktoren zerlegen." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "You inspect the output cell to se e if it is what you want. If it is not, then go back and change the in put cell, and reexecute it. " }{TEXT 289 1 " " }}{PARA 0 "" 0 "" {TEXT -1 29 "Certain Maple words such as " }{TEXT 269 4 "plot" } {TEXT -1 196 " generate a separate window containing a picture or a p age of text (see factor in the next section). You can copy and paste \+ these items into an output cell of your worksheet if the need arises. \n" }{TEXT 290 217 "Deutsch:\nEinige Maple-Befehle wie \"plot\", \366f fnen ein seperates Fenster mit einem Graphen/Schaubild oder einem Text . Den Inhalt dieser seperaten Fenster k\366nne Sie mit copy and paste \+ in ihr aktuelles Worksheet kopieren." }{TEXT -1 2 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(x^3-x+4, x=-2..2); " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 260 "" 0 "" {TEXT 271 9 "Exer cise:" }{TEXT -1 163 " Execute the following plot command. Then \+ copy the graph from the plot window (use the Edit Menu in that wi ndow) and paste it into your worksheet.\n" }{TEXT 291 159 "\334bu ng: F\374hren Sie folgenden plot-Befehl aus, und kopieren Sie den Grap hen aus dem plot-Fenster in ihr Worksheet (benutzen Sie das Edit-Menu \+ in diesem Fenster)." }{TEXT -1 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " plot(x^3-x+4,x=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 256 22 "Text or Comment Cells:" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 3 "A " } {TEXT 269 10 "Text Cell" }{TEXT -1 373 " is to record remarks and ex planations of the solution to the problem you are working on. All of \+ the comments here are typed into text cells. It is a good idea to be \+ liberal with text cells. Undocumented calculations are for the most p art worthless to anyone but the person who made the calculations, and \+ even then the value is a rapidly decreasing function of time. " }} {PARA 0 "" 0 "" {TEXT -1 258 "You have very good control over the cell s in your worksheet with the Menus at the top of this worksheet. Depe nding on what platform you are using (Windows, X, or Mac), the menus m ay vary in their titles, but the effects are the same with minor diffe rences:\n" }{TEXT 292 8 "Deutsch:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 293 494 "Text oder Kommentar-Zellen:\nIn Textzellen k\366nne Sie Bemerkungen und Erkl\344rungen zu mathematischen Problem eingeben, di e Sie bearbeiten. Die Texte die Sie in diesem Worksheet lesen k\366nne n, sind alle in Text-Zellen geschrieben. Man verwendet Text-Zellen um \+ Berechnungen und Untersuchungen zu dokumentieren. Dokumentierte Worksh eets sind leichter verst\344ndlich, als reine Aufreihungen von Befehle n. Mit der Men\374leiste im Kopf des Worksheets k\366nnen Sie Text-Zel len und Text leicht ver\344ndern. " }}{PARA 267 "" 0 "" {TEXT -1 1 " " }{TEXT 272 55 "You change an input cell to a text cell and ba ck again." }{TEXT -1 2 " " }}{PARA 267 "" 0 "" {TEXT -1 1 " " }{TEXT 273 53 "You can split a cell (input or text) and join cells. " }} {PARA 267 "" 0 "" {TEXT -1 1 " " }{TEXT 274 61 "You open up new cells \+ (input or text) between existing cells." }}{PARA 267 "" 0 "" {TEXT -1 1 " " }{TEXT 275 64 "You can erase cells (input, text, or output) at y our discretion." }}{PARA 267 "" 0 "" {TEXT 276 73 "You can copy cells \+ (input or text) and paste them into another location.\n" }{TEXT 294 8 "Deutsch:" }{TEXT 295 1 "\n" }{TEXT 296 247 "Sie k\366nnen aus Input-Z ellen Textzellen machen und umgekehrt.\nSie k\366nne Zellen Trennen un d zusammensetzen (Input und Text).\nSie k\366nne zwischen bestehenden \+ Zellen neue \366ffnen.\nSie k\366nnen Zellen l\366schen:\nSie k\366nne n Zellen mit copy und paste kopieren " }}{PARA 0 "" 0 "" {TEXT -1 199 "These controls make it relatively easy to work away on a worksheet, d oing computations, recording observations, explanations, etc and then \+ go back and polish the worksheet up into a public document. " }}{PARA 0 "" 0 "" {TEXT -1 475 "The worksheet does not replace pencil and pape r or the chalk board in the problem solving process. When you are in \+ the middle of analyzing a problem and deciding how to solve it, these \+ tools are extremely useful. It is easier to draw a rough diagram by h and than by Maple. After you have decided on a plan and need to do so me numerical calculation, some symbolic manipulation, or some plotting to carry out the plan, then a knowledge of the Maple language becomes useful.\n" }{TEXT 297 33 "Deutsch:\nMit diesen M\366glichkeiten" } {TEXT -1 1 " " }{TEXT 298 539 "k\366nnen Sie ihren Rechenweg oder ihre Untersuchung, Dokumentieren, Erl\344utern, Fragen dazu stellen, und a m Schlu\337 ein Worksheet f\374r die \366ffentlichkeit daraus machen. \nDas Worksheet ersetzt aber nicht Bleistift und Papier, oder Kreide u nd Tafel. Wenn Sie dabei sind ein Problem zu analysieren, sind diese a lten Methoden extrem n\374tzlich. Es ist einfacher ein grobes Diagram \+ mit der Hand zu zeichnen, als mit Maple. Maple ist dazu gedacht ihnen \+ die Rechenarbeit zu erleichtern, und den L\366sungsvorgang mathematisc her Probleme zu dokumentieren. " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Get to know the language " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 253 " Maple has a large built in vocabulary of words especially defi ned to carry out many of the algorithms you have learned in your previ ous math classes. There are Maple words like factor , expand , \+ simplify , etc. You can learn about them with " }{TEXT 259 11 "onlin e Help" }{TEXT -1 4 ". " }}{PARA 0 "" 0 "" {TEXT -1 173 "There is a \+ Browser available in both X and Windows Maple which has the Maple vo cabulary nicely indexed by category. Alternatively, you can ask for \+ help in an input cell." }}{PARA 0 "" 0 "" {TEXT -1 53 "For example, to find out about factor just type " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?factor" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 299 201 "Deutsch:\nLernen Sie die Maple-Sprache:\nMaple hat ein gro\337en \+ Befehls-Wortschatz, hinter dem viele mathematische Algorithmen stecken . Sie k\366nnen mit der Maple online-Hilfe mehr \374ber Maple-Befehle \+ lernen." }}{PARA 0 "" 0 "" {TEXT 300 150 "Maple enth\344lt einen Brows er in dem der Maple Befehls-Wortschatz nach Kategorien aufgelistet ist . Sie k\366nnen auch \374ber die Input-Zellen Hilfe bekommen." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Knowing the word is one thing, but you also need to know the " }{TEXT 259 6 "syntax" }{TEXT -1 946 " of the word. What is syntax? Every algorithm requires certain input in formation in order to be performed. After it has been performed, cert ain output information is produced. To know the syntax of a Maple wor d is to know the input information needed and the output information p roduced by the word. The help screen gives you the syntax of the wor d, and thus tells you how to use it. For example, the help screen for factor tells us (in CALLING SEQUENCES) that there are one and pos sibly two inputs needed and one output produced by factor. The most u seful part of the help screen is the bottom part, where there are exam ples of the usage of the word in question. These examples can be copi ed into a worksheet and tested out, which gives you a chance to develo p a feel for the word by experimenting with its use. In fact, there i s a Maple word example which brings up a page of examples of the u sage of the word, in many cases." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 301 691 "Deutsch:\nUm einen Maple-Befehl auszuf\374hren mu \337 man auch dessen Syntax kennen. Was hei\337t das? Jeder Befehl bra ucht bestimmte Informationen um ausgef\374hrt zu werden, oder einen b estimmten Output auszugeben. Man nennt das auch die sog. \"calling seq uence\". Der Befehl mu\337 zum Beispiel wissen nach welcher Variablen er aufl\366sen soll, usw. In der Maple-Hilfe gibt es zu fast jedem Be fehl einen Hilfe-Bildschirm. Dort wird erkl\344rt wie man den Befehl b enutzt, und wie seine Syntax aussieht. Im unteren Teil jedes Hilfe-Bil dschirms findet man Beispiele, die man in sein eigenes Worksheet kop ieren kann (mit copy and paste). So kann man die Befehle selbst\344ndi g lernen und mit ihnen experimentieren." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 262 9 "Problems:" }}{EXCHG {PARA 260 "" 0 "" {TEXT 268 9 "Exerci se:" }{TEXT -1 80 " Discover the difference between factor and \+ ifactor using ?ifactor . " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 306 89 "Benutzen Sie die Maple-Hilfe um den Unterschied zwischen factor und i factor rauszufinden." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 260 "" 0 " " {TEXT 267 9 "Exercise:" }{TEXT -1 58 " Use ifactor to factor yo ur social security number. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 307 72 "Benutzen Sie ifactor um ihre Sozialversicherungsnummer zu faktorisieren." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 260 "" 0 "" {TEXT 266 9 "Ex ercise:" }{TEXT -1 60 " Use nextprime to find the first 30 prime s after 5000." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 308 71 "Benutzen Sie ne xtprime um die ersten 30 Primzahlen nach 5000 zu finden." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 260 "" 0 "" {TEXT 265 9 "Exercise:" }{TEXT -1 74 " How do collect , coeff and e xpand work? Use them to expand " }{XPPEDIT 18 0 "(x+2*y)^4" "6#*$ ,&%\"xG\"\"\"*&\"\"#F&%\"yGF&F&\"\"%" }{TEXT -1 106 " , collect the re sult into a polynomial in x, and find the coefficient of the x^3 te rm of that result. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 309 110 "Lernen Sie wie man die Befehle c ollect, coeff und expand benutzt. Wenden Sie diese Befehle an einem Te rm an: " }{XPPEDIT 310 0 "(x+2*y)^4" "6#*$,&%\"xG\"\"\"*&\"\"#F&%\"yG F&F&\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 " Experiment!" }}{EXCHG {PARA 0 "" 0 "exam ple" {TEXT -1 539 " Experimentation is a prime source of learning. W e are constantly conducting little experiments, learning from them, an d using that knowledge in some way. The same holds true when you are l earning Maple and/or working on some math problem. The help facility \+ is a great aid to experimentation. Say you are working on a math prob lem and you need to carry out some algorithm, like solve an equation y ou have set up. You know the Maple word solve will carry out the a lgorithm, but you have forgotten the syntax. You can use the word " }{TEXT 269 7 "example" }{TEXT -1 95 " to list some examples of its us age, rather than bring up the entire help sheet on solve . " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "exa mple(solve);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 302 8 "Deutsch:" }} {PARA 0 "" 0 "" {TEXT 303 428 "Das Experimentieren ist die beste Art z u lernen. Wir f\374hren fortlaufen kleine Experimente durch, lernen au s ihnen, und benutzen dieses neugewonne Wissen. Auf die selbe Wese sol lten Sie auch mit Maple arbeiten. Sie m\374ssen zum Beispiel eine Glei chung l\366sen die sie aufgestellt haben. Sie wissen man benutzt dazu \+ den Befehl solve, aber Sie wissen nicht wie man den Befehl benutzt? Fr agen Sie Maple doch einfach nach einem Beispiel." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 254 " Kee p in mind that the help sheets are written for general use by both nov ices and experts, so don't be intimidated by unfamiliar terminology. \+ Often the examples at the bottom of the sheet suffice to tell you what you need to know. Keep using help! " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 304 204 "Vergessen Sie aber nicht, da\337 die Maple-Hilfe sowohl f\374 r Einsteiger als auch f\374r Experten geschrieben wurde. Lassen Sie si ch nicht von ungewohnter Termonologie einsch\374chtern. Benutzen Sie d ie Maple-Hilfe!" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 8 "Problems" }}} {EXCHG {PARA 260 "" 0 "" {TEXT 263 9 "Exercise:" }{TEXT -1 175 " Spen d a few minutes with the online help deciding what the terms list a nd set mean in Maple. In particular, what is the main differen ce between a list and a set? " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 311 126 "Beispiel:Finden Sie mit der Maple-Hilfe die Funktion von list und set raus. Was ist der Untereschied zwischen diesen Befehlen?" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "example(list);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "example(set);" }}}{EXCHG {PARA 260 "" 0 "" {TEXT 264 9 "Exercise:" }{TEXT -1 131 " If you haven't alread y, find out the usage of the terms seq , NULL , subsop as used \+ in the example sheet for set and list." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Beispiel:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 439 "Experiment is used at the beginning of solving a problem to generate data to conjecture a solution. Towards the end of the pr ocess, experiment is used to test the solution. Maple makes the act o f experimentation easier to carry out and easier to modify. A Maple Wo rksheet makes it easier to carry on work from one session to the next, and to prepare public documents, ie, homework assignments, reseach pa pers, etc for public consumption." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 305 379 "Durch Experimentieren sammelt man Informationen die zu einem \+ L\366sungsweg f\374hrt, und durch experimentieren k\366nnen Sie ihren \+ L\366sungsweg \374berpr\374fen. Maple hilft ihnen einen L\366sungsweg \+ zu finden, und ihre einzelnen Arbeitsschritte miteinander zu verbinden . Mit Maple k\366nnen Sie aus ihren Ergebnissen ein \366ffentliches Do kument machen, z.B. Referate, Untersuchungen, Dissertetionen usw." }}} }}{EXCHG {PARA 0 "" 0 "bottom" {HYPERLNK 17 "Inhaltsverzeichnis" 1 "ha nd0.mws" "" }}}}{MARK "0 2 7 3 0" 15 }{VIEWOPTS 1 1 0 1 1 1803 }