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-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 278 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 "" 0 279 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 "" 0 280 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 "" 0 281 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 "" 0 282 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 266 "" 0 "" {TEXT -1 0 "" }}{PARA 267 "" 0 "" {TEXT -1 9 "Math 2250" }}{PARA 268 "" 0 "" {TEXT -1 35 "MAPLE TUTORIAL and PRO JECT I HINTS" }}{PARA 274 "" 0 "" {TEXT 338 0 "" }{TEXT -1 9 "Fall 200 1" }}{PARA 270 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 383 " 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 2250-4 home page " }{TEXT 337 51 "http://www.math.uta h.edu/~korevaar/2250fall01.html." }}{PARA 271 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 275 "The Math 2250 projects can be done in ve rsions five and above of Maple, with minor changes. The Math Lab uses version 7, whereas the EMCB and Marriott Labs have version 6. A stud ent version of Maple for home computers is available from the bookstor e for approximately $100." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 273 "" 0 "" {TEXT -1 32 "1) Using the Math Computer Lab:" }}{PARA 0 " " 0 "" {TEXT -1 467 "The Math Department Computer Lab is located in th e South Physics 205, i.e. on the East (uphill) end of the second floo r of then brick building immediately north of the Math building JWB. \+ Room 205 is just inside the East entrance. Until construction of the \+ new Math Center is complete this winter, Physics and Math share this l ab. Useful information about most aspects of the lab can be found by \+ following links from the Math Department web pages, e.g. starting at" }{TEXT 340 1 " " }{TEXT 350 35 "http://www.math.utah.edu/ugrad/lab." } {TEXT 351 2 " " }{TEXT -1 90 "You can find out about X-windows, Unix \+ commands, Maple, Netscape, file editing, mail, etc." }}{PARA 278 "" 0 "" {TEXT -1 0 "" }}{PARA 277 "" 0 "" {TEXT -1 15 "1a) Logging on:" }} {PARA 0 "" 0 "" {TEXT -1 409 "Almost all students who are registered i n Math 2250, or in any other math class, will already have accounts s et up in our lab. Since these accounts are created from University cl ass lists, late-registering students may not be accounted for. If yo u fit in this case the lab assistant can help you apply for an account - provided you have brought your student I.D. to show that you are a \+ University student." }}{PARA 0 "" 0 "" {TEXT -1 147 " The lab mach ines are left on - move the mouse or hit a key to wake yours up. The re are two possibilities for the dialog box which appears. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 481 "(A) If you get a dialog window asking you to \"select a server to log on to\", use t he mouse to select one which has \".math\" in its name. Then O.K. you r choice by clicking in the \"accept\" box. In a few seconds a login \+ window should appear, asking for your login name and password, and hav e \"Mathematics\" written in red on the top. (If the login window s ays \"Physics\" you have accidently chosen a physics server, and you s hould type \"control C\" to go back to the previous step.) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 301 "(B) If inste ad you get a dialog window which says \"Welcome to Orion\", highlight \+ \"options\" with your mouse, and from its submenu choose \"remote logi n\" and then \"choose host from list\". This will get you the window \+ in (A), from which you proceed as above. If you are confused, ask the lab assistant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "Your " }{TEXT 352 10 "login name" }{TEXT -1 47 " is made o ut of your initials. If your name is" }{TEXT 341 2 " K" }{TEXT -1 4 " arl " }{TEXT 342 1 "F" }{TEXT -1 4 "red " }{TEXT 343 1 "G" }{TEXT -1 3 "aus" }{TEXT 344 1 "S" }{TEXT -1 704 ", then your login name is c-gs kf, following the recipe: c-(first letter of last name)(last letter o f last name)(first letter of first name)(middle initial). If there ar e multiple people registered this term with the same initials, then ra ther than c-gskf, they are assigned login names with a numerical suff ix, c-gskf1, c-gskf2, c-gskf3, etc. Mr. Gauss would not know beforeh and which case he fell into, so would probably try c-gskf first, foll owed by his password. In case of failure he would then try c-gskf1, t hen 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 an d the cursor should be in the password box. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 5 "Your " }{TEXT 353 16 "initial p assword" }{TEXT -1 528 " is just the gskf part of your login name foll owed by the last four digits of your student I.D. number. If Mr. Gau ss has ID number 000735421 then his initial password is gskf5421, rega rdless whether his login name was c-gskf or c-gskf3. If the login f ails try again and then try the different login names suggested above. One possibility is that your account was created using your social s ecurity number (which used to be used for student ID number). If fail ure continues find a lab assistant and he/she will help you. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 425 "Once you are logged in successfully a ``local'' window 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 po inter (called cursor) moves around the screen. If you want to work in \+ a window, the cursor should be in it. You can make multiple local win dows by pressing the right mouse button and highlighting \"local\". \+ " }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 307 23 "1b ) Changing password:" }{TEXT -1 198 " Some time within the first sev eral weeks of classes you must change your default password into a per sonal one. You do this as follows: Get your cursor into a local windo w. Type the unix command " }{TEXT 308 6 "passwd" }{TEXT -1 640 ", fol lowed by return, and follow the directions. Your new password should \+ be exactly 8 characters long. Don't choose a word in the dictionary o r a proper name. Composites of dictionary words, like strawdog, are g ood. Even better is to use one or two upper case letters, e.g. strAwd og. For still more security, use some digits, e.g. strAw4o9. It tak es about 15 minutes for a new password to take effect. If a password \+ is not changed within the first several weeks of class, then your comp uter account will be disabled for security reasons. Make sure to writ e down your password in a secure place, in case your memory is not per fect." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 309 17 "1c) Logging out:" }{TEXT -1 221 " Move the cursor out of all windows (into the background), press the left mouse button and choose the las t menu item: Exit X-Windows. (You probably don't want to do this now, but at least locate the menu item for later.)" }}{PARA 0 "" 0 "" {TEXT -1 62 " At this point you are ready to get used to the X-win dows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 310 51 "2) X-windows, opening netscape, maple, mail, more:" }{TEXT -1 4 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 256 "Xwindows are not so different from \+ P.C. windows or Mac windows; on the other hand they have their own idi osyncracies, so you should experiment to see how to open and close win dows, resize them, move them about, and find them if they happen to g et hidden. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 187 "For your Math 2250 purposes you need to be able to open Netsca pe (to download files) and Maple (to work on them). Open Netscape by moving your cursor into a local window and then typing" }{TEXT 345 11 " netscape &" }{TEXT -1 27 ", followed by . The" }{TEXT 346 2 " &" }{TEXT -1 175 " tells X-windows to create a separate proces s for netscape, keeping your local window free for more UNIX commands. Once netscape opens, go to the Math undergraduate pages at " }{TEXT 347 30 "http://www.math.utah.edu/ugrad" }{TEXT -1 62 ", and follow the links to explore computer lab information. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 128 "Finally, open a Maple wi ndow one of two ways: from the middle mouse button you may choose xma pleV7, or you can type the command" }{TEXT 348 9 " xmaple &" }{TEXT -1 321 ", followed by , into a local window. The Math Departme nt's site license for version 7 of Maple only allows a certain number \+ of people to use it at once. If this number is exceeded you won't be \+ able to run version 7, but you can use the Mouse to open xmapleV5.1, f or which our site license allows unlimited use. " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 311 11 "3) Ma ple: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 235 " If you are st arting the tutorial at this point (because you're doing it on your own at another location or already knew the Math Lab system), you should \+ have opened a mapleV6 or mapleV7 (worst case V5) window as well as a w eb browser." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 860 "Maple is partly just a very fancy calculator; it can do practi cally any undergraduate mathematics computation or symbolic manipulati on. You can write programs in Maple and draw pictures as well. If yo u are doing a homework assignment you can intersperse text with comput ations 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, form ats, and use other standard text editing tools by choosing appropriate menu items. This document you are reading is a Maple document even t hough it is largely text. You will learn by doing - and by asking you r neighbor or the lab assistant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 359 18 "New User's Tour: " }}{PARA 0 "" 0 "" {TEXT -1 649 "Under the Help button at the top right of your Maple win dow 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 ch oice Maple may hide the beginning of the tour behind other active wind ows; use the \"Window\" menu item to bring the tour window to the fr ont. If you wish you can explore now, or you can continue with the M ath 2250 notes below and come back to the tour later. To close the ne w 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 354 25 "Entering Maple commands: " }}{PARA 0 "" 0 "" {TEXT -1 508 "To give you a flavor of what Maple can do, we \+ will try a few commands. Move your cursor into the \"Untitled\" (new) Maple window which you created in step (2). Commands begin on lines having a command prompt ``>'', and should be ended with either a sem icolon ; or a colon : If you end with a semicolon you will see visibl e output, if you end with a colon the output will be suppressed even t hough the command is executed. Maple will not execute a command until you type the ``return'' or ``enter'' key. " }{TEXT 312 87 "If you ha ve a multiline command use ``shift-return'' to change lines without ex ecuting." }{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 unexecutable you will g et a ``syntax error'' message and Maple will try to point out your mis take with the cursor and cryptic diagnostic phrases. After a while yo u will become good at fixing these mistakes but they can be annoying a t first. Spaces are ignored in Maple, so you may use them to make inp ut easier to read. You can enter explanatory comments in a command li ne by inserting a ``#'' to the left of the comments; Maple ignores any text after the #. Sometimes this is more informative then entering n earby 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 co mmands, the editorial comments were only added to explain what the par ticular 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 #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 use *, so aft er\n #trying the command as given, insert a * to fix the\n \+ #resulting 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, unexpec ted 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 #de cimal approximation instead of an algebraic \n #expression. N otice that if given a choice, Maple \n #computes powers first , then multiplies and divides, \n #and finally adds or subtra cts." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "diff(x^2,x); #``di fferentiate x^2 with respect to x''" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "diff(exp(sin(x))*x^3,x); #a harder differentiation p roblem\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 #funct ion, 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); #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 integration constant.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "int(t^3*exp(sin(t)),t); #this shows that Maple is no t 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 #antid erivative 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 coul d do\n #a definite integral (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 355 14 "Entering Text:" }}{PARA 0 "" 0 "" {TEXT -1 145 "Scroll to somewhere in your worksheet and add some text \+ with the ``T'' menu item. (If you move your cursor to a command field and the press the " }{TEXT 356 2 "[>" }{TEXT -1 128 " button with you r mouse, Maple makes a new command field directly below it. If you mo ve to the new command field and press the " }{TEXT 357 1 "T" }{TEXT -1 127 " button you will have a text field into which you may write, u sing the rudimentary word processing tools on the Maple menu bar." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 369 "Now scro ll to the top of your file and insert the title ``My first Maple works heet'' (center it with the menu option on the right side of the toolba r), as well as your name and today's date. When you are doing your Map le projects you will be expected to hand in more than a page of comput ations: You will be expected to add text explanations of what you've b een doing. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 279 "" 0 "" {TEXT -1 13 "Saving Files:" }}{PARA 0 "" 0 "" {TEXT -1 415 "It is alwa ys a good idea to save your maple file periodically. Do this now usin g the tool bar, using the \"save\" option 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 wan t 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 file is a " } {TEXT 331 1 "M" }{TEXT -1 5 "aple " }{TEXT 332 1 "W" }{TEXT -1 4 "ork \+ " }{TEXT 333 1 "S" }{TEXT -1 544 "heet. If your directory is new you \+ probably haven't made any subdirectories yet (unix command mkdir, in a local window), but as you create more files you may wish to organize \+ where you save them using the tree structure of Unix directories, whi ch you can follow in the right side of your saving box. Unfortunately our UNIX is not set up so that you can visually see your directory/fi le tree like in PC windows or Macs. You use various UNIX commands in \+ your local window to organize your directories. For more information \+ about this, go to" }{TEXT 349 49 " http://www.math.utah.edu/ugrad/hel pforunix.html." }{TEXT -1 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 280 "" 0 "" {TEXT -1 9 "Printing:" }} {PARA 0 "" 0 "" {TEXT -1 10 "Go to the " }{TEXT 313 4 "file" }{TEXT -1 28 " menu option and choose the " }{TEXT 314 5 "print" }{TEXT -1 72 " option. You get a little printer setup box. If you then click o n the " }{TEXT 316 14 "print command " }{TEXT -1 52 "diamond, followed by ``enter'' or by a click on the " }{TEXT 315 5 "print" }{TEXT -1 192 " box at the bottom of the window, a paper copy will come out of o ne of the printers at the side of the lab. Do this now. Alternately, if you want to use a different printer, you can use the " }{TEXT 317 14 "output to file" }{TEXT -1 558 " diamond to create a postscript fil e which you can then print anywhere, using the appropriate unix comman ds. For example, to print a postscript file to the lab printers from \+ a local window, the command would be \"lpr -P b129lab1\", or \"lpr -P b129lab2\", followed by the return key. You do not put in the quote \+ marks, but you are careful to leave spaces exactly as indicated. The \+ lpr stands for line printer, the -P stands for print, and the b129lab1 or b129lab2 are the names of the two printers. If you have trouble p rinting ask a lab assistant for help." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 360 28 "Downloading Maple documents:" }} {PARA 0 "" 0 "" {TEXT -1 114 " This xeroxed tutorial is available onli ne in several formats, if you follow the links from the 2250-4 homepag e at" }{TEXT 334 50 "http://www.math.utah.edu/~korevaar/2250fall01.htm l" }{TEXT -1 503 ". Files with suffix \".mws\" or \".txt\" can be dow nloaded from your browser and then opened from Maple. The \".mws\" su ffix means the file is a Maple Worksheet, and should open from Maple t o look just like this file. The \".txt\" suffix is Maple text, and yo u should only try it if the \".mws\" file doesn't open. It's a cruder form of this file, but potentially more universal. The \".pdf\" vers ions of the file are for reading from your browser (with Acrobat reade r), but you can't execute these from Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 111 "Go to the course homepage addr ess using your browser, follow the link to the Maple page, and find an d save the " }{TEXT 335 15 "2250falltut.mws" }{TEXT -1 29 " file to yo ur 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 336 15 "2250falltut.mws" }{TEXT -1 501 ". It s hould appear in the central box after you choose \"open\". Click on i t with the mouse to highlight it and then click ``OK'' or type ``retur n''. 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 \"W indow\" menu item at the top of your Maple window to change between va rious 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 the front.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 224 "If you know the exact URL of a Maple file, and you are in version 6 or 7 of Maple, you can use the \"open URL\" option under \"File\" t o have Maple do the downloading and opening for you. This saves steps if it works correctly." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 245 "If you couldn't open the Maple worksheet file, go b ack to your browser and save the \".txt\" version of the tutorial. Th en go back to Maple, and follow these directions: In order to open a \+ ``Maple text'' document, which this is, you must chose " }{TEXT 325 4 "open" }{TEXT -1 10 " from the " }{TEXT 326 4 "file" }{TEXT -1 32 " \+ menu option. In the resulting " }{TEXT 327 9 "open file" }{TEXT -1 22 " dialog box go to the " }{TEXT 328 9 " filetype" }{TEXT -1 595 " b ox at the bottom, click on the triangle to see the list of choices, an d use your mouse to choose ``Maple text.'' At this point ``2250tutori al.txt should appear as a choice in the central box. Click on it with the mouse to highlight it and then click ``OK'' or type ``return''. \+ A copy of this tutorial should then appear in your Maple window, as a \+ Maple document that you can work in. The copy is not as pretty as you r xerox (the execution groups are all single lines, and the text forma tting 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 1 " " }} {PARA 0 "" 0 "" {TEXT 358 17 "Execution Groups:" }}{PARA 0 "" 0 "" {TEXT -1 368 "You can modify the text and input using the toolbar and \+ menu options. You will notice many brackets on the left of the docume nt. These are execution groups. Maple will execute everything in one execution group at once, and then move the cursor to the next executi on group. You can create large execution groups by highlighting secti ons of a document, going to the " }{TEXT 321 4 "Edit" }{TEXT -1 20 " o ption and picking " }{TEXT 322 24 "join execution groups. " }{TEXT -1 252 "You can remove brackets by highlighting them with the mouse an d deleting them with the delete key or the menu option. And you alrea dy learned how to insert new prompts or new text wherever your cursor \+ is, by using the [> and T buttons on your toolbar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 323 3 "4) " }} {PARA 275 "" 0 "" {TEXT -1 0 "" }{TEXT 339 25 "INTRODUCTION TO PROJECT I" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 281 "" 0 "" {TEXT 362 0 " " }{TEXT -1 0 "" }{TEXT 361 35 "A preliminary paragraph of advice: " } {TEXT -1 1 " " }}{PARA 282 "" 0 "" {TEXT -1 987 "Students often approa ch the task of reading mathematical material as if they were reading a novel; they sort of skim along quickly. That approach is O.K. to ge t an overview, but in order to have a chance at real understanding you must be prepared to proceed much more slowly, sentence by sentence an d thought by thought. Otherwise you will almost certainly find yourse lf partly lost after several paragraphs and completely lost after seve ral more. (This might happen anyway.) If you are working properly it can easily take half an hour to read through one page of mathematica l text. This takes a certain amount of discipline, patience, and prac tice. With the Math 2250 computer projects there is the added temp tation of having Maple execute commands in successive command section s by repeatedly hitting the enter (return) key, without pausing to d igest 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 -1 432 " Open your text b ook to page 55, and follow along. We will go through the Maple comman ds and text corresponding to the section 1.5 Computing Project of Edwa rds-Penney. If you go through this section carefully now, then your \+ life should be relatively easy when you download the solution template from the course home page. Make sure you understand what each comman d 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 furt her information about syntax and options related to commands below, us e 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 any thing 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 DEtools\n # package, end your comma nd 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#*&-%$expG6#% \"tG!\"\",(\"\"$\"\"\"*&F$F+F'F+F+F$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 99 "Error, (in pdsolve/sys/info) required an \+ indication of the dependent variables in the given system\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 437 "This command didn't work. It wou ld've worked, except that you have defined y(t) just above here, so wh en Maple evaluates the differential equation \"deqtn\" which you defin ed 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 problem by never using the same symbols twice, or more practicall y, by restarting, to clear out conflicting defintions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "restart: #clears all definitions an d memory\nwith(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 363 25 "Rest arting and Reopening:" }{TEXT -1 246 " Every time you reopen a Maple \+ file you will neet to re-enter commands and definitions. Similarly, i f you restart but want some old definitions to hold, move your cursor \+ to the appropriate command fields and reenter them using the k ey.." }}}{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 wor k, and even give an answer\n #which agrees with your ealier one" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deqtnG/,&-%%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 discu ssion 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 ambient 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 ke y while you hit\n #\"enter\" or \"return\", to prevent premature exec ution" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGf*6#%\"tG6\"6$%)operato rG%&arrowGF(,(%#a0G\"\"\"*&%#a1GF.-%$cosG6#*&%&omegaGF.9$F.F.F.*&%#b1G F.-%$sinGF3F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "d eqtn3:=diff(u(t),t)=-k*(u(t)-A(t));\n #we name our DE \"deqtn3\" sinc e 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 -1 445 "We will find the general solution to deq tn3 first, with all the free parameters, and then fix the parameters f or a July day in Athens Georgia second. You should be able to use the \+ integral table entries 49,50, or alternately have the computer follow \+ the recipe method we just outlined to find the general solution. Howe ver, it is easier to just use dsolve. You should verify that the solu tion 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)F2!\"\"F2,.*&)F1 \"\"#F2%#a1GF2F2*(F1F2%#b1GF2%&omegaGF2F3*&%#a0GF2F6F2F2*&F=F2)F;F7F2F 2*&%#u0GF2F6F2F3*&FAF2F?F2F3F2,&*$F6F2F2*$F?F2F2F3F3*&,.FF2*(F6F2 F8F2-%$cosG6#*&F;F2F)F2F2F2**F1F2F8F2F;F2-%$sinGFKF2F2**F1F2F:F2F;F2FI F2F3*(F6F2F:F2FNF2F2F2FCF3F2" }}}{PARA 0 "" 0 "" {TEXT -1 142 "Now we \+ set the parameters equal to the values at the bottom of page 56, so th at we are studying something like summer days in Athens Georgia: " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 405 "a0:=80;\n #average ambien t 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 rang e from 70 to 90 degrees,\n #for trigonometric temp oscillation.\nome ga:=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 12 " " 1 "" {XPPMATH 20 "6#>%&eqtn5G/-%\"uG6#%\"tG,,-%$expG6#,$F)$!+++++?!# 5$!+k0^L#)!\")$\"#!)\"\"!\"\"\"*&F+F8%#u0GF8F8*&$\"+Cc5NB!\"*F8-%$cosG 6#,$F)$\"+yQ*zh#F1F8F8*&$\"+Czg.cF>F8-%$sinGFAF8!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 311 "Read along with the text on page 57. Notice that no matter what the initial house temper ature was, the negative exponential terms die out rapidly and one is l eft with the steady periodic solution given by equation (6) in the tex t. We can extract it from our eqtn5 above, by using the mouse to cut \+ and paste: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "usp:=t-> 80 + 2.335105624*cos(.2617993878*t)-5.603 607924*sin(.2617993878*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$uspGf *6#%\"tG6\"6$%)operatorG%&arrowGF(,(\"#!)\"\"\"*&$\"+Cc5NB!\"*F.-%$cos G6#,$9$$\"+yQ*zh#!#5F.F.*&$\"+Czg.cF2F.-%$sinGF5F.!\"\"F(F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "We can reproduce figure 1.5.10 (i t would take more work to get all the labels in) as follows" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "with(plots):\n #this is the plotting package. End with ; \n #to see command list" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "ambient:=plot(A(t),t=0 ..50, color=red):\n #this is a plot of ambient temp defined\n #above , with Athens parameters. Make sure\n #to end this command with colon , not semicolon,\n #or you will get a very long list of points. \nin side:=plot(usp(t),t=0..50, color=black):\n #the steady periodic insid e temperature\ndisplay(\{ambient,inside\}, title=\"inside-outside\"); \n #display both plots together" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7er7$$\"\"!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$$\"3*QL$3xwq4RF6$\"3N%R`bPz-+(F27$$\"3\"QLeR A'*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$$\"3E++]i^Z]7F2$\"3h)=9v'yu4')F27$$\"3C+++v\" =YI\"F2$\"3_IabjSg:()F27$$\"3/++](=h(e8F2$\"3W%HEeV1r!))F27$$\"38++]7! 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time delay, relative to the outside temperature. (The ann ual seasonal temperature variations on earth lag behind the solstice-e quinox dates, for a similar reason.) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 187 "We can recover figure 1.5.9, togeth er with the slope field, with a DEplot command. This picture illustra tes geometrically the fact that all solutions converge to the steady p eriodic one:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "DEplot(deqtn3,u(t),t=0..50,\{[u(0)=65],[u(0)=70 ],\n [u(0)=75],[u(0)=80],[u(0)=85],[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 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6acn7$7$$!3Dgu`Wp8xC!#=$\"3J^#46Ed/X' !#;7$$\"3Dgu`Wp8xCF*$\"3q[2*)QFa\\lF-7$7$$\"3bRK@d.&GP\"!#<$\"3r/&o)*4 lFX'F-7$$\"3uDd&[]Da2#F7$\"3I&\\J,!\\BZlF-7$7$$\"3!Gq\"4'o_9,$F7$\"3%R '[B7zSbkF-7$$\"3!yAY!Q!*4&)QF7$\"31O^w(3#fWlF-7$7$$\"3QUJDF^rdZF7$\"3G qu)[\"QlakF-7$$\"3TaP&*eC6(e&F7$\"3tHD6&=Y`a'F-7$7$$\"3R&f!H/>+&e'F7$ \"3xPB+2=x^kF-7$$\"3\"eE&)Ra,\"3sF7$\"3Biw*H>G#[lF-7$7$$\"35y'GoM(\\-% )F7$\"3'pzF`.g*\\kF-7$$\"3_Zh^j>))Q))F7$\"3/.Ank*R+b'F-7$7$$\"3!e>\"H3 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the end of the tutorial. To download your instrucitons a nd template for project 1, follow the links from " }{TEXT 364 50 "http ://www.math.utah.edu/~korevaar/2250fall01.html" }{TEXT -1 1 "." }}}} {MARK "137 0 0" 174 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }