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-1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 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 "" 0 259 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 "" 0 260 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 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 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 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 264 1 {CSTYLE "" -1 -1 "" 0 1 0 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 } {PSTYLE "" 0 265 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {PARA 256 "" 0 "" {TEXT -1 9 "Math 2250" }}{PARA 257 "" 0 "" {TEXT -1 35 "MAPLE TUTORIAL and PROJECT I HINTS" }}{PARA 263 "" 0 "" {TEXT 305 0 "" }{TEXT -1 11 "Spring 2001" }}{PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 322 " This document is a tutori al for Math 2250 students who may not have done previous work with MAP LE or in our lab, or who may just want to brush up on their skills. A t the end there is an introduction to the first project. You should \+ download the precise template for your project answers from the cour se home page " }{TEXT 304 52 "http://www.math.utah.edu/~korevaar/2250 spring01.html" }{TEXT -1 40 ", where this tutorial is also available. " }}{PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT 289 0 " " }{TEXT -1 0 "" }{TEXT 288 33 "0) A preliminary word of Advice: " } {TEXT -1 988 " Students often approach the task of reading mathematica l material as if they were reading a novel; they sort of skim along qu ickly. That approach is O.K. to get an overview, but in order to hav e a chance at real understanding you must be prepared to proceed much \+ more slowly, sentence by sentence and thought by thought. Otherwise y ou will almost certainly find yourself partly lost after several parag raphs and completely lost after several more. (This might happen anyw ay.) If you are working properly it can easily take half an hour to \+ read through one page of mathematical text. This takes a certain amou nt of discipline, patience, and practice. With the Math 2250 compute r projects there is the added temptation of having Maple execute co mmands in successive command sections by repeatedly hitting the ente r (return) key, without pausing to digest the interlaced text or the m eaning of the commands. There is a seductive appeal in having this c apability. Resist it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 " " 0 "" {TEXT -1 211 "We will assume you are working in the Math Depart ment computer lab. If you are in another lab (e.g. Engineering lab in EMCB or Library lab in Marriot) or on your own computer, you will ge t started differently." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 38 "1a) Logging in to a Math Lab machine:" }{TEXT -1 375 " The Math Department Computer Lab is located in the South Physic s 205, i.e. inside the 2-story brick building just north of the Math \+ building JWB, and south-east of the physics classrooms in the circular part of JFB. Room 205 is in the back (East) of the building, on th e second floor (from the west), which equals the level of the ground o n the uphill, east entrance." }}{PARA 0 "" 0 "" {TEXT -1 106 " \+ The following information about logging in and your initial password i s summarized from the handout " }{TEXT 257 111 "Introduction to the Un dergraduate Computer Lab Department of Mathematics, University of Utah , SLC, Utah 84112 ." }{TEXT -1 1 " " }{TEXT 258 82 " This and other us eful handouts are available on a table in the front of the lab. " }} {PARA 0 "" 0 "" {TEXT -1 479 " Everyone who is registered in Math 2250 should automatically have an account set up in our lab. These \+ accounts are created from University class lists so it sometimes happe ns that late-registering people don't have accounts yet. If you turn \+ out to be one of these people you will need to consult the lab assista nt about getting an account. Make sure to bring your student I.D. bec ause the first thing the assistant must do is verify that you are a Un iversity student. " }}{PARA 0 "" 0 "" {TEXT -1 778 " If your mach ine looks asleep jiggle the mouse or hit any key to wake it back up. \+ A window should appear which asks you to select a server. Since the \+ Math Department is sharing this lab with Physics, there are physics an d math server computers. You want to select one from the list of choi ces which has \".math\" in its name. If a \".physics\" computer is h ighlighted, use your cursor to choose one of the \".math\" computers, \+ and then O.K. your choice by clicking in the \"accept\" box. In a few seconds a login window should appear, asking for your login name and \+ password, and have \"Mathematics\" written in red on the top. (If t he login window says \"Physics\" you have accidently chosen a physics \+ server, and you should type \"control C\" to go back to the previous s tep.)" }}{PARA 0 "" 0 "" {TEXT -1 873 " Your default login name i s made out of your student I.D. number and your actual name, as follow s. All names from classes begin with ``c-''. If your name is Karl F red GausS, then your login name is c-gskf, following the recipe: c-(f irst letter of last name)(last letter of last name)(first letter of fi rst name)(middle initial). If there are multiple people registered th is term who would have the same login name, say c-gskf, then they are \+ instead assigned login names as c-gskf1, c-gskf2, c-gskf3, etc. Mr. G auss would not know beforehand which case he fell into, so would proba bly try c-gskf first, followed by his password. In case of failure h e would then try c-gskf1, then c-gskf2, etc, through c-gskf4. Then he \+ would find a lab assistant. 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 -1 560 " Your initial password is just the c-gskf part of your login name followed by the last four digits o f your student I.D. number. If Mr. Gauss has ID number 000735421 the n 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 th e different login names suggested above. Another possibility is that \+ your account was created using your social security number (which used to be used for student ID number). If failure continues find a lab a ssistant and he/she will help you. " }}{PARA 0 "" 0 "" {TEXT -1 332 " Once you are logged in successfully a ``local'' window should app ear. 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 it s pad your pointer (called cursor) moves around the screen. If you wan t to work in a window, the cursor should be in it. " }}{PARA 0 "" 0 " " {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 259 23 "1b) Changing passwo rd:" }{TEXT -1 197 " Sometime within the first several weeks of class es you must change your default password into a personal one. You do \+ this as follows: Get your cursor into a local window. Type the unix c ommand " }{TEXT 260 6 "passwd" }{TEXT -1 583 ", followed by return, an d follow the directions. Your new password should be exactly 8 charac ters long. Don't choose a word in the dictionary or a proper name. C omposites of dictionary words, like strawdog, are good. Even better i s to use one or two upper case letters, e.g. strAwdog. For still more security, use some digits, e.g. strAw4o9. Note that it takes about \+ 30 minutes for a new password to take effect. Also, you should be awa re that if a password is not changed within the first two weeks of cla ss, then your computer account will be disabled for security reasons. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 17 "1c) \+ Logging out:" }{TEXT -1 221 " Move the cursor out of all windows (int o the background), press the left mouse button and choose the last men u 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 get used to the X-windows:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 51 "2) X-wi ndows, opening netscape, maple, mail, more:" }{TEXT -1 26 " Go throug h the document " }{TEXT 263 35 "Introduction to Xwindows in the Lab" } {TEXT -1 472 ", which you should have a copy of. There should also be copies of this document in the front of the room. Xwindows are like most windows in most ways; your aim here is to experiment to see how \+ to open and close windows, resize them, move them about, and find the m if they happen to get hidden. When you get to the end of the documen t you should also have opened a NETSCAPE window and a MAPLE window. \+ Note: The command for the current (default) version of Maple is " } {TEXT 264 10 "xmaple &, " }{TEXT 290 60 "which you can type into a loc al window, followed by ." }{TEXT -1 196 " This is version 6, \+ and you can also find it as an option on one of your mouse buttons, it 's your choice. If you are using an earlier version of Maple (V5 or \+ V4, for example), there are slight" }}{PARA 0 "" 0 "" {TEXT -1 76 "dif ferences in commands and syntax, and they may confuse you once or twic e. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 21 "F urther information: " }{TEXT -1 123 " If you want more in-depth inform ation about the computing facilities in this lab, you might pick up a \+ copy of the handout " }{TEXT 266 32 "A Crash Course on CSC Facilities " }{TEXT -1 23 ", from the front table." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 177 " If \+ you are starting the tutorial at this point (because you're doing it o n your own at another location), you should have opened a mapleV6 wind ow and a web browser window. " }}{PARA 0 "" 0 "" {TEXT 267 31 "3a) Ma th Department resources:" }{TEXT -1 193 " There is introductory mate rial about Maple on our web pages. If you wish to see what's availabl e use the browser window you made in step (2) above, and go to the Mat h Department home page " }{TEXT 268 26 "http://www.math.utah.edu/." } {TEXT -1 253 " By following links from here you can find current and \+ future course offerings, faculty information, and much more. Since yo u are students, interested in Maple information, click on \"students \" (at the upper left of the page), and you are directed to " }{TEXT 291 31 "http://www.math.utah.edu/ugrad/" }{TEXT -1 46 ", the undergrad uate home page. If you choose " }{TEXT 294 1 "\"" }{TEXT -1 26 "Under graduate Computer Lab" }{TEXT 292 1 "\"" }{TEXT -1 14 ", followed by \+ " }{TEXT 293 29 "\"Selected software and tools\"" }{TEXT -1 49 ", you \+ will find some links to Maple information. " }}{PARA 0 "" 0 "" {TEXT 296 5 "3b) " }{TEXT 269 19 "More Information. " }{TEXT 295 79 "Maple has its own introduction, as well as a new user's tour, see item 5 be low." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 270 11 " 4) Maple: " }{TEXT -1 873 " Move your cursor into the \"Untitled\" (n ew) Maple window which you created in step (2). Maple is partly just \+ a very fancy calculator; it can do practically any undergraduate mathe matics computation or symbolic manipulation. You can write programs i n Maple and draw pictures as well. If you are doing a homework assign ment you can intersperse text with computations using the toolbar: to get a computation prompt click on the ``[>'' box near the top. To in sert text click on the ``T'' box. Or you can change command fields (s tarting with \"[>\") into text fields by putting the cursor into them \+ and then choosing \"T\". You can use the mouse to cut, paste, and edi t a document. You can change fonts, formats, and use other standard t ext editing tools by choosing appropriate menue items. This document \+ you are reading is a Maple document even though it is largely text." } }{PARA 0 "" 0 "" {TEXT -1 429 " To give you a flavor of what Mapl e can do, we will try a few commands. They should begin on a line hav ing a command prompt ``>'', and should be ended with either a semicol on ; or a colon : If you end with a semicolon you will see visible ou tput, if you end with a colon the output will be suppressed even thoug h the command is executed. Maple will not execute a command until you type the ``return'' or ``enter'' key. " }{TEXT 271 87 "If you have a multiline command use ``shift-return'' to change lines without execut ing." }{TEXT -1 644 " If you mess up your parentheses or brackets or d o something else which makes your command unexecutable you will get a \+ ``syntax error'' message and Maple will try to point out your mistake. After 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 us e them to make input easier to read. You can enter explanatory commen ts in a command line by inserting a ``#'' to the left of the comments; Maple ignores any text after the #. Sometimes this is more informati ve then entering nearby explanatory text, especially if you are explai ning various steps in a subroutine." }}{PARA 0 "" 0 "" {TEXT -1 222 " \+ Now, let's try some commands. (You try just the math commands, the editorial comments were only added to explain what the particular com mands are illustrating ! ) Check that you understand what each comman d 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 wi ll not be shown\n #even though all three will be done, illust rating 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 use *, so after\n #t rying the command as given, insert a * to fix the\n #resultin g syntax error. You can execute 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 command gives a \n #decimal approximat ion instead of an algebraic \n #expression. Notice that if gi ven a choice, Maple \n #computes powers first, then multiplie s 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 for defining a \n #function, in this case t he function we just \n #differentiated" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "diff(f(x),x ); #should 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 integ ration constant.)" }}}{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 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)); #But you could do\n \+ #a definite integral (numerically) even if Maple\n #can't co mpute 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 -1 415 "It is always a good idea to save your maple file periodically. Do this now using the tool bar, using the \"save\" opt ion 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 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 Ma ple knows this file is a " }{TEXT 298 1 "M" }{TEXT -1 5 "aple " } {TEXT 299 1 "W" }{TEXT -1 4 "ork " }{TEXT 300 1 "S" }{TEXT -1 371 "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. If you need more help saving your file see the in structions in the " }{TEXT 297 59 "Introduction to Maple V.4 in the Un dergraduate Computer Lab" }{TEXT -1 180 " handout at the front of the \+ lab, or ask an assistant. It will probably happen some time that you \+ will crash Maple long after your last save. This will not make you fe el happy. " }}{PARA 0 "" 0 "" {TEXT -1 506 " Now we will see how \+ to print a hard copy of our file. First, scroll to somewhere in your worksheet and add some text with the ``T'' menu item. Maybe scroll t o the top and put the title ``My first Maple worksheet'' (center it wi th the menu option on the right side of the toolbar), as well as your \+ name and today's date. When you are 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 20 " Now, go to the " }{TEXT 272 4 "file " }{TEXT -1 28 " menu option and choose the " }{TEXT 273 5 "print" } {TEXT -1 72 " option. You get a little printer setup box. If you the n click on the " }{TEXT 275 14 "print command " }{TEXT -1 52 "diamond, followed by ``enter'' or by a click on the " }{TEXT 274 5 "print" } {TEXT -1 192 " box at the bottom of the window, a paper copy will come out of one of the printers at the side of the lab. Do this now. Alt ernately, if you want to use a different printer, you can use the " } {TEXT 276 14 "output to file" }{TEXT -1 558 " diamond to create a post script file which you can then print anywhere, using the appropriate u nix commands. For example, to print a postscript file to the lab prin ters from a local window, the command would be \"lpr -P b129lab1\", o r \"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 indica ted. The lpr stands for line printer, the -P stands for print, and th e b129lab1 or b129lab2 are the names of the two printers. If you have trouble printing ask a lab assistant for help." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 59 "5) Differential Equatio ns, and using Maple's help windows:" }{TEXT -1 367 " So, it looks lik e Maple might be interesting to use in Calculus, but how do we find ou t what it can do for us in that subject, or in another subject, say di fferential equations? An answer for DE's can be obtained by perusing \+ your Computing Projects textbook (which you can pick up for free at t he main Math office JWB 233) , but it is also instructive to use the \+ " }{TEXT 283 4 "Help" }{TEXT -1 107 " directory located at the upper r ight-hand corner of the maple window. That's what you're going to do \+ now." }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 278 54 "5a) In mapleV6 (and V5) there's an online tutorial: " }{TEXT -1 856 "Click on the ``Help'' box, and then on the choice \+ ``New User's Tour''. Probably this tour will superimpose onto your cu rrent Maple session. Or maybe you can't see the new tour because its \+ hidden behind your current window. In the latter case use the ``windo w''menu option to change windows. The tutorial gives examples from m any areas of mathematics, including differential equations, which you \+ can peruse at your leisure. In this tour you will be able to put your \+ cursor onto any command line, type return, and see what the command do es. If you wish you can explore now, or you can continue with the Mat h 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 t he front, use ``window'' menu item." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 279 56 "5b) Getting an on-line \+ copy of this Math 2250 tutorial: " }{TEXT -1 197 " (This is also the process you will go through to get your project solution templates. ) This xeroxed tutorial is available online in several formats, if yo u to first to our course homepage at " }{TEXT 301 52 "http://www.math. utah.edu/~korevaar/2250spring01.html" }{TEXT -1 450 ". Files with suf fix \".mws\" or \".txt\" can be downloaded from your browser and then \+ opened from Maple. The \".mws\" suffix means the file is a Maple Work sheet, and should open from Maple to look just like this file. The \" .txt\" suffix is Maple text, and you should only try it if the \".mws \" file doesn't open. It's a cruder form of this file, but potentiall y more universal. The \".pdf\" or \".html\" are versions of the file \+ which you can read from your" }}{PARA 0 "" 0 "" {TEXT -1 73 "browser ( or with Acrobat reader), but you can't execute these from Maple." }} {PARA 0 "" 0 "" {TEXT -1 69 " Go to the course homepage address in your browser, and save the " }{TEXT 302 17 "2250springtut.mws" } {TEXT -1 29 " file to your home directory." }}{PARA 0 "" 0 "" {TEXT -1 76 " Now return to your Maple window and use the ``file'' menu \+ item to open " }{TEXT 303 17 "2250springtut.mws" }{TEXT -1 501 ". It \+ should appear in the central box after you choose \"open\". Click on \+ it with the mouse to highlight it and then click ``OK'' or type ``retu rn''. A copy of this tutorial should then appear 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 window to change between v arious open 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 th e front.)" }}{PARA 0 "" 0 "" {TEXT -1 250 " If you couldn't open t he Maple worksheet file, go back to your browser and save the \".txt\" version of the tutorial. Then go back to Maple, and follow these dir ections: In order to open a ``Maple text'' document, which this is, \+ you must chose " }{TEXT 284 4 "open" }{TEXT -1 10 " from the " }{TEXT 285 4 "file" }{TEXT -1 32 " menu option. In the resulting " }{TEXT 286 9 "open file" }{TEXT -1 22 " dialog box go to the " }{TEXT 287 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 ``2250tutorial.txt should appear as a choice in the ce ntral 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 groups are all sing le lines, and the text formatting is not as neat, and some output may \+ be lost), but it is O.K. It has text and it has Maple input. " }} {PARA 0 "" 0 "" {TEXT -1 373 " You can modify the text and input u sing the toolbar and menu options. You will notice many brackets on t he left of the document. These are execution groups. Maple will exec ute everything in one execution group at once, and then move the curso r to the next execution group. You can create large execution groups \+ by highlighting sections of a document, going to the " }{TEXT 280 4 "E dit" }{TEXT -1 20 " option and picking " }{TEXT 281 24 "join execution groups. " }{TEXT -1 231 "You can remove brackets by highlighting the m with the mouse and deleting them with the delete key or the menu opt ion. And you can insert new prompts or new text wherever your cursor \+ is, by using the > or T buttons on your toolbar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 282 3 "6) " }} {PARA 265 "" 0 "" {TEXT -1 0 "" }{TEXT 306 25 "INTRODUCTION TO PROJECT I" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 442 " \+ You should open your book to page 55, and follow along. We will go through the Maple commands and text corresponding to the section 1.5 \+ Computing Project of Edwards-Penney. If you go through this section \+ carefully now, then your life should be relatively easy when you downl oad the solution template from the course home page. Make sure you un derstand what each command is doing, and what each equation is saying, in the work below. " }}{PARA 0 "" 0 "" {TEXT -1 154 " For furthe r 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. restart does this. \n #Of course, \+ then you must then reload any packages you need\n #and redefine anyth ing you need as well." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "w ith(DEtools): #load diffeq tools, for later. If you want\n #to se e 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 of the the project, on page 55, we see how to automate the method of solving a general first ord er DE initial value problem, see equation (11) on page 48. So P(x) an d Q(x) will be as shown there, except we will use lower case p and q l ike on page 55. On page 55 we are considering the particular first o rder linear differential equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "deqtn:=diff(y(t),t) + y(t) = t;\n #notice how we write the derivative of y \n #with respect to t " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deqtnG/,&-%%diffG6$-%\"yG6#%\"t GF-\"\"\"F*F.F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "Following the algorithm on page 48 (with the roles of x and t reversed as on page 55!) the text tells 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 command 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 solution 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, with 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#%\"tGF&F+F&F&F(!\"\"F&F(F," }}}{PARA 264 "" 1 "" {TEXT -1 537 "You might want to verify this answer to the initial value prob lem by hand. Of course Maple can solve DE's symbolically too, with th e single command \"dsolve.\" If you want to read about the syntax req uired for this command, you should use the Help menu item at the upper right corner of your Maple window, and search the topic \"dsolve\". \+ Once you have a rough idea about a command it is often helpful to scan down to the bottom of the help file to see worked out examples. If y ou 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 95 "Error, (in sdsolve/info) required an indi cation of the dependent variables in the given system\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 355 "This command would've worked, except tha t you have defined y(t) just above here, so when Maple evaluates the d ifferential equation \"deqtn\" which you defined earlier, it plugs in \+ the y(t) you defined subsequently, so that the deqtn evaluates to t=t, yielding the error message. ???!!!! You can fix this by restarting to clear out conflicting defintions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart:with(DEtools):" }}}{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. Now\n #it should work, and even give an answer\n #whi ch agrees with your ealier one" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&d eqtnG/,&-%%diffG6$-%\"yG6#%\"tGF-\"\"\"F*F.F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,(F'\"\"\"F)!\"\"*&\"\"$F)-%$expG6#,$F'F* F)F)" }}}{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 #formula for amb ient temperature, with free\n #parameters a0, a1, b1, omega. This is equation\n #(1) on the top of page 56. When you enter multi-line\n \+ #commands hold down the shift key while you hit\n #\"enter\" or \"ret urn\", to prevent premature execution" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGR6#%\"tG6\"6$%)operatorG%&arrowGF(,(%#a0G\"\"\"*&%#a1GF.-%$co sG6#*&%&omegaGF.9$F.F.F.*&%#b1GF.-%$sinGF3F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "deqtn3:=diff(u(t),t)=-k*(u(t)-A(t));\n \+ #we name our DE \"deqtn3\" since it's equation (3) \n #on page 56." } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'deqtn3G/-%%diffG6$-%\"uG6#%\"tGF,, $*&%\"kG\"\"\",*F)F0%#a0G!\"\"*&%#a1GF0-%$cosG6#*&%&omegaGF0F,F0F0F3*& %#b1GF0-%$sinGF8F0F3F0F3" }}}{PARA 0 "" 0 "" {TEXT -1 435 "We will fin d the general solution first, with all the free parameters, and then f ix the parameters for a July day in Athens Georgia second. You should \+ be able to use the integral table entries 49,50, or alternately have t he computer follow the recipe method we just outlined to find the gene ral solution. However, it is easier to just use dsolve. You should v erify that the solution you get below agrees with equation (4) on page 56." }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eqtn4:=dsolve(\{deqtn3,u(0)=u0\},u(t));" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%&eqtn4G/-%\"uG6#%\"tG,&*&*&-%$expG6#,$*&%\"kG \"\"\"F)F3!\"\"F3,.*&)F2\"\"#F3%#a1GF3F3*(F2F3%#b1GF3%&omegaGF3F4*&%#a 0GF3F7F3F3*&F>F3)F " 0 "" {MPLTEXT 1 0 405 "a0 :=80;\n #average ambient temp in Georgia in July\na1:=-5;\nb1:=-5*sq rt(3.0);\n #the a1 and b1 values were worked out by hand, \n #usin g the cosine addition\n #angle formula, assuming 4 a.m. temp min and 4 p.m max,\n #and range from 70 to 90 degrees,\n #for trigonometr ic temp oscillation.\nomega:=Pi/12;\n #this makes the period equal to 24 (hours)\nk:=0.2;\n #constant for a well-insulated building \n" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "With the se parameter values, we get equation (5) on the bottom of page 56:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "eqtn5:=simplify(eqtn4);\n #It automatically plugged in the param eter\n #values I defined above. I asked for \"simplify\"\n #because otherwise the expression looked too messy.\n" }{XPPMATH 20 "6#>%&eqtn 5G/-%\"uG6#%\"tG,,-%$expG6#,$F)$!+++++?!#5$!+k0^L#)!\")$\"#!)\"\"!\"\" \"*&F+F8%#u0GF8F8*&$\"+Cc5NB!\"*F8-%$cosG6#,$F)$\"+yQ*zh#F1F8F8*&$\"+C zg.cF>F8-%$sinGFAF8!\"\"" }}}{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 expone ntial terms die out rapidly and one is left with the steady periodic s olution 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-> 8 0 + 2.335105624*cos(.2617993878*t)-5.603607924*sin(.2617993878*t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$uspGR6#%\"tG6\"6$%)operatorG%&arrow GF(,(\"#!)\"\"\"*&$\"+Cc5NB!\"*F.-%$cosG6#,$9$$\"+yQ*zh#!#5F.F.*&$\"+C zg.cF2F.-%$sinGF5F.!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "We can reproduce figure 1.5.10 (it would take more work to get all t he labels in) as follows" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "with(plots):\n #this is the plotting package. End with ; \n #to se e command list" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name chang ecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "ambient:=plot(A(t),t=0..50, color=red):\n #this is a plot of a mbient temp defined\n #above, with Athens parameters. Make sure\n #t o end this command with colon, not semicolon,\n #or you will get a ve ry long list of points. \ninside:=plot(usp(t),t=0..50, color=black): \n #the steady periodic inside temperature\ndisplay(\{ambient,inside \}, title=\"inside-outside\");\n #display both plots together" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7er7 $$\"\"!F)$\"#vF)7$$\"3)pmm;a)G\\a!#=$\"3P!\\w1?\\>Q(!#;7$$\"3RLLL3x&)* 3\"!#<$\"3`LKSMfXwsF27$$\"3)***\\i!R(*Rc\"F6$\"3se%Gl+fl>(F27$$\"3zmm \"H2P\"Q?F6$\"3pVbx$F6$\"3O*GVyRE<+(F27$$\"3*QL$3xwq4 RF6$\"3N%R`bPz-+(F27$$\"3\"QLeRA'*Q/%F6$\"3Zf(p@.m++(F27$$\"3lJ'4j'3,qF27$$\"3GnT5:j=XWF6$\"3#eH3&3Uy1qF27$$\"3Q+]PfyG7ZF6$ \"3**p>GAkLVB$)F6 $\"3%Gdy0'Q.vvF27$$\"3KmmTg()4_))F6$\"3)f)[J4K)Rq(F27$$\"3n++DJbw!Q*F6 $\"38#G(HjRfQyF27$$\"3aM$ekGkX#**F6$\"38La+gAD!)zF27$$\"3%ommTIOo/\"F2 $\"3')4l*385B7)F27$$\"33+]7GTt%4\"F2$\"3Ok*3$*fyaC)F27$$\"3]LL3_>jU6F2 $\"3[sj0m@zk$)F27$$\"3!om\"HdNb'>\"F2$\"3Gs044e;#\\)F27$$\"3E++]i^Z]7F 2$\"3h)=9v'yu4')F27$$\"3C+++v\"=YI\"F2$\"3_IabjSg:()F27$$\"3/++](=h(e8 F2$\"3W%HEeV1r!))F27$$\"38++]7!Q4T\"F2$\"3+$4YdA')*z))F27$$\"3A++]P[6j 9F2$\"3@`GE5d\"F2$\"3I,9xGuI(**)F27$$\"3)pTg_ d[ge\"F2$\"3YG8&e/L$***)F27$$\"3$)e9T))Q8+;F2$\"3%4#\\vQ*******)F27$$ \"3K+Dc,#>Uh\"F2$\"3eARv+sI***)F27$$\"3!=a8Z^/$G;F2$\"3_#Q;Pxbs**)F27$ $\"3l$eky#)*QU;F2$\"3Ovg#oW[Q**)F27$$\"3]Dc,T^Zc;F2$\"3vB-z_)*3*)*)F27 $$\"3*pmmTXg0n\"F2$\"3PP2ahk)H)*)F27$$\"3+nmT&)))G=F2$\"31tUIs&zpl)F27$$\"3#omm;pW`(>F2$\"3.d*o$)o>[b)F27 $$\"3eLe9TOEH?F2$\"3)G['[%G]AV)F27$$\"3L+]i!f#=$3#F2$\"3+,1Ua@3,$)F27$ $\"3A++D\"=EX8#F2$\"3tnh\"4\">dq\")F27$$\"36+](=xpe=#F2$\"3ARQ99W)p.)F 27$$\"3dLeRA9WRAF2$\"39dW*)*)f#p*yF27$$\"3-nm\"H28IH#F2$\"3ngC'Rs\"*)e xF27$$\"3%p;a8d3AM#F2$\"3mj6V%3Sij(F27$$\"3%om\"zpSS\"R#F2$\"3%\\9\">u Sh>vF27$$\"3?+v$41oWW#F2$\"3[!yte\"=z-uF27$$\"3cLL3_?`(\\#F2$\"3Y!)QP9 mZ(H(F27$$\"3dL3_D1l_DF2$\"3V1'))QSTC?(F27$$\"3fL$e*)>pxg#F2$\"3A(HsDd %)R7(F27$$\"3#pmm\"z+vbEF2$\"30UwjtXYqqF27$$\"3D+]Pf4t.FF2$\"3AId'GC#f JqF27$$\"3c$3F>HT'HFF2$\"32cDQim\"p,(F27$$\"3'o;zWi^bv#F2$\"3'[\">\"p$ Gw1qF27$$\"3^3_v!z1&oFF2$\"30yk+'*pR.qF27$$\"3<]7.d>Y\"y#F2$\"36Ooipu< ,qF27$$\"3#=H2L7ST$GF2$\"3unx7H;*R+(F27$ $\"3;$ekG:Cv%GF2$\"3ed>jK*Hx+(F27$$\"3jm;H2\"34'GF2$\"36#pS/O'o7qF27$$ \"3cLe9;gn()GF2$\"3Z,5uixAEqF27$$\"39+++DRW9HF2$\"3)3Z$*>O\\X/(F27$$\" 3K+]7y#=o'HF2$\"3UZf()G+'Q4(F27$$\"3:++DJE>>IF2$\"3h-?+5,=grF27$$\"3I+ v$4^n)pIF2$\"3AN8F:)o$RsF27$$\"35+]i!RU07$F2$\"3Y&e)*\\JD>L(F27$$\"39+ vo/#3o<$F2$\"3\">%>;X?P[uF27$$\"3#)***\\(=S2LKF2$\"3Oj1ndlwwvF27$$\"3D L$3_NJOG$F2$\"3v&)oH+%Q+q(F27$$\"3nmmm\"p)=MLF2$\"3qs1FevbGyF27$$\"3aL LeR%p\")Q$F2$\"3!4J!z;E.pzF27$$\"3U++](=]@W$F2$\"30Lf(z6D,6)F27$$\"3wm \"H#oZ1\"\\$F2$\"3#>)oe*)\\:O#)F27$$\"35L$e*[$z*RNF2$\"3yy\\hvuJe$)F27 $$\"3]m\"Hd!fX$f$F2$\"3@pAIb-4&[)F27$$\"3e++]iC$pk$F2$\"3?Z*R%41P-')F2 7$$\"3[Le*[t\\sp$F2$\"35'4t??(*>q)F27$$\"3Rm;H2qcZPF2$\"3c;H]I(f%*y)F2 7$$\"3X+]7.\"fF&QF2$\"3B9LU\\'>m#*)F27$$\"3]Lek`8=/RF2$\"3s5YxD6qo*)F2 7$$\"3amm;/OgbRF2$\"3Y')o\\`HD$**)F27$$\"3ie*[o=i!pRF2$\"35vT](p@n**)F 27$$\"3)*\\7`p2_#)RF2$\"3i@WNqJ&*)**)F27$$\"3MTN@_$zf*RF2$\"3/t'H?gW** **)F27$$\"3ULe*[$zV4SF2$\"3K*[D=w%p***)F27$$\"3]D\"yv^'*G-%F2$\"3cv'y) fR?)**)F27$$\"3'oTg-5bj.%F2$\"3/$G#yYSZ&**)F27$$\"3B3F%Ho8)\\SF2$\"3q, %)G6%3:**)F27$$\"3I+]ilAFjSF2$\"32h:5w>J')*)F27$$\"3ym\"zW7@^6%F2$\"3g ksQie#\\&*)F27$$\"3(RLLL)*pp;%F2$\"3@\"GP$3>(f!*)F27$$\"3NL$3-$H**>UF2 $\"3m9>c[1oQ))F27$$\"3WLL3xe,tUF2$\"3y]2TpXDb()F27$$\"3z+v=n(*fDVF2$\" 3%=!\\-uW;e')F27$$\"3Vn;HdO=yVF2$\"3#4EVr)3i[&)F27$$\"3)R$e9\"z-lU%F2$ \"3*)**p#=rc(Q%)F27$$\"3`+++D>#[Z%F2$\"3ItOk))3)=K)F27$$\"3qL$3_5,-`%F 2$\"3m[]NCyr\"=)F27$$\"3(om;aG!e&e%F2$\"3gF2se@!y(F27$$\"3cn\"z>6but %F2$\"3HcW**Q*fyk(F27$$\"3m+]iSjE!z%F2$\"3R-H%edGA_(F27$$\"3M+++DM\"3% [F2$\"3)zYsjC$\\5uF27$$\"3u+]P40O\"*[F2$\"3)fI')Q:m!4tF27$$\"3P+voa-oX \\F2$\"3C/T&*oK,n9:)F27$F4$\"3 F?T#H'fMm!)F27$F:$\"3#*>l(*\\S7\"*zF27$F?$\"3O%p%GB(Qg\"zF27$FD$\"3l;$ [tk(>LyF27$FI$\"37'\\Kz!=g`xF27$FS$\"3Oz)3XDB$ywF27$Fao$\"3Uo'*G;iQ4wF 27$F[p$\"3)zlSEe?%[vF27$Fep$\"3kB<*G2ti\\(F27$Fjp$\"31j]s!*QpcuF27$F_q $\"3d\\QH#>OiU(F27$$\"3')***\\PMaM\\'F6$\"3yOT3!=EUT(F27$Fdq$\"33s=Bb[ &[S(F27$$\"3RLL3_DG1qF6$\"3)**pw>Vk\")R(F27$Fiq$\"3my.7[]=%R(F27$$\"3% om;Hd)G&R(F6$\"3'GE%3!4(>$R(F27$$\"3cLLe*[!)y_(F6$\"3%eb6(H-%HR(F27$$ \"3D++D1CZgwF6$\"35VnZwZT$R(F27$F^r$\"3M^!H'e,i%R(F27$$\"3M++Dc\"[#e!) 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