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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 }{PSTYLE "" 0 271 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 257 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 9 "Math 2250" }}{PARA 259 "" 0 "" {TEXT -1 35 "MAPLE TUTORIAL and PRO JECT I HINTS" }}{PARA 264 "" 0 "" {TEXT 275 0 "" }{TEXT -1 9 "Fall 200 2" }}{PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 402 " This document is a tutorial for Math 2250 students who may not hav e done previous work with MAPLE or in the Math lab, or who may just wa nt to brush up on their skills. At the end of the tutorial there is \+ an introduction to the first project. Links to the precise template f or your project answers and to an on-line version of this tutorial can be found at the home page for 2250 maple projects, " }{TEXT 274 45 " http://www.math.utah.edu/~korevaar/2250fall02" }}{PARA 262 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 256 "The Math 2250 projects c an be done in versions five and above of Maple, with minor changes. T he Math Lab, EMCB, and Marriott Library all have version 7 of Maple. \+ A student version for home computers is available from the bookstore f or approximately $100." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 263 " " 0 "" {TEXT -1 32 "1) Using the Math Computer Lab:" }}{PARA 0 "" 0 " " {TEXT -1 351 "The Math Department has a walk-in computer lab in the \+ Math Student Center, located underneath the plaza connecting JWB to LC B. There is also a computer classroom in LCB 115, where introductory \+ tutorials will be held. Useful information about most aspects of the l ab can be found by following links from the Math Department web pages, e.g. starting at" }{TEXT 277 1 " " }{TEXT 285 35 "http://www.math.uta h.edu/ugrad/lab." }{TEXT 286 2 " " }{TEXT -1 102 "You can find out ab out lab hours, X-windows, Maple, Unix commands, Netscape, file editin g, mail, etc." }}{PARA 267 "" 0 "" {TEXT -1 0 "" }}{PARA 266 "" 0 "" {TEXT -1 15 "1a) Logging on:" }}{PARA 0 "" 0 "" {TEXT -1 409 "Almost a ll students who are registered in Math 2250, or in any other math clas s, will already have accounts set up in our lab. Since these account s are created from University class lists, late-registering students \+ may not be accounted for. If you fit in this case the lab assistant c an help you apply for an account - provided you have brought your stud ent I.D. to show that you are a University student." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 166 "The lab machines are l eft on - move the mouse or hit a key to wake yours up. The Math syste m is UNIX based. If your machine is on the login screen you may click on " }{TEXT 299 7 "options" }{TEXT -1 7 ", then " }{TEXT 300 7 "sessi on" }{TEXT -1 30 ", and then choose between the " }{TEXT 301 4 "CDE " }{TEXT -1 36 "(Common desktop environment) or the " }{TEXT 302 11 "ope nwindows" }{TEXT -1 73 " environments. If you're used to MS windows o r MACs you probably prefer " }{TEXT 303 3 "CDE" }{TEXT -1 80 ", which \+ is more graphically designed. If you like command based systems choos e " }{TEXT 304 11 "openwindows" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "Now it is time to log on: Your " }{TEXT 287 10 "login name" }{TEXT -1 47 " is made out of your initials. If your name is" }{TEXT 278 2 " K" }{TEXT -1 4 "arl " } {TEXT 279 1 "F" }{TEXT -1 4 "red " }{TEXT 280 1 "G" }{TEXT -1 3 "aus" }{TEXT 281 1 "S" }{TEXT -1 716 ", then your login name is c-gskf, foll owing the recipe: c-(first letter of last name)(last letter of last n ame)(first letter of first name)(middle initial). If there are multip le people registered this term with the same initials, then rather tha n c-gskf, they are assigned login names with a numerical suffix, c-g skf1, c-gskf2, c-gskf3, etc. Mr. Gauss would not know beforehand whic h case he fell into, so would probably try c-gskf first, followed by \+ his password (see below). In case of failure he would then try c-gskf 1, then c-gskf2, etc, through c-gskf4. Then he would find a lab assist ant. After entering your try at a login name, type 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 288 16 "ini tial password" }{TEXT -1 556 " is just the gskf part of your login nam e (NOT the numerical suffix), 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 diff erent login names suggested above. One possibility is that your accou nt was created using your social security number (which used to be use d for student ID number). If failure continues find a lab assistant a nd he/she will help you. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "If you chose the " }{TEXT 305 3 "CDE" }{TEXT -1 224 " environment a desktop will appear after your successful login, w ith various icons. At the bottom of the screen you will see a Maple l eaf-like object which is the icon for MAPLE. Also note a netscape ico n for the internet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 573 "If you chose the openwindows environment a ``local'' w indow should appear. Notice that it has various parts: borders on the top (title bar), borders on the side (scroll bar), etc. If you move \+ your mouse on its pad your pointer (called cursor) moves around the sc reen. If you want to work in a window, the cursor should be in it. Yo u can make multiple local windows by pressing the right mouse button a nd highlighting \"local\". In this environment you can find X MAPLE V 7 on your middle mouse button. Netscape lives under WWW Browsers, al so on the middle mouse button. " }}{PARA 0 "" 0 "" {TEXT -1 2 " " }} {PARA 0 "" 0 "" {TEXT 256 23 "1b) Changing password:" }{TEXT -1 320 " Some time within the first several weeks of classes you must change \+ your default password into a personal one. You do this as follows: In CDE create a terminal window using the icon at the bottom of your des ktop, and move your cursor to it. In openwindows get your cursor into a local window. Type the unix command " }{TEXT 257 6 "passwd" } {TEXT -1 640 ", followed by return, and follow the directions. Your n ew password should be exactly 8 characters long. Don't choose a word \+ in the dictionary or a proper name. Composites of dictionary words, l ike strawdog, are good. Even better is to use one or two upper case l etters, e.g. strAwdog. For still more security, use some digits, e.g. strAw4o9. It takes about 15 minutes for a new password to take effe ct. If a password is not changed within the first several weeks of cl ass, then your computer account will be disabled for security reasons. Make sure to write down your password in a secure place, in case you r memory is not perfect." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 258 17 "1c) Logging out:" }{TEXT -1 298 " In CDE there i s a logout icon at the bottom of your desktop. In openwindows move th e cursor out of all windows (into the background), press the left mous e button 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 late r.)" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 40 "2) Opening netscape, maple, mail , more:" }{TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 306 "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. In openwindows use the \+ middle mouse button, or alternately move your cursor into a local wind ow and then type" }{TEXT 282 11 " netscape &" }{TEXT -1 27 ", followed by . The" }{TEXT 283 2 " &" }{TEXT -1 156 " tells X-windows t o create a separate process for netscape, keeping your local window fr ee for more UNIX commands. You start Maple the same way, by typing " }{TEXT 306 8 "xmaple &" }{TEXT -1 22 ", followed by ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 104 "You can find o ut more information about the student services in the Math Department \+ by going to the URL " }{TEXT 307 32 "http://www.math.utah.edu/ugrad. \+ " }{TEXT -1 70 " If you choose the Undergraduate Computer Lab link, or go directly to " }{TEXT 308 35 "http://www.math.utah.edu/ugrad/lab " }{TEXT -1 48 "you can find out about lab hours, software, etc." }} {PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 260 11 "3) Maple: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 239 " If you are starting the tutorial at this point (because you're d oing it on your own at another location or already knew the Math Lab s ystem), you should have opened a mapleV7 ( V5 and V6 should also work ) window as well as a web browser." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 860 "Maple is partly just a very fancy calcul ator; it can do practically any undergraduate mathematics computation \+ or symbolic manipulation. You can write programs in Maple and draw pi ctures as well. If you are doing a homework assignment you can inters perse text with computations using the toolbar: to get a computation \+ prompt click on the ``[>'' box near the top. To insert text click on \+ the ``T'' box. Or you can change command fields (starting with \"[>\" ) into text fields by putting the cursor into them and then choosing \+ \"T\". You can use the mouse to cut, paste, and edit a document. You can change fonts, formats, and use other standard text editing tools \+ by choosing appropriate menu items. This document you are reading is \+ a Maple document even though it is largely text. You will learn by do ing - and by asking your neighbor or the lab assistant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 294 27 "New User's Tour and more: " }}{PARA 0 "" 0 "" {TEXT -1 649 "Under the Help button at the 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 t our behind other active windows; use the \"Window\" menu item to bri ng the tour window to the front. If you wish you can explore now, or you can continue with 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 inside the ``file'' menu item. To keep the tour open but bring another window to the front, use ``window'' menu item." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "Another g ood introduction to Maple is located at " }{TEXT 310 44 "http://www.ma th.utah.edu/~gardiner/Intro.mws" }{TEXT -1 116 ". If you have a brows er open you can open Maple files directly off the internet by using cl icking successively on " }{TEXT 309 16 "File -> Open URL" }{TEXT -1 143 ", in the Maple menu items at the top of the Maple window. Altern ately you can save .mws files from your browser and then open them fro m Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 289 25 "Entering Maple commands: " }} {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 \"Untit led\" (new) Maple window which you created in step (2). Commands begi n on lines having a command prompt ``>'', and should be ended with e ither a semicolon ; or a colon : If you end with a semicolon you will see visible output, if you end with a colon the output will be suppre ssed even though the command is executed. Maple will not execute a co mmand until you type the ``return'' or ``enter'' key. " }{TEXT 261 87 "If you have a multiline command use ``shift-return'' to change lin es 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 command unexecutab le you will get a ``syntax error'' message and Maple will try to point out your mistake with the cursor and cryptic diagnostic phrases. Aft er a while you will become good at fixing these mistakes but they can \+ be annoying at first. Spaces are ignored in Maple, so you may use the m to make input easier to read. You can enter explanatory comments in a command line by inserting a ``#'' to the left of the comments; Mapl e ignores any text after the #. Sometimes this is more informative th en 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 added to expl ain 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; #o ne of these computations will not be shown\n #even though all three will be done, illustrating the \n #difference between \+ a semicolon and a colon\n " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 428 "(3+4)7; #if you want to multiply you must us e *, so after\n #trying the command as given, insert a * to f ix the\n #resulting syntax error. You can execute a line or \n #execution group (bracketed on the left) if\n #yo ur 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 "Er ror, 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 command gives a \+ \n #decimal approximation instead of an algebraic \n \+ #expression. Notice that if given a choice, Maple \n #comput es 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 differe ntiation problem\n #you should get output:" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&*(-%$cosG6#%\"xG\"\"\"-%$expG6#-%$sinGF'F))F(\"\"$F )F)*(F0F)F*F))F(\"\"#F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "f:= x-> exp(sin(x))*x^3; #this is the syntax for defining a \n \+ #function, in this case the function we just \n #differ entiated" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 62 "diff(f(x),x); #should get the same answer a s before. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "int(t^2*exp (t),t); #``integrate (t^2)*exp(t) with respect\n #to t'' (M aple doesn't put in the integration constant.)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 84 "int(t^3*exp(sin(t)),t); #this shows that Mapl e is not God, you \n #will get" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$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 elementary function \n \+ #antiderivative it just echos what you put in. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "evalf(int(t^3*exp(sin(t)),t=0..1)); #Bu t you could do\n #a definite integral (numerically) even if M aple\n #can't compute an elementary antiderivative" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "Pi;exp(1);evalf(Pi);evalf(ex p(1));infinity;\n #some important numbers" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 290 14 "Entering Text:" }} {PARA 0 "" 0 "" {TEXT -1 145 "Scroll to somewhere in your worksheet an d add some text with the ``T'' menu item. (If you move your cursor to a command field and the press the " }{TEXT 291 2 "[>" }{TEXT -1 128 " button with your mouse, Maple makes a new command field directly belo w it. If you move to the new command field and press the " }{TEXT 292 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 Map le 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 f irst Maple worksheet'' (center it with the menu option on the right si de of the toolbar), as well as your name and today's date. When you ar e doing your Maple projects you will be expected 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 268 "" 0 "" {TEXT -1 13 "Saving Files:" }}{PARA 0 "" 0 "" {TEXT -1 415 "It is always a good idea to save your maple file periodically. D o this now using the tool bar, using the \"save\" option under the \"F ile\" menu item. The first time you save a new file, and any time you \+ use the \"save as\" option, you will be asked to name your file and sa y 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 knows this fi le is a " }{TEXT 268 1 "M" }{TEXT -1 5 "aple " }{TEXT 269 1 "W" } {TEXT -1 4 "ork " }{TEXT 270 1 "S" }{TEXT -1 436 "heet. If your direc tory is new you probably haven't made any subdirectories yet (unix com mand mkdir, in a local window), but as you create more files you may w ish to organize where you save them using the tree structure of Unix \+ directories, which you can follow in the right side of your saving box . You use various UNIX commands in your local or terminal window to o rganize your directories. For more information about this, go to" } {TEXT 284 55 " http://www.math.utah.edu/ugrad/unix/unix-commands.html " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 163 "It w ill probably happen some time that you will crash Maple long after you r last save. This will not make you feel happy but will teach you an \+ important lesson. " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 269 " " 0 "" {TEXT -1 9 "Printing:" }}{PARA 0 "" 0 "" {TEXT -1 39 "In the me nu bar click successively on " }{TEXT 262 11 "file->print" }{TEXT 311 2 "->" }{TEXT 264 16 "print command. " }{TEXT 313 25 "Then in the print command" }{TEXT 312 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 room 115 is called mc155c, so you want \+ to enter " }{TEXT 320 11 "lpr -Pmc155" }{TEXT -1 52 " into the print c ommand box, and then click on the " }{TEXT 263 5 "print" }{TEXT -1 108 " box at the bottom of the window and your file should print. The \+ print command in the room LCB 115 would be " }{TEXT 319 14 "lpr -P lcb 115." }{TEXT -1 2 " " }{TEXT 314 131 "If you have trouble printing as k a lab assistant for help. One glitch which seems to occur is that f igures don't print correctly. " }{TEXT -1 211 " If this happens try mo difying the print command to lpr -l-Pmc155 or lpr -oraw-Pmc155. You c an also print postscript files to your math directory by using the \"o utput to file\" choice in the printing dialog box." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 295 28 "Downloading Maple docume nts:" }}{PARA 0 "" 0 "" {TEXT -1 119 " This xeroxed tutorial is availa ble online in several formats, if you follow the links from the 2250 \+ Maple homepage at" }{TEXT 271 46 "http://www.math.utah.edu/~korevaar/2 250fall02." }{TEXT -1 100 " Files with suffix \".mws\" or \".txt\" ca n be downloaded from your browser and then opened from Maple." }} {PARA 0 "" 0 "" {TEXT -1 76 "Go to the course homepage address using y our browser, and find and save the " }{TEXT 272 15 "2250falltut.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 273 15 "2250falltut.m ws" }{TEXT -1 501 ". It should appear in the central box after you ch oose \"open\". Click on it with the mouse to highlight it and then cl ick ``OK'' or type ``return''. A copy of this tutorial should then ap pear in your Maple window, as a Maple document that you can work in. \+ Notice you can use the \"Window\" menu item at the top of your Maple w indow to change between various open files. (Sometimes when you open \+ a new file it goes to the back of your pile. Then use the Window opti on to bring it back to the front.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 78 "If you know the exact URL of a Maple file and have a browser open you can use " }{TEXT 317 14 "File->Open URL" }{TEXT -1 97 " to have Maple do the downloading and opening for you. \+ For example, the URL of this tutorial is " }{TEXT 315 61 "http://www.m ath.utah.edu/~korevaar/2250fall02/2250falltut.mws" }{TEXT 316 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 293 17 "Executio n Groups:" }}{PARA 0 "" 0 "" {TEXT -1 361 "You can modify the text and input using the toolbar and menu options. You will notice many brack ets on the left of the document. These are execution groups. Maple w ill execute everything in one execution group at once, and then move t he cursor to the next execution group. You can create large execution groups by highlighting sections of a document, using " }{TEXT 265 42 "Edit->Split or Join->Join Execution Groups" }{TEXT 266 1 "." }{TEXT 318 2 " " }{TEXT -1 252 "You can remove brackets by highlighting them with the mouse and deleting them with the delete key or the menu opti on. And you already learned how to insert new prompts or new text whe rever your cursor is, by using the [> and T buttons on your toolbar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 267 3 "4) " }}{PARA 265 "" 0 "" {TEXT -1 0 "" }{TEXT 276 25 "INT RODUCTION TO PROJECT I" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 270 " " 0 "" {TEXT 297 0 "" }{TEXT -1 0 "" }{TEXT 296 35 "A preliminary para graph of advice: " }{TEXT -1 1 " " }}{PARA 271 "" 0 "" {TEXT -1 987 "S tudents often approach the task of reading mathematical material as if they were reading a novel; they sort of skim along quickly. That app roach is O.K. to get an overview, but in order to have a chance at re al understanding you must be prepared to proceed much more slowly, sen tence by sentence and thought by thought. Otherwise you will almost c ertainly find yourself partly lost after several paragraphs and comple tely lost after several more. (This might happen anyway.) If you are working properly it can easily take half an hour to read through one page of mathematical text. This takes a certain amount of discipline , patience, and practice. With the Math 2250 computer projects ther e is the added temptation of having Maple execute commands in succes sive command sections by repeatedly hitting the enter (return) key, \+ without pausing to digest the interlaced text or the meaning of the co mmands. There is a seductive appeal in having this capability. Resi st it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 432 " Open your text book to page 55, and follow along. We will go th rough the Maple commands and text corresponding to the section 1.5 Com puting Project of Edwards-Penney. If you go through this section car efully now, then your life should be relatively easy when you download the solution template from the course home page. Make sure you under stand what each command is doing, and what each equation is saying, 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 new work it is often a good idea\n #to clear all old definitions etc. restar t does this. \n #Of course, then you must then reload any packages yo u need\n #and redefine anything you need as well." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "with(DEtools): #load diffeq tools, for la ter. If you want\n #to see the list of commands in the DEtools\n \+ # package, end your command with \";\" rather than \":\" " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 353 "At the start o f the the project, on page 55, we see how to automate the method of s olving a general first order DE initial value problem, see equation (1 1) on page 48. So P(x) and Q(x) will be as shown there, except we wil l use lower case p and q like on page 55. On page 55 we are consider ing the particular first order linear differential equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "de qtn:=diff(y(t),t) + y(t) = t;\n #notice how we write the derivative o f y \n #with respect to t" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deqtn G/,&-%%diffG6$-%\"yG6#%\"tGF-\"\"\"F*F.F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "Following the algorithm on pag e 48 (with the roles of x and t reversed as on page 55!) the text tel ls us to set" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 383 "p:=t->1;\n \+ #this is how to define functions in Maple;\n #the command is saying \+ p(t)=1. The := should\n #be read as \"is defined to be.\" The arrow \n #can be thought of as saying \"goes to\"\nq:=t->t;\n #this comman d is saying q(t)=t\nr:=t->exp(int(p(x),x=t0..t));\n #the integrating factor r(t)\ny:=t->(1/r(t))*(y0+int(r(x)*q(x),x=t0..t));\n #the sol ution y(t) to the IVP with y(t0)=y0." }}{PARA 11 "" 1 "" {TEXT -1 0 " " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 98 "For \+ example, if we wanted to solve the differential equation on page 55, w ith y(0)=2, we would set" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " t0:=0;\ny0:=2;\n" }}}{PARA 0 "" 0 "" {TEXT -1 12 "and evaluate" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "y(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$expG6#%\"tG!\"\",(\"\"$\"\"\"*&F$F+F'F+F+F$F(F+" } }}{PARA 256 "" 1 "" {TEXT -1 537 "You might want to verify this answer to the initial value problem by hand. Of course Maple can solve DE's symbolically too, with the single command \"dsolve.\" If you want to read about the syntax required for this command, you should use the H elp menu item at the upper right corner of your Maple window, and sear ch the topic \"dsolve\". Once you have a rough idea about a command i t is often helpful to scan down to the bottom of the help file to see \+ worked out examples. If you do this you will eventually decide to try something like" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "dsolve(\{ deqtn,y(0)=2\},y(t));" }}{PARA 8 "" 1 "" {TEXT -1 99 "Error, (in pdsol ve/sys/info) required an indication of the dependent variables in the \+ given system\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 437 "This command d idn't work. It would've worked, except that you have defined y(t) jus t above here, so when Maple evaluates the differential equation \"deqt n\" which you defined earlier, it plugs in the y(t) you defined subseq uently, so that the deqtn evaluates to t=t, yielding the error message . ???!!!! You can fix problem by never using the same symbols twice, or more practically, by restarting, to clear out conflicting defint ions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "restart: #clears a ll definitions and memory\nwith(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 298 25 "Restarting and Reopening:" }{TEXT -1 246 " Every time y ou reopen a Maple file you will neet to re-enter commands and definiti ons. Similarly, if you restart but want some old definitions to hold, move your cursor to the appropriate command fields and reenter them u sing the key.." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 215 " deqtn:=diff(y(t),t) + y(t) = t;\n #I moused in same deqtn from above \ndsolve(\{deqtn,y(0)=2\},y(t));\n #and same dsolve command above. No w\n #it should work, and even give an answer\n #which agrees with yo ur ealier one" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "We now continue with the book's discussion at the top of \+ page 56." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 303 "A:=t->a0 + a1*cos(omega*t) + b1*sin(omega*t);\n #fo rmula for ambient temperature, with free\n #parameters a0, a1, b1, om ega. This is equation\n #(1) on the top of page 56. When you enter m ulti-line\n #commands hold down the shift key while you hit\n #\"ent er\" or \"return\", to prevent premature execution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "deqtn3:=diff(u(t),t)=-k*(u(t)-A(t));\n #w e name our DE \"deqtn3\" since it's equation (3) \n #on page 56." }} {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 445 "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, or alt ernately have the computer follow the recipe method we just outlined t o find the general solution. However, it is easier to just use dsolve . You should verify that the solution you get below agrees with equat ion (4) on page 56." }}{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 -1 142 "Now \+ we set the parameters equal to the values at the bottom of page 56, so that we are studying something like summer days in Athens Georgia: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 405 "a0:=80;\n #average ambi ent temp in Georgia in July\na1:=-5;\nb1:=-5*sqrt(3.0);\n #the a1 an d 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 ra nge from 70 to 90 degrees,\n #for trigonometric temp oscillation.\no mega:=Pi/12;\n #this makes the period equal to 24 (hours)\nk:=0.2;\n \+ #constant for a well-insulated building \n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "With these parameter values, we get equation (5) on the bottom of page 56:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "eqtn5:=simplify(e qtn4);\n #It automatically plugged in the parameter\n #values I defi ned above. I asked for \"simplify\"\n #because otherwise the express ion looked too messy.\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 " " 1 "" {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 m atter what the initial house temperature was, the negative exponential terms die out rapidly and one is left with the steady periodic soluti on given by equation (6) in the text. We can extract it from our eqtn 5 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);" }} {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 " We can reproduce figure 1.5.10 (it would take more work to get all th e labels in) as follows" }}}{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 change coords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "ambient:=plot(A(t),t=0..50, color=red):\n #this is a plot of amb ient 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 points. \ninside:=plot(usp(t),t=0..50, color=black):\n \+ #the steady periodic inside temperature\ndisplay(\{ambient,inside\}, \+ title=\"inside-outside\");\n #display both plots together" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 289 "As th e text remarks, you see that the inside temperature oscillates trigono metrically 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 -1 187 " We can recover figure 1.5.9, 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 "" }}}{PARA 0 "" 0 "" {TEXT -1 34 "Thi s is the end of the tutorial. " }}}{MARK "144 0" 34 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }