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{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 257 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 256 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 0 "" }{TEXT 256 25 "Making a \+ Start with Maple" }}{PARA 19 "" 0 "" {TEXT -1 13 "J. A. Ziegler" }} {PARA 257 "" 0 "" {TEXT -1 44 "http://www2.SPSU.edu/math/ziegler/index .html" }}{PARA 256 "" 0 "" {TEXT -1 16 "January 15, 2004" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "This introduction is designed to be used \+ with an initially blank Maple " }{TEXT 358 9 "worksheet" }{TEXT -1 27 " as \"workspace.\" Click on " }{TEXT 359 6 "Window" }{TEXT -1 8 " on the " }{TEXT 360 8 "Menu Bar" }{TEXT -1 151 " and see if there is a b lank worksheet already available. If so, it will be called Untitled(1 ). If not, click on the left-most of the buttons on the " }{TEXT 361 8 "Tool Bar" }{TEXT -1 16 ", then click on " }{TEXT 362 6 "Window" } {TEXT -1 88 " and return to this document. When the introduction assu mes you are working on a blank " }{TEXT 363 9 "worksheet" }{TEXT -1 187 ", go to the one you now have. Going back and forth is a bit of a nuisance. If it is too annoying, just print out the part of this docu ment on which you happen to be working at the time. " }{TEXT 364 1 " \+ " }{TEXT -1 179 "Now make a start with Maple by opening the first para graph. To do this, just click on the \"plus\" box beside it. To clos e it, click on what will then have become the \"minus\" box." }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 " On and Off" }}{EXCHG {PARA 4 " " 0 "" {TEXT -1 2 "On" }}{PARA 0 "" 0 "" {TEXT -1 89 " If you have \+ gotten this far, you obviously have figured out how to get Maple start ed!" }}{PARA 4 "" 0 "" {TEXT -1 3 "Off" }}{PARA 0 "" 0 "" {TEXT -1 46 " There are several ways to turn off Maple. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "1. The usual way is to cl ick on the \"close\" button at the upper right hand corner of the " } {TEXT 365 9 "Title Bar" }{TEXT -1 3 ". " }{TEXT 369 5 "Note:" }{TEXT -1 19 " When you do this," }{TEXT 351 2 " y" }{TEXT -1 33 "ou will ge t a Dialog Box saying, " }{TEXT 371 81 "\"The worksheet \"Making_A_Sta rt.mws\" has been modified. Do you wish to save it?\" " }{TEXT -1 58 "It is important to know that what this actually means is, " }{TEXT 372 121 "\"Do you wish to replace the version of this file with which \+ you began with one incorporating the changes you have made?\" " } {TEXT -1 11 "Answering, " }{TEXT 373 5 "\"No,\"" }{TEXT -1 6 " will " }{TEXT 375 4 "not " }{TEXT -1 186 "cause the original version to disap pear! Also, Maple will often consider that a change has been made eve n when one has not, at least, not that you can notice. For example, o pening the " }{TEXT 377 10 "On and Off" }{TEXT -1 162 " paragraph coun ts as a change, even if you close it again without doing anything else at all. So, quite often, the right answer to the Dialog Box's questi on is, " }{TEXT 378 6 "\"No.\" " }{TEXT -1 84 "But if you have made ch anges that you want to save, then of course you must answer, " }{TEXT 381 6 "\"Yes.\"" }{TEXT -1 1 " " }{TEXT 379 40 " Try this now, then tu rn Maple on again." }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 35 "2. A second way is to click on the " } {TEXT 354 4 "File" }{TEXT -1 21 " menu, then click on " }{TEXT 355 4 " Exit" }{TEXT -1 31 " , at the bottom of the list. " }{TEXT 356 39 "Tr y this now, then turn Maple on again." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 57 "3. A third way, as you will have seen when you looked at " }{TEXT 357 5 "Exit," }{TEXT -1 70 " is to press \+ \"Alt + F4\", that is, press these keys at the same time. " }{TEXT 353 39 "Try this now, then turn Maple on again." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 236 "4. As an emergency measu re, if Maple seems to be \"stuck\" and is not responding, or is just i nvolved in a seemingly interminable calculation which even pressing th e \"Stop\" button does not stop, press all together \"Ctrl + Alt + Del ete\". " }{TEXT 352 60 "Perhaps it would be best if you would not try this just now." }{TEXT -1 161 " If some time you have to do this, rem ember that you will lose, from all of your open worksheets, anything y ou have not saved. So remember to \"save\" frequently." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 6 "Saving" }}{PARA 0 "" 0 "" {TEXT -1 110 "This would be a good time to give the \"Untitled(1) .mws\" a name. As usual, just go to the File menu, click on " }{TEXT 382 7 "Save as" }{TEXT -1 375 ", delete the \"*.mws\" from the Name bo x, and type in your name. The suffix \"mws\" will be added automatica lly. Before you save it, take a good look at the location in which Ma ple is planning to put it. You can, naturally, change this if you lik e, but in order to save it to a floppy later, you will need to know wh ere to find it. It might be a good plan to write this down." }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 " The User Interface" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 523 "Maple's \"user interface\" is graphical, so that we can see both what we are telling Maple and what Maple is t elling us. Once we have learned a few basic words in the language Mapl e understands, it is easy enough to use, if we can type. When we began to study Maple, we began with a brief tour of inspection of this Grap hical User Interface, GUI, for short, pronounced, I believe, \"Gooey, \" in the appalling jargon of the computer scientists. Here is a brie f introduction. More detail will be provided in First Steps, below." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 " The Bars" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 257 9 "Title Bar" }{TEXT -1 2 ", " } {TEXT 258 12 "The Menu Bar" }{TEXT -1 2 ", " }{TEXT 261 12 "The Tool B ar" }{TEXT -1 2 ", " }{TEXT 259 15 "The Context Bar" }{TEXT -1 6 ", an d " }{TEXT 260 14 "The Status Bar" }{TEXT -1 3 ". " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 135 " The first three of these follow the usual \+ Windows patterns and are, nearly, self-explanatory. However, the acti ons of some of the " }{TEXT 345 8 "Tool Bar" }{TEXT -1 85 " buttons ar e easy to forget if they are not used often, so it is a good idea to h ave " }{TEXT 346 12 "Balloon Help" }{TEXT -1 280 " turned on. Then, w hen a button is touched with the cursor, a brief description of its us e is displayed. If this is not On, go to the File menu, then click on Preferences. When the dialog box appears, the Balloon Help check box is in the lower left hand corner. Check it. The " }{TEXT 347 11 "Con text Bar" }{TEXT -1 83 " naturally depends on what one is doing and wi ll be discussed as we go along. The " }{TEXT 348 10 "Status Bar" } {TEXT -1 18 " can be ignored. " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 " Regions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "The are two basic types of regions in the GUI: mathematic s regions and text regions." }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 19 "Ma thematics Regions" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 182 "There are a lso two types of mathematics regions: equation regions and graphics re gions. To see the difference, place the cursor anywhere in each of th e following commands and press " }{TEXT 349 5 "Enter" }{TEXT -1 28 ". \+ Do this for each command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Int(x^3*sin(2*x),x)=int(x^3*sin(2*x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "Int(x^3*sin(2*x),x=0..Pi/2)=int(x^3*sin(2*x),x=0 ..Pi/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot(x^3*sin(2* x),x=0..Pi/2,scaling=constrained,thickness=2);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 150 "By se lecting an equation region or the graphic region, we can see the corre sponding context bars. Notice the distinctive mathematics region \"pr ompt.\"" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 12 "Text Regions" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "This, obviously, is a text region, but if we press the " }{XPPEDIT 18 0 "Sigma;" "6#%&SigmaG" }{TEXT -1 15 " button on the " }{TEXT 350 8 "Tool Bar" }{TEXT -1 76 ", we open a special region for introducing mathematical expressions such as " } {XPPEDIT 18 0 "int(x^3*sin(x),x);" "6#-%$intG6$*&%\"xG\"\"$-%$sinG6#F' \"\"\"F'" }{TEXT -1 6 " , or " }{XPPEDIT 18 0 "Sigma;" "6#%&SigmaG" } {TEXT -1 2 " ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 189 "To create a ne w text region, first, press the \" [> \" button on the tool bar, then \+ press the \" T \" button, also on the tool bar. To end the text region , just press the \" [> \" button again. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 273 "There is much more that can be done with a Maple Workshe et, but for the moment we will just remember that if we use the Topic \+ Search in the Help menu to look up \"worksheet\" we will find over 500 references, so there really is much more that can be learned about wo rksheets." }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 34 " The Structure o f a Maple Command" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 " The usual \+ form of a Maple command is " }{TEXT 328 7 "command" }{TEXT 329 70 "(ob ject-to-be-acted-upon,essential information, optional informantion)" } {TEXT 330 3 ". " }{TEXT -1 312 "This must be followed by a \";\" if w e want Maple to tell us the result, or by \":\" if we do not. As an e xample of this, suppose we want Maple to \"Do this and that and the ot her, then put those things together like this.\" after which we want t o ask, \"Now what have you got?\" We only want a \";\" after the ques tion." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 "In our introduction to \+ Maple, after learning the most basic facts, the most important topics \+ are those connected with pictures, color, and action. " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 " First Steps" }}{EXCHG {PARA 3 "" 0 "" {TEXT -1 15 "Before We Begin" }}{PARA 0 "" 0 "" {TEXT -1 436 "The oute rmost \"window\" on your screen should have the title, in white on dar k blue, \"Maple V Release 5.1\". If, inside this, there is another wi ndow entitled \"Introduction\", note for future exploration the fact t hat there is such a topic (which can be found again in the Help menu), then close this window in the usual way. What you have left is a Map le \"worksheet\" on which you will enter commands and produce various \+ forms of output." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 14 "More on Savin g" }}{PARA 0 "" 0 "" {TEXT -1 220 " If you did not give the blank wo rksheet a name before, do this now. Now, thinking ahead for a moment, \+ suppose you have been getting Maple to do some mathematical work for y ou. Perhaps this will include some graphs. " }{TEXT 334 0 "" }{TEXT 335 9 "WARNING! " }{TEXT 336 427 "Before saving, ALWAYS remove the Out put from your worksheet, especially if this contains any graphs. Clic k on Edit, on the Menu Bar, then Remove Output > From Worksheet. To c ontinue your work, use Edit > Execute > Worksheet. Worksheets with di splayed graphs, particularly 3-dimensional graphs, can use many kiloby tes, even megabytes, of memory. With the output removed, quite a long worksheet seldom uses even 50 kilobytes." }}{PARA 4 "" 0 "" {TEXT -1 16 "Finding it again" }}{PARA 0 "" 0 "" {TEXT -1 827 " You do not ha ve to be much concerned about this as Maple will find it for you, prov ided you let it put it where it wants. Just click on the \"file folde r\" button. If, as in the present case, you have recently been using \+ it, you can click on the File menu and your file will be listed just b efore \"Exit\". Of course, all this is standard \"Windows\" procedure . However, as we said before, if you are planning to copy your worksh eet file onto a floppy, then you do need to pay attention to where Map le has filed it. If you have forgotten, but can remember the file nam e of your worksheet, then you course Windows can find it for you throu gh the Start menu. If you have also forgotten the name (Hello!), open Maple and click on the File menu. The names of the most recently use d files can be read from the box which appears." }}}{EXCHG {PARA 3 "" 0 "" {TEXT -1 15 "Getting Started" }}{PARA 0 "" 0 "" {TEXT 383 60 "Not e: The following should be done on your blank worksheet." }{TEXT 384 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 209 "1. If there is a \+ \"highlighted\" question mark just after the [> , then click on the le ft-most button on the Context Bar; the one with the \"x\". The questi on mark will disappear. Probably there will not be one." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 377 "2. Now go to the \+ Menu Bar and click on the Help menu. The next to last item is \"Ballo on Help\". If there is not a check mark beside this, then click this \+ and then close the menu. Now when you touch a button with the mouse p ointer, a little \"balloon\" appears with a message about the purpose \+ of that button. You can turn it off whenever you like, but I find it \+ very helpful. " }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 17 "Entering Comman ds" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "As \+ an illustration, we will evaluate " }{XPPEDIT 18 0 "int(2*(x-a)^7,x = \+ 0 .. 2);" "6#-%$intG6$*&\"\"#\"\"\"*$,&%\"xGF(%\"aG!\"\"\"\"(F(/F+;\" \"!\"\"#" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 30 "At the promp t, >, type " }{MPLTEXT 0 21 26 "int(2*(x-a)^7,x = 0 .. 2);" } {TEXT -1 268 " just like this, but do not press Enter. Note that \+ the multiplication must be specified and do not forget the semi-colon. Every Maple command must end with either a semi-colon or a colon. I f you want to see the output, use the semi-colon; if not, use the colo n." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 19 "Context Bar Buttons" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 718 "Before w e execute this command, let us use the mouse pointer to investigate th e buttons on the Context Bar. Start with the one with the \"x\". Pre ss it and see what happens. Press it again to return to \"Maple notat ion.\" Note that, either way, the expression is printed in red. This is to indicate that both forms are \"live\". Now try the button with the maple leaf. When it is pressed,the expression is rewritten in bl ack, indicating that it is now \"dead.\" Now press it again. Did the color change back to red? Has the > returned? Now place the mouse p ointer on the \"!\" button. Press it. Congratulations! You have just used Maple's capacity to do symbolic mathematics, its fundamental rea son for existance. " }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 19 "Copying a nd Pasting" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 228 "Copying, cutting, and pasting work as in any \"Windows\" word \+ processor. Copy the integrate command (be sure to include the semi-co lon) and paste it at the new >. Now press Enter. So there are two wa ys of executing a command. " }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 43 "E ntering A Command in Mathematical Notation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 147 "The cursor should be at a new \+ >. If it is, press the x-button on the Context Bar. Notice that the \+ context bar has changed. Now start typing " }{MPLTEXT 0 21 18 "in t(x^2*sin(x),x) " }{TEXT -1 326 "No semi-colon this time. As you type , nothing happens on the worksheet, but the command begins to appear i n the long white box on the context bar, where it is hard to see. The re seems no way to make this box larger. Now press Enter. The integr al appears in red, but nothing else has happened. Press Enter a secon d time. " }{MPLTEXT 0 21 1 " " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "int(x^2*sin(x),x);" "6#-%$intG6$*&%\"xG\"\"#-%$sin G6#F'\"\"\"F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 212 "A tedious \"par ts\" integral is found almost instantaneously. Maple is becoming more attractive. Of course, it \"just\" finds one anti-derivative and lea ves us to add on the \"+ C\" for ourselves, but we can do that." }} {PARA 5 "" 0 "" {TEXT -1 10 "Comment: " }}{PARA 0 "" 0 "" {TEXT -1 204 "To use Maple effectively, there is a rather small collection of c ommands which it is well to know. Once these have been have been lear ned, entering them in \"Maple notation\" usually proves easiest to do. " }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 9 "Exercises" }}{PARA 0 "" 0 "" {TEXT -1 27 "Now try these for yourself." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 337 86 "First, let us do some easy ones, so that it is obv ious that Maple does them correctly." }}{PARA 0 "" 0 "" {TEXT -1 4 "1. " }{XPPEDIT 18 0 "int(x^2,x);" "6#-%$intG6$*$%\"xG\"\"#F'" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 " 2. " }{XPPEDIT 18 0 "int(cos(x),x);" "6#-%$intG6$-%$cosG6#%\"xGF)" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "3. " } {XPPEDIT 18 0 "int(1/x,x);" "6#-%$intG6$*&\"\"\"\"\"\"%\"xG!\"\"F)" } {TEXT -1 72 " . Aha! Maple wrongly omits the absolute value, so watc h out for this." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "4. The exponential function is known to Maple as exp(x). Now find " }{XPPEDIT 18 0 "int(exp(2*x),x);" "6#-%$intG6$-%$expG6#* &\"\"#\"\"\"%\"xGF+F," }{TEXT -1 34 " . Did you remember to type 2*x \+ ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "For \+ more complicated integrals, such as " }{TEXT 339 1 " " }{TEXT -1 0 " " }{XPPEDIT 18 0 "int(exp(3*x)*sin(5*x),x);" "6#-%$intG6$*&-%$expG6#*& \"\"$\"\"\"%\"xGF,F,-%$sinG6#*&\"\"&F,F-F,F,F-" }{TEXT -1 177 " , the result is best checked by differentiating. How can we have Maple do \+ this for us? Call the (blue) output F(x). Use your mouse to copy the output. Then use the command" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(F(x),x);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "only, in place of the F(x), paste in what you copied. Try it \+ with " }{XPPEDIT 18 0 "int(exp(3*x)*sin(5*x),x)" "6#-%$intG6$*&-%$ex pG6#*&\"\"$\"\"\"%\"xGF,F,-%$sinG6#*&\"\"&F,F-F,F,F-" }{TEXT -1 2 " . " }}}{EXCHG {PARA 3 "" 0 "" {TEXT -1 16 "Names for Things" }}{PARA 0 " " 0 "" {TEXT -1 158 "Referring to things by name is obviously much mor e efficient than referring to them by description. Giving a Maple obj ect a name is easy. The procedure is " }{TEXT 338 16 "name := objec t." }{TEXT -1 36 " For example, if we wanted to call " }{XPPEDIT 18 0 "sqrt(x^2-3);" "6#-%%sqrtG6#,&*$%\"xG\"\"#\"\"\"\"\"$!\"\"" }{TEXT -1 22 " Sam, we would write, " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Sam:=sqrt(x^2-3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Then S am to the 4th power is" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Sa m^4;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "and to find Sam's value w hen x = 7 we would use" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "s ubs(x=7,Sam);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Still," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Sam;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 258 "We are not likely to confuse Sam with something else, but we use \"names\" like a and b and c so often that it is easy to f orget that we have already used them and this can lead to surprises. \+ For example, suppose we let a be a \"nickname\" for Sam. Then we say " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:=Sam;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "and later, having forgotten about this, w e write " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a*x^2+b*x+c;" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "this is not at all what we expec ted. To recover the free use of \"a\", we write" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:='a';" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Then" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a*x^2+b*x+c;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "but " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Sam;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 125 "It is a \+ good practice to \"unassign\", as one says, a name when you are done w ith it. However, it is often not clear that one " }{TEXT 344 2 "is" } {TEXT -1 398 " done with it and after an hour or so it is tedious to g o back and try to find the names which are causing surprises. The Map le command to fix this is \"restart\". This tells Maple to \"forget e verything I have told you.\" And it does, too. Try it. Note that th is time we have used the colon. It does not really matter here, but r emember that we use it only when we do not want to see any output." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Sam;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a; " }}}{PARA 3 "" 0 "" {TEXT -1 8 "Review I" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "This seems a good time \+ to list the topics to which we have been introduced." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 20 "Matters of Procedure" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "1. How \+ to start and stop." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 147 "2. The \"Windows\" bars. Having turned on \"balloon he lp\" in the Help menu, we can use the mouse to give us some informatio n on what the buttons do." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "3. Saving and retrieving a worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "4. Entering a ma thematics command in Maple notation. " }}{PARA 0 "" 0 "" {TEXT -1 54 " The use of the important symbols \" ; \" and \" : \"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 126 "5. The action s of the Context Bar buttons \" x \", \" Maple leaf \", and \" ! \" an d the use of the Enter key to execute a command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "6. Copying and Pasting i n the usual \"Windows\" way." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "7. Entering a mathematics command in mathemati cal notation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "8. Giving names and taking them away." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 33 "Finding Integrals and D erivatives" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "9. For an indefinite integral (anti-derivative) we write: int (" }{TEXT 340 31 "integrand, independent variable" }{TEXT -1 79 ") fo llowed by a \" ; \" if we want to see the result, but by \" : \" if we do not." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "10. For a definite integral we write: int(" }{TEXT 341 31 "integr and, independent variable" }{TEXT -1 1 "=" }{TEXT 342 26 "lower limit \+ .. upper limit" }{TEXT -1 29 ") followed by \" ; \" or \" : \"." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "11. For \+ a derivative we write: diff(" }{TEXT 343 31 "expression,independent v ariable" }{TEXT -1 23 ") then \" ; \" or \" : \"." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 31 " Colored Pictures: 2-Dimensions" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 278 19 "Graphs of Functions" }} {EXCHG {PARA 3 "" 0 "" {TEXT 264 59 " If y = f(x), the command to d raw the graph of f(x) is " }{TEXT 267 5 " plot" }{TEXT 268 39 "(f(x), x=a .. b, options) followed by " }{TEXT 269 2 "; " }{TEXT 275 4 " or " }{TEXT 276 2 " :" }{TEXT 277 234 " , where [a, b] is the interval \+ over which the graph is to be drawn. There are many options. Some of them are the color and thickness. We will have a look at these prese ntly. To see all of them, use Help to do a Topic Search for " }{TEXT 270 12 "plot,options" }{TEXT 271 1 "." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "For old times' sake, we will use the same examples we use d then. " }{TEXT 272 60 "The first was f(x) = x^3 on [-2, 2]. We fi rst graphed the " }{TEXT 273 10 "expression" }{TEXT 274 1 " " } {XPPEDIT 18 0 "x^3;" "6#*$%\"xG\"\"$" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(x^3,x=-2..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "If f is defined as the function f: x -> " } {XPPEDIT 18 0 "x^3;" "6#*$%\"xG\"\"$" }{TEXT -1 2 ", " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=x->x^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "we \+ may write " }{TEXT 265 4 "plot" }{TEXT -1 1 "(" }{TEXT 262 23 "f(x), \+ x=a .. b, options" }{TEXT -1 23 "); , as before. Thus," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(x),x=-2..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "or we may write " }{TEXT 266 4 "plot" } {TEXT -1 1 "(" }{TEXT 263 18 "f, a .. b, options" }{TEXT -1 34 "); No tice the differences. Thus," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot(f,-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 " Graphs of Equations" }}{EXCHG {PARA 4 "" 0 "" {TEXT 279 238 "There is a one to one correspondence be tween equations and graphs, but drawing the graph of an equation can b e very difficult if we cannot rewrite it in the form y = f(x). Luckil y, Maple knows how to do this. The necessary command is " }{TEXT 280 12 "implicitplot" }{TEXT 281 1 "(" }{TEXT 282 57 "equation, one va riable=a..b, other variable=c..d, options" }{TEXT 283 186 ") then \" ; \" or \" : \". As a practical matter, it is important to know at lea st one point on the graph, even approximately, so that the rectangle [ a,b] x [c, d] can be placed around it. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "We first loaded the " }{TEXT 285 5 "plots" }{TEXT -1 8 " \+ package" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 284 10 "Then tried" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "implicitplot(x^2*y^5-3*x+2*y = 2,x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "It is \+ not very fancy, but using Maple is certainly easier than the alternati ve. Notice that, as it should, the graph passes through (0, 1)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 18 " Parametric Curves" }}{EXCHG {PARA 4 "" 0 "" {TEXT 286 89 "We also learned to draw the parametric curve x = f(t), y = g(t) on [t1, t2], by writing " }{TEXT 318 30 " plot([f(t), g(t), t=t1..t2]); " }{TEXT 319 4 " (or" }{TEXT 320 2 " :" }{TEXT 321 155 ").\nFor exampl e, suppose we want to draw the parametric curve x = 2 sin (t) , y = 3 \+ cos (t) for t in [0, 2 Pi]. We write (the capital P in Pi is essentia l)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot([2*sin(t),3*cos( t),t=0..2*Pi]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 99 "This does not \+ look very elliptical. We can fix that by pressing the 1:1 button on t he context bar." }{TEXT 287 0 "" }{TEXT 288 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Parametirc curves need not be the graphs of function s and can really be quite surprising." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "plot([t+4*sin(t),cos(t)/(t^2+1),t=2*Pi/5..6*Pi],color =blue,thickness=4,axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 " Plot Options" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "We learned that we could fix the \+ circular appearance of our ellipse ahead of time by using the plot opt ion, " }{TEXT 291 19 "scaling=constrained" }{TEXT -1 7 ". Thus" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot([2*sin(t),3*cos(t),t=0. .2*Pi],scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "T o color the curve blue, we added the optional information " }{TEXT 289 10 "color=blue" }{TEXT -1 19 ". Now press enter." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot([2*sin(t),3*cos(t),t=0..2*Pi], scaling=constrained,color=blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "We learned that if we used a lighter color, say, yellow" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "plot([2*sin(t),3*cos(t),t=0. .2*Pi],scaling=constrained,color=yellow);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Then the curve was hard to see. By using the plot option " }{TEXT 290 1 " " }{TEXT -1 1 " " }{TEXT 292 11 "thickness=4" }{TEXT -1 4 " , " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "plot([2*sin(t ),3*cos(t),t=0..2*Pi],scaling=constrained,color=yellow,thickness=4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 163 "we could make a definite impro vement. So remember, the lighter the color, the thicker the curve nee ds to be. Thickness runs from n = 0, the defualt, to n = 15. " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 16 " Multiple Curves" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "We learned to draw two or more graphs on the same set of axes in the \+ following way. We let " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " f:=x^3-2*x+1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "and its derivati ve be" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "df:=3*x^2-2;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "then drew their graphs together on [-2,2], coloring the first blue and the second red." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot([f,df],x=-2..2,color=[blue,red]);" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 195 "It is important to use the [ , \+ ] notation as this creates an ordered list. The first element of each list is plotted, then the second element, and so on. Each option is \+ handled in the same way." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 " Elementary Animations" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "We also learned how to make simple animations by using " }{TEXT 293 12 "animatecurve" }{TEXT -1 43 ", to animate the drawing of the curve, and " }{TEXT 295 7 "animate" } {TEXT -1 33 ", to make a sequence of pictures." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 87 "animatecurve([2*sin(t),3*cos(t),t=0..2*Pi],sca ling=constrained,color=navy,thickness=4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Here is another example. The " }{TEXT 35 6 "frames" } {TEXT -1 217 " option allows one to specify the number of frames to be displayed. The default is 16. The rest of the options are the same as those available for the plot command. Use ?animatecurve, this time, t o read the Help Page." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "an imatecurve(sin(2*x),x=-2*Pi..2*Pi,color=green, numpoints=150,thickness =3,frames=20);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "We used " } {TEXT 296 8 "animate " }{TEXT -1 88 "to make a sequence of ellipses. \+ You can use the \"frames\" option with this command, too." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "animate([2*u*sin(t),3*u*cos(t),t=0. .2*Pi],u=0..1,scaling=constrained,color=blue,thickness=4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 294 9 "Reminder:" }{TEXT -1 112 " An easy way to param eterize the graph of a function, y = f(x), is to let x = t. Then y = \+ f(t) and instead of " }{TEXT 317 1 " " }{TEXT 297 19 "plot(f(x), x=a.. b);" }{TEXT -1 8 " we use " }{TEXT 298 22 "plot([t,f(t),t=a..b]);" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 " Review of 2-D Plots" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "We learned how to use " }{TEXT 300 5 "plo t " }{TEXT -1 71 "to graph functions, to graph curves defined parametr ically, and to use " }{TEXT 301 13 " implicitplot" }{TEXT -1 40 " to p roduce the graphs of equations (or " }{TEXT 299 9 "relations" }{TEXT -1 44 "). We also saw how to use some of the plot " }{TEXT 302 7 "opt ions" }{TEXT -1 191 " to control the color and thickness of the curves and the scaling of the coordinate axes. We learned how to draw more \+ than one curve on a single set of axes. Finally, we were introduced t o " }{TEXT 303 12 "animatecurve" }{TEXT -1 5 " and " }{TEXT 304 8 "ani mate," }{TEXT -1 71 " saw the difference between them and something of how they may be used." }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 " Ann otating Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:wit h(plots):" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 7 " Labels" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "We begin with a multiple graph of many co lors." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "plot([seq((x-n/2) ^2,n=-4..4)],x=-3..3,color=[aquamarine,coral,cyan,gold,magenta,maroon, plum,turquoise,blue],thickness=5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 225 "We learned how to use plot options to control the number of ti ck-marks on the x- and y-axes, the labels on the axes, and the size an d style of type in which they and the numbers appear. Making a sequen ce of suitable choices," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 " Q:=xtickmarks=10,ytickmarks=10,labels=[\"x\",\"y\"],labelfont=[TIMES,B OLD,12],axesfont=[TIMES,BOLD,10]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "we can add this to our plot to see the results." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "plot([seq((x-n/2)^2,n=-4..4)],x=-3..3,co lor=[aquamarine,coral,cyan,gold,magenta,maroon,plum,turquoise,blue],th ickness=5,Q);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Notice carefully the use of capital letters." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "W e also learned how to give our graph a title. We will add its specifi cation to Q as follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " Q:=Q,title=\"Curves and Colors\",titlefont=[HELVETICA,BOLD,14]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "plot([seq((x-n/2)^2,n=-4..4 )],x=-3..3,color=[aquamarine,coral,cyan,gold,magenta,maroon,plum,turqu oise,blue],thickness=5,Q);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 " Textplot" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "When we were learning how to use \"textplot\", which is more flexible and also mor e trouble to use than " }{TEXT 308 0 "" }{TEXT 309 5 "title" }{TEXT 310 0 "" }{TEXT -1 57 ", we considered the graph of a simple rational \+ function: " }{XPPEDIT 18 0 "y = 1/(x-1);" "6#/%\"yG*&\"\"\"\"\"\",&%\" xGF'\"\"\"!\"\"F+" }{TEXT -1 52 ". We learned that we needed to use t he plot option " }{TEXT 311 0 "" }{TEXT 312 12 "discont=true" }{TEXT 313 0 "" }{TEXT -1 40 " to help Maple draw the graph correctly." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot(1/(x-1),x=-4..4,y=-10.. 10,discont=true,color=red,thickness=2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Now let us use the plot option" }{TEXT 314 1 " " }{TEXT 316 0 "" }{TEXT -1 0 "" }{TEXT 315 9 " textplot" }{TEXT -1 202 " to ad d the words, \"Discontinuous at x = 1.\" We placed the word, \"Disco ntinous,\" at (-3, 8) and \"at x = 1\" at (-3, 6). To display this me ssage and our plot together, we gave names to both, then used " } {TEXT 305 7 "display" }{TEXT -1 1 "." }{TEXT 306 0 "" }{TEXT -1 0 "" } {TEXT 307 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "T:=textp lot(\{[-3,8,\"Discontinuous\"],[-3,6,\"at x = 1\"]\},font=[HELVETICA,B OLD,12]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "P:=plot(1/(x-1 ),x=-4..4,y=-10..10,discont=true,color=red,thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "display(T,P);" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 98 "Now let us use Times, Bold, 10 pt. for the axesfon t and Helvetica, Bold, 12 pt. for the labelfont." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "P:=plot(1/(x-1),x=-4..4,y=-10..10,discont=tr ue,color=red,thickness=2,axesfont=[TIMES,BOLD,10],labelfont=[HELVETICA ,BOLD,12]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "display(T,P) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 " Some \"Plot Tools\"" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 183 "Maple has built-in routines for drawing many standard fi gures in both two and three dimensions. These are collected into the \+ \"plottools package\". Let us have a look at its contents." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(plottools);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Some of these are useful for animations. \+ We will have a quick look at " }{TEXT 322 23 "line, disk, rectangle, \+ " }{TEXT -1 4 "and " }{TEXT 323 8 "polygon." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 5 " Line" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 182 "Let us first draw a line (segment ) between (-2, 3) and (3, -2), color it green and make its thickness 4 . Once the end-points have been given, all of the applicable other op tions of " }{TEXT 324 4 "plot" }{TEXT -1 13 " may be used." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "line([-2,3],[3,-2],color=green,thic kness=4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "What is wrong? Well , we must always use " }{TEXT 325 7 "display" }{TEXT -1 115 " from the \"plots\" package to exhibit the picture of a \"plottools\" object. \+ It is a good practice to do it this way:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "L:=line([-2,3],[3,-2],color=green,thickness=4):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "display(L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 5 " Disk" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Let us add to this \+ a red disk of radius 0.5, centered at (2, 1). Use " }{TEXT 326 5 "?di sk" }{TEXT -1 130 " to see the other possible options. Remark: We mus t not try to call it \"D\" as that is the differentiation operator for functions." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "d:=disk([2,1 ],0.5,color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "displa y(d,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Now \+ let us display the disk and the line together." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 33 "display(d,L,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 " Rectangle" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 194 "A colored re ctangle makes a good background. It is specified by its upper left-ha nd corner and its lower right-hand corner. We will make a yellow one \+ and display it with the disk and the line." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "R:=rectangle([-2,3],[3,-2],color=yellow):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "display(d,R,L,scaling=constr ained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "The order matters for R and d, but apparantly not for L. With Maple there are always surpr ises. Try" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "display(R,d,L ,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 " Polygon" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Finally, we will use " }{TEXT 327 7 "polygon" } {TEXT -1 19 " to add a triangle." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "TA:=polygon([[-1.5,1],[1,2],[-1,-1]],color=blue):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "display(TA,d,R,L,scaling=co nstrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 187 "Additions will be made from time to time. If you discover any errors, or have suggestions for improvements, please sen d them to jziegler@spsu.edu. Comments are welcome, too. Thank you." }}}{MARK "1 0 14" 167 }{VIEWOPTS 1 1 0 1 1 1803 }