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{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 }3 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 }{PSTYLE "" 0 263 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 "" 0 264 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 "" 0 265 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 "" 0 266 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 "" 0 267 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 "" 0 268 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 "" 0 269 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 270 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 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 -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 9 "Math 2250" }}{PARA 258 "" 0 "" {TEXT -1 35 "MAPLE TUTORIAL and PRO JECT I HINTS" }}{PARA 263 "" 0 "" {TEXT 269 11 "Summer 2004" }}{PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 365 " This do cument is a tutorial for Math 2250 students who may not have done prev ious work with MAPLE or in the Math lab, or who may just want to brush up on their skills. At the end of the tutorial there is material re lated to section 1.4 of the text, from which your actual Project 1b is drawn. An on-line version of this tutorial, without Maple output, is at " }{URLLINK 17 "http://www.math.utah.edu/~korevaar/2250fall04/225 0falltut.mws" 4 "http://math.utah.edu/~korevaar/2250fall03/2250maple.h tml" "" }}{PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 257 "The Math 2250 projects can be done in versions five and above of \+ Maple, with minor changes. The Math Lab, EMCB, and Marriott Library a ll have version 8 of Maple. A student version of Maple 9, for home co mputers is available from the bookstore for $129.95." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 32 "1) Using the Math Co mputer Lab:" }}{PARA 0 "" 0 "" {TEXT -1 351 "The Math Department has a walk-in computer lab in the Math Student Center, located underneath t he plaza connecting JWB to LCB. There is also a computer classroom in LCB 115, where introductory tutorials will be held. Useful informatio n about most aspects of the lab can be found by following links from t he Math Department web pages, e.g. starting at" }{TEXT 271 3 " " } {URLLINK 17 "http://www.math.utah.edu/ugrad" 4 "http://www.math.utah.e du/ugrad" "" }{TEXT 298 1 " " }{TEXT 297 5 ", or " }{URLLINK 17 "http: //www.math.utah.edu/ugrad/lab" 4 "http://www.math.utah.edu/ugrad/lab" "" }{TEXT 275 1 "." }{TEXT 276 2 " " }{TEXT -1 104 "You can find out \+ about lab hours, X-windows, Maple, Unix commands, Netscape, file edit ing, mail, etc. " }}{PARA 0 "" 0 "" {TEXT -1 506 " You can access Math Department Maple (in its own window as opposed to the cumbersome line command form) remotely from a linux/unix system, from a mac runn ing OSX (download the free X11 xwindows from Apple), or from a PC runn ing windows if you have ssh client capabilities and xwindows capabilit ies. Apparently there is a free package for PC's called cygwin which \+ you can download to enable this. You do not want to try remote access of Maple with only a modem connection, it will be unbearably slow." } }{PARA 266 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "" 0 "" {TEXT -1 15 "1a) \+ Logging on:" }}{PARA 0 "" 0 "" {TEXT -1 473 "Almost all students who a re registered in Math 2250, or in any other math class, will already \+ have accounts set up in our lab. Since these accounts are created fro m University class lists, late-registering students may not be includ ed. Your login information is NOT based on your UNID, see below. If y ou're not on our master list, a lab assistant can help you apply for a n account - provided you have brought your student I.D. to show that y ou are a University student." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 154 "The lab machines are left on - move the mouse \+ or hit a key to wake yours up. There should be a box asking for your \+ login name, and then for you password." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 293 15 "Your login name" }{TEXT -1 489 " wil l be of the form c-azbc, where `a',`b',`c' are your last, first, and m iddle initial, respectively and `z' is the last letter in your last na me. For example, if your name is Ulysses Attila Eratosthenes, your lo gin name will be c-esua. (Many people have the same initials, so to e nsure your login name is unique, a digit may be added after the initia ls, eg. c-esua1, c-esua2, ...). For people with more complex (eg. h yphenated names) only the first character of each name is used.\n\n" } {TEXT 294 9 "Passwords" }{TEXT -1 288 " Your initial password will be the letters as in the login name, followed by the last four digits of your University ID number (e.g., if your UID is 123456789 and your lo gin name is c-esua, then your password is esua6789) or if the login na me is c-esua2 the password is still esua6789).\n" }}{PARA 0 "" 0 "" {TEXT -1 241 "Once you're logged in, the default environment of our un ix-based syste is called the common desktop environment, and you will \+ see a maple leaf icon for MAPLE, as well as a NETSCAPE icon. You can \+ open these programs by clicking on the icons." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 295 23 "1b) Changing password: " }{TEXT -1 674 " Upon first logging in you should change your passwor d. To do so, log in, open an xterm window, then type ``passwd'' (foll owed by RETURN). If there is a problem here try typing ``passwd'' fol lowed by your username (eg. ``passwd c-esua''). Next type your old pas sword (the one you used to login), and then type your new desired pass word twice as instructed. Your new password is effective within 30 mi nutes. If you forget your password, request a new one (from the Lab A ssistant). Your password must consist of at least 6 characters (upper and lower case letters, and digits). You should take care to choose \+ one that is very difficult to guess, and keep it to yourself!" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 17 "1c) Log ging out:" }{TEXT -1 187 " In CDE there is a logout or exit icon at th e bottom of your desktop. You might also be able to find it on your r ight mouse button, after putting your mouse cursor in a background fie ld." }}{PARA 0 "" 0 "" {TEXT -1 5 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 40 "2) Opening netscape, maple, mail , more:" }{TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 259 "For your M ath 2250 purposes you need to be able to open Netscape (to download fi les) and Maple (to work on them). Open Netscape and Maple now: in CD E use the icons at the bottom of the desktop. Alternately, you can ope n an xterm window and type the commands" }{TEXT 272 11 " netscape &" } {TEXT -1 35 ", followed by , as well as " }{TEXT 296 8 "xmaple &" }{TEXT -1 26 ", followed by . The" }{TEXT 273 2 " &" } {TEXT -1 61 " tells X-windows to create separate windows for each proc ess." }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 11 "3) Maple: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 264 "If you are starting the tutorial at this point (because \+ you're doing it on your own at another location or already knew the Ma th Lab system), you should have opened a maple window, probably versi on 8 (versions 5,6,7, 9 should also work), as well as a web browser." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 356 "Maple \+ is partly just a very fancy calculator; it can do practically any unde rgraduate mathematics computation or symbolic manipulation. You can w rite programs in Maple and draw pictures as well. But you can also use it to create documents which mix text with computations, and you can \+ export Maple output to other software to create interesting documents. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 663 "If y ou are doing a homework assignment you can intersperse text with compu tations using the toolbar: to get a computation prompt click on the ` `[>'' box near the top. To insert text click on the ``T'' box. Or yo u can change command fields (starting with \"[>\") into text fields by putting the cursor into them and then choosing \"T\". You can use th e mouse to cut, paste, and edit a document. You can change fonts, for mats, and use other standard text editing tools by choosing appropriat e menu items. This document you are reading is a Maple document even \+ though it is largely text. You will learn by doing - and by asking yo ur neighbor or the lab assistant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 282 27 "New User's Tour and more: " }}{PARA 0 " " 0 "" {TEXT -1 649 "Under the Help button at the top right of your Ma ple window you will find the choice \"New User's Tour\". This is a go od way to learn generally about what Maple can do. After making this \+ menu choice Maple may hide the beginning of the tour behind other acti ve windows; use the \"Window\" menu item to bring the tour window to the front. If you wish you can explore now, or you can continue wit h the Math 2250 notes below and come back to the tour later. To close the new tour (or any other top window), use the ``close'' option insi de the ``file'' menu item. To keep the tour open but bring another wi ndow to the front, use ``window'' menu item." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "Another good introduction to Ma ple is located at " }{URLLINK 17 "http://www.math.utah.edu/~gardiner/I ntro.mws" 4 "" "" }{TEXT -1 369 ". (If your computer is appropriately configured clicking on this hyperlink will open your browser and go t o the indicated URL. You can then save the file to your computer, and then open it from Maple if this does not happen automatically.) Alte rnately, if you have a browser open you can open Maple files directly \+ off the internet by using clicking successively on " }{TEXT 285 16 "F ile -> Open URL" }{TEXT -1 59 ", in the Maple menu items at the top of the Maple window. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 25 "Entering Maple command s: " }}{PARA 0 "" 0 "" {TEXT -1 513 "To give you a brief taste 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). Comman ds begin on lines having a command prompt ``>'', and should be ended with either a semicolon ; or a colon : If you end with a semicolon y ou will see visible output, if you end with a colon the output will be suppressed even though the command is executed. Maple will not execu te a command until you type the ``return'' or ``enter'' key. " } {TEXT 259 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 align parentheses or brackets, or do something else which makes your comman d unexecutable you will get a ``syntax error'' message and Maple will \+ try to point out your mistake with the cursor and cryptic diagnostic p hrases. After a while you will become good at fixing these mistakes b ut they can be annoying at first. Spaces are ignored in Maple, so you may use them to make input easier to read. You can enter explanatory comments in a command line by inserting a ``#'' to the left of the co mments; Maple ignores any text after the #. Sometimes this is more in formative then entering nearby explanatory text, especially if you are explaining various steps in a subroutine." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 218 " Now, let's try some commands. (You try just the math commands, the editorial comments were only add ed to explain what the particular commands are illustrating ! ) Check that you understand what each command is doing." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 202 "3+4; 4+5: 6 * 7; #one of these computations will not be shown\n #eve n though all three will be done, illustrating the \n #differe nce between a semicolon and a colon\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 428 "(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 ex ecute a line or\n #execution group (bracketed on the left) if \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." }}{PARA 8 "" 1 "" {TEXT -1 25 "Error, unexpected number\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 290 "(3+4)^2/7; 3+4^2/7; evalf(3+4^2/7); #the evalf com mand gives a \n #decimal approximation instead of an algebrai c \n #expression. Notice that if given a choice, Maple \n \+ #computes powers first, then multiplies and divides, \n \+ #and finally adds or subtracts." }}}{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 92 "diff(exp(sin(x))*x^3,x ); #a harder differentiation problem\n #you should get output :" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#%\"xG\"\"\"-%$expG6# -%$sinGF'F))F(\"\"$F)F)*(F0F)F*F))F(\"\"#F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "f:= x-> exp(sin(x))*x^3; #this is the syntax f or defining a \n #function, in this case the function we just \+ \n #differentiated" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "diff(f(x),x); #shoul d get the same answer as before. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "int(t^2*exp(t),t); #``integrate (t^2)*exp(t) with \+ respect\n #to t'' (Maple doesn't put in the integration const ant.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "int(t^3*exp(sin(t) ),t); #this shows that Maple is not God, you \n #will get" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&)%\"tG\"\"$\"\"\"-%$expG6# -%$sinG6#F(F*F(" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 " # since if Maple can't find an ele mentary function \n #antiderivative it just echos what you pu t in. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "evalf(int(t^3*e xp(sin(t)),t=0..1)); #But you could do\n #a definite integra l (numerically) even if Maple\n #can't compute an elementary \+ antiderivative" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "Pi;exp(1) ;evalf(Pi);evalf(exp(1));infinity;\n #some important numbers " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 301 28 "Dow nloading Maple documents:" }}{PARA 0 "" 0 "" {TEXT -1 136 " This xerox ed tutorial is available online in several formats, if you follow the \+ links from Professor Korevaar's 2250 Maple homepage at" }{TEXT 300 1 " " }{URLLINK 17 "http://www.math.utah.edu/~korevaar/2250fall04." 4 "h ttp://www.math.utah.edu/~korevaar/2250fall03" "" }{TEXT -1 102 " Fil es with suffix \".mws\" or \".txt\" can be downloaded from your browse r and then opened from Maple. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 335 "Alternately, if you know the URL you wan t, you can use the \"open URL\" file option. Do this now, for this do cument's URL, http://www.math.utah.edu/~korevaar/2250fall04/2250falltu t.mws. Maple will download and open the document, and now you can fol low the tutorial from your computer instead of from your hard copy - s o start doing so." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 131 "Sometimes, if you have several windows open Maple will p ut the wrong one on top. Use the Window menu item to move between win dows." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 278 53 "Making new files which mix text, commands and output:" }}{PARA 0 "" 0 "" {TEXT -1 200 "From the \"File\" menu item, create a new worksheet .(It will start out being called Untitled(2) or something like that. \+ The first time you save it you can pick any name you want, as long as \+ it ends in " }{TEXT 299 4 ".mws" }{TEXT -1 558 ", for Maple worksheet. In your new worksheet turn the command field into a text field by put ting your cursor into it, and then using the``T'' menu item. Type in t he title ``My first Maple worksheet'' (center it with the menu option \+ on the right side of the toolbar), as well as your name and today's da te. When you are doing your Maple projects you will be expected to han d in more than a page of computations: You will be expected to add tex t explanations of what you've been doing. In general, if you move you r cursor to a command field and the press the " }{TEXT 279 2 "[>" } {TEXT -1 128 " button with your mouse, Maple makes a new command field directly below it. If you move to the new command field and press th e " }{TEXT 280 1 "T" }{TEXT -1 127 " button you will have a text field into which you may write, using the rudimentary word processing tools on the Maple menu bar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 190 "Use your mouse to copy the following sequence of co mmands from this worksheet into your new one. Paste into a command fi eld. (Successive lines were entered here without execution by using \+ " }{TEXT 302 12 "shift-return" }{TEXT -1 26 " at the end of each line. )" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 277 "restart: #clear all c urrent definitions from memory \n #(regardless of which windo w was open when \n #the definition was made).\nwith(plots): \+ #load plotting library\nplot(x^2,x=-1..1,color=red,title=`my first par abola`);\n #use ` quotes, not ' or \" ones" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 216 "After pasting, execute this command field in you new window. By clicking on the plot you ar e able to rescale it and avail yourself of various new menu options. \+ You could export this plot to other documents as well." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 267 "" 0 "" {TEXT -1 13 "Saving Files:" }} {PARA 0 "" 0 "" {TEXT -1 542 "It is always a good idea to save your ma ple file periodically. Save all of your documents - this one, which I called 2250tut.mws (you can change the name if you want), as well as \+ your untitled documents. Use the tool bar, using the \"save\" option u nder the \"File\" menu item. The first time you save a new file, and a ny time you use the \"save as\" option, you will be asked to name your file and say where you want to keep it. You name it in the left part of the box, being careful to keep the suffix \".mws\" so that Maple k nows this file is a " }{TEXT 266 1 "M" }{TEXT -1 5 "aple " }{TEXT 267 1 "W" }{TEXT -1 4 "ork " }{TEXT 268 1 "S" }{TEXT -1 436 "heet. If you r directory is new you probably haven't made any subdirectories yet (u nix command mkdir, in a local window), but as you create more files yo u may wish to organize where you save them using the tree structure of Unix directories, which you can follow in the right side of your sav ing box. You use various UNIX commands in your local or terminal wind ow to organize your directories. For more information about this, go to" }{TEXT 274 1 " " }{URLLINK 17 "http://www.math.utah.edu/computing /unix/unix-commands.html" 4 "" "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 163 "It will probably happen some time that y ou will crash Maple long after your last save. This will not make you feel happy but will teach you an important lesson. " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 268 "" 0 "" {TEXT -1 9 "Printing:" }} {PARA 0 "" 0 "" {TEXT -1 39 "In the menu bar click successively on " }{TEXT 260 11 "file->print" }{TEXT 286 2 "->" }{TEXT 262 16 "print com mand. " }{TEXT 288 25 "Then in the print command" }{TEXT 287 1 " " } {TEXT -1 241 "box choose the name of the printer you want to use. In \+ UNIX you also need the prefix lpr -P (spaces important), which stands \+ for line printer - P. For example, the printer in the math center roo m 115 is called mc155c, so you want to enter " }{TEXT 292 11 "lpr -Pmc 155" }{TEXT -1 52 " into the print command box, and then click on the " }{TEXT 261 5 "print" }{TEXT -1 108 " box at the bottom of the windo w and your file should print. The print command in the room LCB 115 wo uld be " }{TEXT 291 14 "lpr -P lcb115." }{TEXT -1 2 " " }{TEXT 289 131 "If you have trouble printing ask a lab assistant for help. One g litch which seems to occur is that figures don't print correctly. " } {TEXT -1 211 " If this happens try modifying the print command to lpr \+ -l-Pmc155 or lpr -oraw-Pmc155. You can also print postscript files to your math directory by using the \"output to file\" choice in the pri nting dialog box." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 281 17 "Execution Groups:" }} {PARA 0 "" 0 "" {TEXT -1 361 "You can modify the text and input using \+ the toolbar and menu options. You will notice many brackets on the le ft of the document. These are execution groups. Maple will execute e verything in one execution group at once, and then move the cursor to \+ the next execution group. You can create large execution groups by hi ghlighting sections of a document, using " }{TEXT 263 42 "Edit->Split \+ or Join->Join Execution Groups" }{TEXT 264 1 "." }{TEXT 290 2 " " } {TEXT -1 252 "You can remove brackets by highlighting them with the mo use and deleting them with the delete key or the menu option. And you already learned how to insert new prompts or new text wherever your c ursor is, by using the [> and T buttons on your toolbar." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 265 3 "4) \+ " }}{PARA 264 "" 0 "" {TEXT -1 0 "" }{TEXT 270 25 "SOME IDEAS FROM PRO JECT I" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT 284 0 "" }{TEXT -1 0 "" }{TEXT 283 35 "A preliminary paragraph of advice: \+ " }{TEXT -1 1 " " }}{PARA 270 "" 0 "" {TEXT -1 987 "Students often app roach the task of reading mathematical material as if they were readin g a novel; they sort of skim along quickly. That approach is O.K. to get an overview, but in order to have a chance at real understanding \+ you must be prepared to proceed much more slowly, sentence by sentence and thought by thought. Otherwise you will almost certainly find you rself partly lost after several paragraphs and completely lost after s everal more. (This might happen anyway.) If you are working properly it can easily take half an hour to read through one page of mathemat ical text. This takes a certain amount of discipline, patience, and p ractice. With the Math 2250 computer projects there is the added t emptation of having Maple execute commands in successive command sect ions by repeatedly hitting the enter (return) key, without pausing t o digest the interlaced text or the meaning of the commands. There is a seductive appeal in having this capability. Resist it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 458 " Open your tex t book to page 56 (page 55 in olde edition), and follow along. We wil l go through the Maple commands and text corresponding to the section \+ 1.5 Computing Project of Edwards-Penney. If you go through this sect ion carefully now, then your life should be relatively easy when you d ownload the solution template from the course home page. Make sure yo u understand what each command is doing, and what each equation is say ing, in the work below. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 148 "For further information about syntax and options \+ related to commands below, use the help menu button at the upper right corner of your Maple window." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 221 "restart: #When you start n ew work it is often a good idea\n #to clear all old definitions etc. \+ restart does this. \n #Of course, then you must then reload any pack ages you need\n #and redefine anything you need as well." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "with(DEtools): #load diffeq tools , for later. If you want\n #to see the list of commands in the DEt ools\n # package, end your command with \";\" rather than \":\" " } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 422 "Every \+ time you reopen Maple you will neet to re-enter commands and definitio ns. Once you do this, these definitions are known in all of the Maple \+ windows you have open, i.e. which can be found in the \"Window\" list \+ at the top of your Maple menu bar. If you \"restart\" during a Maple \+ session, but want some old definitions to hold, move your cursor to t he appropriate command fields and reenter them using the key.. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 117 "We f ollow the book's discussion as it begins to talk about indoor temperat ure oscillations, in the middle of page 56." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 292 "A:=t->a0 + a1*cos (omega*t) + b1*sin(omega*t);\n #formula for ambient temperature, with free\n #parameters a0, a1, b1, omega. This is equation\n #(1) on p age 56. When you enter multi-line\n #commands hold down the shift key while you hit\n #\"enter\" or \"return\", to prevent premature execu tion" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "deqtn3:=diff(u(t),t)=-k*(u(t)-A(t));\n #we name our DE \"deqtn3\" since it's equation (3) \n #on top of page 57." }} {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 425 "We wil l find the general solution to deqtn3 first, with all the free paramet ers, and then fix the parameters for a July day in Athens Georgia seco nd. You should be able to use the integral table entries 49,50, to fin d the general solution. However, it is easier to just use the Maple c ommand dsolve. You should be able to verify, using some messy algebra that the solution you get below agrees with equation (4) on page 57. " }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eqtn4:=dsolve(\{deqtn3,u(0)=u0\},u(t));" }}{PARA 12 " " 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 127 "Now we set the p arameters equal to the values on page 57 so that we are studying somet hing like summer days in Athens Georgia: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 405 "a0:=80;\n #average ambient temp in Georgia in July \na1:=-5;\nb1:=-5*sqrt(3.0);\n #the a1 and b1 values were worked out by hand, \n #using the cosine addition\n #angle formula, assuming 4 a.m. temp min and 4 p.m max,\n #and range from 70 to 90 degrees, \n #for trigonometric temp oscillation.\nomega:=Pi/12;\n #this make s the period equal to 24 (hours)\nk:=0.2;\n #constant for a well-insu lated building \n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "With these parameter values, we get equation (5) on page \+ 57:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "eqtn5:=simplify(eqtn4);\n #It automatically plugged in the parameter\n #values I defined above. I asked for \"simplify \"\n #because otherwise the expression looked too messy.\n" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 311 "Read along with the text on page 57. Notice that no matter what \+ the initial house temperature was, the negative exponential terms die \+ out rapidly and one is left with the steady periodic solution given by equation (6) in the text. We can extract it from our eqtn5 above, by using the mouse to cut and paste: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "usp:=t-> 80 + 2.335105624* cos(.2617993878*t)-5.603607924*sin(.2617993878*t);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "We can reproduce figure 1.5.11 on page 58 (it would take more work to get all the labels in) as follow s" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "with(plots):\n #this \+ is the plotting package. End with ; \n #to see command list" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "ambient:=plo t(A(t),t=0..50, color=red):\n #this is a plot of ambient temp defined \n #above, with Athens parameters. Make sure\n #to end this command \+ with colon, not semicolon,\n #or you will get a very long list of poi nts. \ninside:=plot(usp(t),t=0..50, color=black):\n #the steady peri odic inside temperature\ndisplay(\{ambient,inside\}, title=\"inside-ou tside\");\n #display both plots together" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 305 "As the text remarks, y ou see that the steady periodic inside temperature oscillates trigonom etrically with a smaller amplitude and with a time delay, relative to \+ the outside temperature. (The annual seasonal temperature variations \+ on earth lag behind the solstice-equinox dates, for a similar reason. ) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 188 "W e can recover figure 1.5.10, together with the slope field, with a DEp lot command. This picture illustrates geometrically the fact that all solutions converge to the steady periodic one:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "DEplot(deq tn3,u(t),t=0..50,\{[u(0)=65],[u(0)=70],\n [u(0)=75],[u(0)=80],[u(0)=8 5],[u(0)=90],[u(0)=95]\},\n arrows=line, color=black,linecolor=black ,\n dirgrid=[30,30], stepsize=1,\n title=\"inside temperatures\"); " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 208 "This is the end of \+ the tutorial. To download your instructions and template for project \+ 1, follow the links from your course home page as they become availabl e. If this is fall 2004, you want one of these: " }{URLLINK 17 "http: //www.math.utah.edu/~gustafso/index2250.html" 4 "" "" }{TEXT -1 3 ", \+ " }{URLLINK 17 "http://www.math.utah.edu/~korevaar/2250fall04" 4 "" " " }{TEXT -1 2 ", " }{URLLINK 17 "http://www.math.utah.edu/~vladim/teac hing2004fall.html" 4 "" "" }{TEXT -1 1 "." }}}{MARK "9 0" 32 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }