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0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 256 9 "Math 2270" }{TEXT 311 0 "" }} {PARA 257 "" 0 "" {TEXT 257 14 "MAPLE TUTORIAL" }}{PARA 258 "" 0 "" {TEXT -1 14 " January 2005" }}{PARA 0 "" 0 "" {TEXT -1 23 "(Thanks to N. Korevarr)" }}{PARA 3 "" 0 "" {TEXT 258 425 " The purpose of th is tutorial is to get you going with MAPLE, probably in our Math Lab. \+ You can follow this tutorial to log onto the Math Lab machines, famil iarize yourself with how they operate, introduce yourself to the softw are MAPLE, and use it to do some basic matrix computations. related to the linear algebra we've been talking about. Depending on your previo us eperience you may want to skip various sections. " }}{PARA 0 "" 0 "" {TEXT -1 103 " Your actual Maple assignment can be found by goi ng to the Maple page from our course homepage, at " }{TEXT 310 57 "htt p://www.math.utah.edu/~zobitz/teaching/spring05.html " }{TEXT -1 32 " (This tutorial lives there too.)" }}{PARA 3 "" 0 "" {TEXT 277 1 " " } {TEXT 312 94 " Our class projects can be done in versions five and above of Maple, with minor changes. " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 14 "1 ) Logging on:" }}{PARA 0 "" 0 "" {TEXT -1 409 "Almost all students who are registered in Math 2270, or in any other math class, will alread y have accounts set up in our lab. Since these accounts are created f rom University class lists, late-registering students may not be acco unted for. If you fit in this case the lab assistant can help you app ly for an account - provided you have brought your student I.D. to sho w that you are a University student." }}{PARA 0 "" 0 "" {TEXT -1 147 " The lab machines are left on - move the mouse or hit a key to wak e yours up. There are two possibilities for the dialog box which app ears. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "Your " }{TEXT 275 10 "login name" } {TEXT -1 47 " is made out of your initials. If your name is" }{TEXT 268 2 " K" }{TEXT -1 4 "arl " }{TEXT 269 1 "F" }{TEXT -1 4 "red " } {TEXT 270 1 "G" }{TEXT -1 3 "aus" }{TEXT 271 1 "S" }{TEXT -1 704 ", th en your login name is c-gskf, following the recipe: c-(first letter o f last name)(last letter of last name)(first letter of first name)(mid dle initial). If there are multiple people registered this term with \+ the same initials, then rather than c-gskf, they are assigned login n ames with a numerical suffix, c-gskf1, c-gskf2, c-gskf3, etc. Mr. Ga uss would not know beforehand which case he fell into, so would probab ly try c-gskf first, followed by his password. In case of failure he would then try c-gskf1, then c-gskf2, etc, through c-gskf4. Then he w ould find a lab assistant. After entering your try at a login name, t ype the ``return'' key and the cursor should be in the password box. \+ " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 5 "Your \+ " }{TEXT 276 16 "initial password" }{TEXT -1 528 " is just the gskf pa rt of your login name followed by the last four digits of your student I.D. number. If Mr. Gauss has ID number 000735421 then his initial \+ password is gskf5421, regardless whether his login name was c-gskf or \+ c-gskf3. If the login fails try again and then try the different lo gin names suggested above. One possibility is that your account was c reated using your social security number (which used to be used for st udent ID number). If failure continues find a lab assistant and he/sh e will help you. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 425 "Once you are logged in successfully a ``local'' window s hould appear. Notice that it has various parts: borders on the top (t itle bar), borders on the side (scroll bar), etc. If you move your mo use on its pad your pointer (called cursor) moves around the screen. I f you want to work in a window, the cursor should be in it. You can m ake multiple local windows by pressing the right mouse button and high lighting \"local\". " }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 264 23 "1b) Changing password:" }{TEXT -1 198 " Some time within the first several weeks of classes you must change your defaul t password into a personal one. You do this as follows: Get your curs or into a local window. Type the unix command " }{TEXT 265 6 "passwd " }{TEXT -1 640 ", followed by return, and follow the directions. You r new password should be exactly 8 characters long. Don't choose a wo rd in the dictionary or a proper name. Composites of dictionary words , like strawdog, are good. Even better is to use one or two upper cas e letters, e.g. strAwdog. For still more security, use some digits, e .g. strAw4o9. It takes about 15 minutes for a new password to take e ffect. If a password is not changed within the first several weeks of class, then your computer account will be disabled for security reaso ns. Make sure to write down your password in a secure place, in case \+ your memory is not perfect." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 17 "1c) Logging out:" }{TEXT -1 221 " Move the cu rsor out of all windows (into the background), press the left mouse bu tton and choose the last menu item: Exit X-Windows. (You probably don 't want to do this now, but at least locate the menu item for later.) " }}{PARA 0 "" 0 "" {TEXT -1 62 " At this point you are ready to g et used to the X-windows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 267 51 "2) X-windows, opening netscape, maple, mail, mor e:" }{TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 328 "Xwindows are no t so different from P.C. windows or Mac windows; on the other hand the y have their own idiosyncracies, so you should experiment to see how t o open and close windows, resize them, move them about, and find them if they happen to get hidden. To open up an Xwindow click on the comp uter icon on your lower toolbar. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 263 "For your Math 2270 purposes you need to \+ be able to open Netscape (to download files) and Maple (to work on the m). Open Netscape by finding it on one of your mouse buttons, under \+ the choice \"browsers\", or by moving your cursor into a local window \+ and then typing" }{TEXT 272 11 " netscape &" }{TEXT -1 27 ", followed \+ by . The" }{TEXT 273 2 " &" }{TEXT -1 117 " tells X-windows to create a separate process for netscape, keeping your local window fre e for more UNIX commands. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Finally, open a Maple window by typing the comm and" }{TEXT 274 9 " xmaple &" }{TEXT -1 214 ", followed by , in the Xwindow. This should bring up Version 8 of Maple. Versions 9 and 9.5 are available. This worksheet was written in Version 8, and if y ou decide to use newer versions (done by writing " }{TEXT 313 11 "xmap leV9 & " }{TEXT -1 3 "or " }{TEXT 314 10 "xmapleV9.5" }{TEXT -1 1 " " }{TEXT 315 1 "&" }{TEXT -1 106 " in the Xwindow), the only thing you n eed to worry about is that the file extensions of newer versions is " }{TEXT 316 3 ".mw" }{TEXT -1 13 " rather than " }{TEXT 317 4 ".mws" } {TEXT -1 18 " (this stands for " }{TEXT 318 1 "M" }{TEXT -1 5 "aple " }{TEXT 319 1 "W" }{TEXT -1 3 "ork" }{TEXT 320 1 "s" }{TEXT -1 11 "heet ). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 278 11 "3) Maple: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 212 " If you are starting the tuto rial at this point (because you're doing it on your own at another loc ation or already knew the Math Lab system), you should have opened a m apleV8 or mapleV7 as well as a web browser." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 860 "Maple is partly just a very fa ncy calculator; it can do practically any undergraduate mathematics co mputation or symbolic manipulation. You can write programs in Maple a nd draw pictures as well. If you are doing a homework assignment you \+ can intersperse text with computations using the toolbar: to get a co mputation prompt click on the ``[>'' box near the top. To insert text click on the ``T'' box. Or you can change command fields (starting w ith \"[>\") into text fields by putting the cursor into them and then \+ choosing \"T\". You can use the mouse to cut, paste, and edit a docum ent. You can change fonts, formats, and use other standard text editi ng tools by choosing appropriate menu items. This document you are re ading is a Maple document even though it is largely text. You will le arn by doing - and by asking your neighbor or the lab assistant." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 281 18 "New User 's Tour: " }}{PARA 0 "" 0 "" {TEXT -1 649 "Under the Help button at t he top right of your Maple window you will find the choice \"New User' s Tour\". This is a good way to learn generally about what Maple can \+ do. After making this menu choice Maple may hide the beginning of the tour behind other active windows; use the \"Window\" menu item to b ring the tour window to the front. If you wish you can explore now, \+ or you can continue with the Math 2270 notes below and come back to th e tour later. To close the new tour (or any other top window), use th e ``close'' option inside the ``file'' menu item. To keep the tour op en but bring another window to the front, use ``window'' menu item." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 280 25 "Enterin g Maple commands: " }}{PARA 0 "" 0 "" {TEXT -1 508 "To give you a flav or of what Maple can do, we will try a few commands. Move your cursor into the \"Untitled\" (new) Maple window which you created in step (2 ). Commands begin on lines having a command prompt ``>'', and shoul d be ended with either a semicolon ; or a colon : If you end with a s emicolon you will see visible output, if you end with a colon the outp ut will be suppressed even though the command is executed. Maple will not execute a command until you type the ``return'' or ``enter'' key. " }{TEXT 279 87 "If you have a multiline command use ``shift-return' ' to change lines without executing." }{TEXT -1 1 " " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 696 "If you incorrectly ali gn parentheses or brackets, or do something else which makes your comm and unexecutable you will get a ``syntax error'' message and Maple wil l try to point out your mistake with the cursor and cryptic diagnostic phrases. After a while you will become good at fixing these mistakes but they can be annoying at first. Spaces are ignored in Maple, so y ou may use them to make input easier to read. You can enter explanato ry comments in a command line by inserting a ``#'' to the left of the \+ comments; Maple ignores any text after the #. Sometimes this is more \+ informative then entering nearby explanatory text, especially if you a re explaining various steps in a subroutine." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 222 " Now, let's try some comma nds. (You try just the math commands, the editorial comments were only added to explain what the particular commands are illustrating ! ) C heck that you understand what each command is doing." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "3+4; 4+5: 6 * 7; #one of these computations will not be shown \n # even though all three will be done.\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 432 "(3+4)7; #if you want to mult iply you must use *, so after \n #trying the command as given insert a * to fix the \n #resulting syntax error. You can e xecute a line or\n #execution group (bracketed on the left) i f \n #your cursor is anywhere in it. You can move the \n \+ #cursor with the mouse or the arrow keys. Maple will \n \+ #try to put it in a good place if it detects an error." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 290 "(3+4)^2/7; 3+4^2/7; evalf(3+4^2/7) ; #the evalf command gives a decimal \n #approximation inst ead of an algebraic expression. \n #Notice that if given a c hoice, Maple computes powers \n #first, then multiplies and d ivides, and finally\n #adds or subtracts." }}{PARA 11 "" 1 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "diff(x^2, x); #``differentiate x^2 with respect to x''" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "diff(exp(sin(x))*x^3,x); #a harder differentiat ion problem\n #you should get output:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#%\"xG\"\"\"-%$expG6#-%$sinGF'F))F(\"\"$F)F )*&F*F))F(\"\"#F)F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 203 "f:= x-> exp(sin(x))*x^3;\ndiff(f(x),x); #the same problem done in two steps. \n #The first line shows the format for defining \n #functions in Maple. (Did you use ``shift-ret''?) " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow GF(*&-%$expG6#-%$sinG6#9$\"\"\")F3\"\"$F4F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#%\"xG\"\"\"-%$expG6#-%$sinGF'F))F(\"\"$F)F )*&F*F))F(\"\"#F)F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "int (t^2*exp(t),t); #``integrate (t^2)*exp(t) with respect \n # to t'' (Maple doesn't put in the integration constant.)" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,(*&)%\"tG\"\"#\"\"\"-%$expG6#F&F(F(*&F&F(F)F(! \"#F)F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "int(t^3*exp(sin (t)),t); #this shows that Maple is not God:\n #If it can't f ind an elementary-function\n #antiderivative it just echos wh at you put in.\n #you should get: " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&)%\"tG\"\"$\"\"\"-%$expG6#-%$sinG6#F(F*F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "evalf(int(t^3*exp(sin(t)) ,t=0..1)); #But you could do \n #a definite integral numeric ally even if Maple \n #can't compute an elementary antideriva tive" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*39G6&!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "Pi;exp(1);evalf(Pi);evalf(exp(1));i nfinity; \n #some important numbers" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 299 14 "Entering Text:" }}{PARA 0 "" 0 "" {TEXT -1 145 "Scroll to some where in your worksheet and add some text with the ``T'' menu item. ( If you move your cursor to a command field and the press the " }{TEXT 300 2 "[>" }{TEXT -1 128 " button with your mouse, Maple makes a new c ommand field directly below it. If you move to the new command field \+ and press the " }{TEXT 301 1 "T" }{TEXT -1 127 " button you will have \+ a text field into which you may write, using the rudimentary word proc essing tools on the Maple menu bar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 369 "Now scroll to the top of your file and \+ insert the title ``My first Maple worksheet'' (center it with the menu option on the right side of the toolbar), as well as your name and to day's date. When you are doing your Maple projects you will be expecte d to hand in more than a page of computations: You will be expected to add text explanations of what you've been doing. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 13 "Saving Files:" }}{PARA 0 "" 0 "" {TEXT -1 415 "It is always a good idea to save your maple fi le periodically. Do this now using the tool bar, using the \"save\" o ption under the \"File\" menu item. The first time you save a new file , and any time you use the \"save as\" option, you will be asked to na me your file and say where you want to keep it. You name it in the le ft part of the box, being careful to keep the suffix \".mws\" so that \+ Maple knows this file is a " }{TEXT 293 1 "M" }{TEXT -1 5 "aple " } {TEXT 294 1 "W" }{TEXT -1 4 "ork " }{TEXT 295 1 "S" }{TEXT -1 544 "hee t. If your directory is new you probably haven't made any subdirector ies yet (unix command mkdir, in a local window), but as you create mor e files you may wish to organize where you save them using the tree st ructure of Unix directories, which you can follow in the right side o f your saving box. Unfortunately our UNIX is not set up so that you c an visually see your directory/file tree like in PC windows or Macs. \+ You use various UNIX commands in your local window to organize your di rectories. For more information about this, go to" }{TEXT 298 1 " " }{TEXT -1 1 " " }{TEXT 321 35 "http://www.math.utah.edu/computing/" } {TEXT -1 20 " \"Unix Tutorial.\" " }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 163 "It will probably happen some time that \+ you will crash Maple long after your last save. This will not make yo u feel happy but will teach you an important lesson. " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 262 "" 0 "" {TEXT -1 9 "Printing:" }} {PARA 0 "" 0 "" {TEXT -1 10 "Go to the " }{TEXT 282 4 "file" }{TEXT -1 28 " menu option and choose the " }{TEXT 283 5 "print" }{TEXT -1 72 " option. You get a little printer setup box. If you then click o n the " }{TEXT 285 14 "print command " }{TEXT -1 52 "diamond, followed by ``enter'' or by a click on the " }{TEXT 284 5 "print" }{TEXT -1 192 " box at the bottom of the window, a paper copy will come out of o ne of the printers at the side of the lab. Do this now. Alternately, if you want to use a different printer, you can use the " }{TEXT 286 14 "output to file" }{TEXT -1 558 " diamond to create a postscript fil e which you can then print anywhere, using the appropriate unix comman ds. For example, to print a postscript file to the lab printers from \+ a local window, the command would be \"lpr -P b129lab1\", or \"lpr -P b129lab2\", followed by the return key. You do not put in the quote \+ marks, but you are careful to leave spaces exactly as indicated. The \+ lpr stands for line printer, the -P stands for print, and the b129lab1 or b129lab2 are the names of the two printers. If you have trouble p rinting ask a lab assistant for help." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 303 28 "Downloading Maple documents:" }} {PARA 0 "" 0 "" {TEXT -1 103 " This document is available online in se veral formats, if you follow the links from the course homepage" } {TEXT -1 503 ". Files with suffix \".mws\" or \".txt\" can be downloa ded from your browser and then opened from Maple. The \".mws\" suffix means the file is a Maple Worksheet, and should open from Maple to lo ok just like this file. The \".txt\" suffix is Maple text, and you sh ould only try it if the \".mws\" file doesn't open. It's a cruder for m of this file, but potentially more universal. The \".pdf\" versions of the file are for reading from your browser (with Acrobat reader), \+ but you can't execute these from Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 111 "Go to the course homepage address u sing your browser, follow the link to the Maple page, and find and sav e the " }{TEXT 296 13 "2270proj1.mws" }{TEXT -1 29 " file to your home directory." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "Now return to your Maple window and use the ``file'' menu item \+ to open " }{TEXT 297 13 "2270proj1.mws" }{TEXT -1 501 ". It should ap pear in the central box after you choose \"open\". Click on it with t he mouse to highlight it and then click ``OK'' or type ``return''. A \+ copy of this tutorial should then appear in your Maple window, as a Ma ple document that you can work in. Notice you can use the \"Window\" \+ menu item at the top of your Maple window to change between various op en files. (Sometimes when you open a new file it goes to the back of \+ your pile. Then use the Window option to bring it back to the front.) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 245 "If y ou couldn't open the Maple worksheet file, go back to your browser and save the \".txt\" version of the tutorial. Then go back to Maple, an d follow these directions: In order to open a ``Maple text'' document , which this is, you must chose " }{TEXT 289 4 "open" }{TEXT -1 10 " \+ from the " }{TEXT 290 4 "file" }{TEXT -1 32 " menu option. In the res ulting " }{TEXT 291 9 "open file" }{TEXT -1 22 " dialog box go to the \+ " }{TEXT 292 9 " filetype" }{TEXT -1 596 " box at the bottom, click on the triangle to see the list of choices, and use your mouse to choose ``Maple text.'' At this point ``2270tutorial.txt\" should appear as \+ a choice in the central box. Click on it with the mouse to highlight \+ it and then click ``OK'' or type ``return''. A copy of this tutorial \+ should then appear in your Maple window, as a Maple document that you \+ can work in. The copy is not as pretty as your xerox (the execution g roups are all single lines, and the text formatting is not as neat, an d some output may be lost), but it is O.K. It has text and it has Map le input." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 302 17 "Execution Groups:" }}{PARA 0 "" 0 "" {TEXT -1 368 "You can mod ify the text and input using the toolbar and menu options. You will n otice many brackets on the left of the document. These are execution \+ groups. Maple will execute everything in one execution group at once, and then move the cursor to the next execution group. You can create large execution groups by highlighting sections of a document, going \+ to the " }{TEXT 287 4 "Edit" }{TEXT -1 20 " option and picking " } {TEXT 288 24 "join execution groups. " }{TEXT -1 252 "You can remove \+ brackets by highlighting them with the mouse and deleting them with th e delete key or the menu option. And you already learned how to inser t new prompts or new text wherever your cursor is, by using the [> and T buttons on your toolbar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 4 "4a) " }{TEXT -1 1 " " }{TEXT 260 47 "Linear Algebra, and using Maple's help window s" }{TEXT -1 315 ": So, it looks like Maple might be interesting to u se in Calculus, but how do we find out what it can do for us in that s ubject, or in another subject, say linear algebra? It is instructive to use the Help directory located at the upper right-hand corner of t he maple window. That's what you're going to do now." }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 205 " Can Maple do \+ matrix operations, or even define matrices???? Of course!!! Here's h ow you would try to find the right commands if you didn't know them al ready, or if I wasn't going to tell you below:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 129 " Click on the Help o ption at the upper right corner of your Maple window. A little window opens with further choices. Pick " }{TEXT 304 12 "Topic Search" } {TEXT -1 192 ", by highlighting it, and a help window should appear. \+ (If it doesn't, it's hidden behind your worksheet; use the ``window'' \+ option in your menu to bring it to the front.) Try searching for " } {TEXT 305 1 " " }{TEXT 306 15 "linear algebra." }{TEXT 307 2 " " } {TEXT -1 240 "At this point you should get a help window about the lin ear algebra library. There seem to be a lot of commands. You could tr y finding the one you wanted from this page, or you could do a more sp ecific search. For example, either look up " }{TEXT 308 6 "matrix" } {TEXT -1 187 ", or click on it from the linear algebra page. Notice i f you go to the bottom of a help window, you can often figure out how \+ the command works without reading all the fine print above. " }} {PARA 0 "" 0 "" {TEXT -1 77 " We can use matrices if we load the l inear algebra library of procedures:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "with(linalg); #to hide \+ the list of commands in this\n #package use a colon instead of a s emicolon" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "And now we copy the commands from the " }{TEXT 309 7 "matrix " } {TEXT -1 53 "help window: (For long ones we would use our mouse!)" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "matrix(2,2,[5,4,6,3]); #a 2 by 2 matrix with\n #successive entries as indicated" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"&\"\"%7$\"\"'\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "matrix([[5,4],[6,3]]); #sam e matrix" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"&\"\"% 7$\"\"'\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 104 " So that's how to make \+ a matrix. By the way, to close the help files after you've used them use the ``" }{TEXT 259 11 "file/close " }{TEXT -1 222 "'' sequence in the toolbar, or the equivalent key stroke given next to it, which is \+ simultaneous ``control-F4'' on my work station. Or you can keep them \+ around and return to your worksheet with the ``window'' menu option." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 3 "4b)" } {TEXT -1 1 " " }{TEXT 263 36 " Some Linear Algebra computations: " } {TEXT -1 237 " Can you figure out the syntax of the commands and their meanings? Some of these commands will be useful later, use the help windows for more details about them. This simple example could easil y be done by hand; larger ones could not." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "A:=matrix([[1,1,1],[2,3,2],[3,8,2]]);\n #coeffi cient matrix for a linear system,\n #``:='' is used to define the object on\n #its left by the construction on its right" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A[2,3]; #one of the entries of A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "b:=vector([1,1,-3] ); #the right-hand side for\n #a linear system Ax=b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "augAb:=augment(A,b); #the augmented matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "C:=rref(augAb); \+ #compute the reduced row echelon form\n #of the augmented matrix " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "x:=col(C,4); #read off the solution vector to Ax=b " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 202 "evalm(A&*x)=evalm(b); #check your answer\n #NOTE A good wa y to do matrix operations use the evalm\n #command. Addition is \+ +, but matrix multiplication\n #is &*. (Scalar times matrix is * .)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "x:=linsolve(A,b); #a nother way to solve linear systems." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "Ainv:=inverse(A); #the inverse matrix (it it exists)! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "x:=evalm(Ainv &* b); # yet another way, for nonsingular matrices,\n #to solve Ax=b" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "evalm(A&*Ainv); evalm(Ainv&* A); #just checking!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "ev alm(A^3); evalm(A&*A&*A); evalm(A+3*A); \n transpose(A);\n \+ #matrix powers, multiplications, addition,\n #transpose (wha t's that?) " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{MARK "80 8" 149 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }