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}{CSTYLE "" -1 325 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 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 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 256 9 "Math 2270" }}{PARA 257 "" 0 "" {TEXT 257 9 "PROJECT 1" }}{PARA 258 "" 0 "" {TEXT -1 16 " September 2 000" }}{PARA 3 "" 0 "" {TEXT 258 388 " In this project you will l og onto the Math Lab machines, familiarize yourself with how they oper ate, introduce yourself to the software MAPLE, and use it to do some c omputations related to the linear algebra in chapter 1 of our text. De pending on your previous eperience you may want to skip various sectio ns. It is only material from section (6) that you will be asked to ha nd in." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT 286 0 "" }{TEXT -1 0 "" }{TEXT 285 33 "0) A preliminary word of Advice: " }{TEXT -1 977 " Students often approach the task of reading mathematic al material as if they were reading a novel; they sort of skim along q uickly. That approach is O.K. to get an overview, but in order to ha ve a chance at real understanding you must be prepared to proceed much more slowly, sentence by sentence and thought by thought. Otherwise \+ you will almost certainly find yourself partly lost after several para graphs and completely lost after several more. (This might happen any way.) If you are working properly it can easily take half an hour to read through one page of mathematical text. This takes a certain amo unt of discipline, patience, and practice. With the computer project s there is the added temptation of having Maple execute commands in \+ successive command sections by repeatedly hitting the enter (return) key, without pausing to digest the interlaced text or the meaning of \+ the commands. There is a seductive appeal in having this capability. Resist it." }}{PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 260 37 "1a) Logg ing in to a Math Lab machine" }{TEXT 263 378 ": The Math Department C omputer Lab is located in the South Physics 205, i.e. inside the 2-st ory 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 the second floor (from the wes t), which equals the level of the ground on the uphill, east entranc e. " }}{PARA 0 "" 0 "" {TEXT -1 106 " The following information \+ about logging in and your initial password is summarized from the hand out " }{TEXT 287 111 "Introduction to the Undergraduate Computer Lab D epartment of Mathematics, University of Utah, SLC, Utah 84112 ." } {TEXT -1 1 " " }{TEXT 288 82 " This and other useful handouts are avai lable on a table in the front of the lab. " }}{PARA 3 "" 0 "" {TEXT 259 472 " Everyone who is registered in Math 2270 should have an \+ account set up in our lab already. These accounts are created from Un iversity class lists so it sometimes happens that late-registering peo ple don't have accounts yet. If you turn out to be one of these peopl e you will need to consult the lab assistant about getting an account. Make sure to bring your student I.D. because the first thing the ass istant must do is verify that you are a University student. " }} {PARA 0 "" 0 "" {TEXT -1 778 " If your machine 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 shar ing this lab with Physics, there are physics and math server computers . You want to select one from the list of choices which has \".math \" in its name. If a \".physics\" computer is highlighted, use your c ursor to choose one of the \".math\" computers, and then O.K. your cho ice by clicking in the \"accept\" box. In a few seconds a login windo w should appear, asking for your login name and password, and have \" Mathematics\" written in red on the top. (If the login window says \+ \"Physics\" you have accidently chosen a physics server, and you shoul d type \"control C\" to go back to the previous step.)" }}{PARA 0 "" 0 "" {TEXT -1 873 " Your default login name is made out of your s tudent I.D. number and your actual name, as follows. All names from c lasses begin with ``c-''. If your name is Karl Fred GausS, then your login name is c-gskf, following the recipe: c-(first letter of last \+ name)(last letter of last name)(first letter of first name)(middle ini tial). If there are multiple people registered this term who would ha ve the same login name, say c-gskf, then they are instead assigned log in names as c-gskf1, c-gskf2, c-gskf3, etc. Mr. Gauss would not know \+ beforehand which case he fell into, so would probably try c-gskf first , followed by his password. In case of failure he would then try c-g skf1, then c-gskf2, etc, through c-gskf4. Then he would find a lab ass istant. 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 of your student I.D. \+ number. If Mr. Gauss has ID number 000735421 then his initial passwo rd is gskf5421, regardless whether his login name was c-gskf or c-gskf 3. If the login fails try again and then try the different login na mes suggested above. Another possibility is that your account was cre ated using your social security number (which used to be used for stud ent ID number). If failure continues find a lab assistant and he/she \+ will help you. " }}{PARA 0 "" 0 "" {TEXT -1 332 " Once you are lo gged in successfully a ``local'' window should appear. Notice that it has various parts: borders on the top (title bar), borders on the sid e (scroll bar), etc. If you move your mouse on its pad your pointer ( called cursor) moves around the screen. If you want to work in a windo w, the cursor should be in it. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 265 23 "1b) Changing password:" }{TEXT -1 159 " Sometime within the first two weeks of classes (now would be a good \+ time) you must change your default password into a personal one. You \+ do this as follows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 60 "Get your cursor into a local window. Type the unix com mand " }{TEXT 264 6 "passwd" }{TEXT -1 50 ", followed by return, and f ollow the directions. " }{TEXT 266 592 "Your new password should be e xactly 8 characters long. Don't choose a word in the dictionary or a \+ proper name. Composites of dictionary words, like strawdog, are good. Even better is 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, yo u should be aware that if a password is not changed within the first t wo weeks of class, then your computer account will be disabled for sec urity reasons. Write your password down somewhere in case you forget \+ it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 267 18 "1 c) Logging out: " }{TEXT -1 117 "Move the cursor out of all windows ( into the background), press the left mouse button and choose the last \+ menu item: " }{TEXT 268 14 "Exit X-Windows" }{TEXT -1 89 ". (You prob ably 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 rea dy to get used to the X-windows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 289 51 "2) X-wi ndows, opening netscape, maple, mail, more:" }{TEXT -1 26 " Go throug h the document " }{TEXT 290 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 291 10 "xmaple &, " }{TEXT 294 60 "which you can type into a loc al window, followed by ." }{TEXT -1 273 " 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 differences in commands and syntax, and they may confuse you once or twice. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 292 21 "Further information: " }{TEXT -1 123 " If you want more in-depth information about the computing facili ties in this lab, you might pick up a copy of the handout " }{TEXT 293 32 "A Crash Course on CSC Facilities" }{TEXT -1 23 ", from the fro nt table." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 295 37 "3a) Math Department Maple resour ces:" }{TEXT -1 193 " There is introductory material about Maple on \+ our web pages. If you wish to see what's available use the browser wi ndow you made in step (2) above, and go to the Math Department home p age " }{TEXT 296 26 "http://www.math.utah.edu/." }{TEXT -1 253 " By f ollowing links from here you can find current and future course offeri ngs, faculty information, and much more. Since you are students, int erested in Maple information, click on \"students\" (at the upper left of the page), and you are directed to " }{TEXT 297 31 "http://www.mat h.utah.edu/ugrad/" }{TEXT -1 46 ", the undergraduate home page. If yo u choose " }{TEXT 300 1 "\"" }{TEXT -1 26 "Undergraduate Computer Lab " }{TEXT 298 1 "\"" }{TEXT -1 14 ", followed by " }{TEXT 299 29 "\"Sel ected software and tools\"" }{TEXT -1 49 ", you will find some links t o Maple information. " }}{PARA 0 "" 0 "" {TEXT 302 24 "3b) More Infor mation. " }{TEXT 301 79 "Maple has its own introduction, as well as a new user's tour, see item 5 below." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 303 21 "4a) Map le commands: " }{TEXT -1 873 " Move your cursor into the \"Untitled\" (new) Maple window which you created in step (2). Maple is partly ju st a very fancy calculator; it can do practically any undergraduate ma thematics computation or symbolic manipulation. You can write program s in Maple and draw pictures as well. If you are doing a homework ass ignment you can intersperse 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 th em and then choosing \"T\". You can use the mouse to cut, paste, and \+ edit a document. You can change fonts, formats, and use other standar d text editing tools by choosing appropriate menue items. This docume nt 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 M aple can do, we will try a few commands. They should begin on a line \+ having a command prompt ``>'', and should be ended with either a semi colon ; or a colon : If you end with a semicolon you will see visible output, if you end with a colon the output will be suppressed even th ough the command is executed. Maple will not execute a command until \+ you type the ``return'' or ``enter'' key. " }{TEXT 304 87 "If you hav e a multiline command use ``shift-return'' to change lines without exe cuting." }{TEXT -1 644 " If you mess up your parentheses or brackets o r do something else which makes your command unexecutable you will get a ``syntax error'' message and Maple will try to point out your mista ke. After a while you will become good at fixing these mistakes but t hey can be annoying at first. Spaces are ignored in Maple, so you may use them to make input easier to read. You can enter explanatory com ments in a command line by inserting a ``#'' to the left of the commen ts; Maple ignores any text after the #. Sometimes this is more inform ative then entering nearby explanatory text, especially if you are exp laining various steps in a subroutine." }}{PARA 0 "" 0 "" {TEXT -1 222 " Now, let's try some commands. (You try just the math command s, the editorial comments were only added to explain what the particul ar commands are illustrating ! ) Check that you understand what each \+ command is doing." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "3+4; 4+5: 6 * 7; #one of these computati ons will not be shown \n #even though all three will be done. \n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 432 "(3+ 4)7; #if you want to multiply you must use *, so after \n \+ #trying the command as given insert a * to fix the \n #res ulting 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 arro w keys. Maple will \n #try to put it in a good place if it de tects an error." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 290 "(3+4)^2 /7; 3+4^2/7; evalf(3+4^2/7); #the evalf command gives a decimal \n \+ #approximation instead of an algebraic expression. \n \+ #Notice that if given a choice, Maple computes powers \n #f irst, then multiplies and divides, and finally\n #adds or sub tracts." }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "diff(x^2,x); #``differentiate x^2 with respect to x' '" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "diff(exp(sin(x))*x^3,x ); #a harder differentiation problem\n #you should get outpu t:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#%\"xG\"\"\"-%$expG6 #-%$sinGF'F))F(\"\"$F)F)*&F*F))F(\"\"#F)F0" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 203 "f:= x-> exp(sin(x))*x^3;\ndiff(f(x),x); #t he same problem done in two steps. \n #The first line shows \+ the format for defining\n #functions in Maple. (Did you use ` `shift-ret''?) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6 $%)operatorG%&arrowGF(*&-%$expG6#-%$sinG6#9$\"\"\")F3\"\"$F4F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#%\"xG\"\"\"-%$expG6#-%$si nGF'F))F(\"\"$F)F)*&F*F))F(\"\"#F)F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "int(t^2*exp(t),t); #``integrate (t^2)*exp(t) with \+ respect \n #to t'' (Maple doesn't put in the integration cons tant.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&)%\"tG\"\"#\"\"\"-%$expG 6#F&F(F(*&F&F(F)F(!\"#F)F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "int(t^3*exp(sin(t)),t); #this shows that Maple is not God:\n \+ #If it can't find an elementary-function\n #antiderivat ive it just echos what you put in.\n #you should get: " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&)%\"tG\"\"$\"\"\"-%$expG6#- %$sinG6#F(F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "evalf(in t(t^3*exp(sin(t)),t=0..1)); #But you could do \n #a definite integral numerically even if Maple \n #can't compute an elem entary antiderivative" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*39G6&!#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "sum(3^(-n),n=1..100); \+ #add a geometric series part way,\n #this is the series 1/3 \+ +1/9 +1/27 + ... " }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalf(%); #get its decimal value" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "Sum(3^(-n),n=1..infinity); evalf(%); #add the series \n # al l the way to infinity. Sum with captial\n #S writes the sum b ut doesn't evaluate it,\n #but then evalf(%) does.\n \+ " }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$)\"\"$,$% \"nG!\"\"/F);\"\"\"%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ ++++]!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 277 "Sum((.001)*(n/ 1000)^2, n=1..1000); evalf(%);\n #This is a Riemann sum for th e integral of x^2\n #from 0 to 1, with 1000 equal subdivisions .\n #Sum with capital S writes the summation, but\n #d oesn't evaluate it. evalf(%) gives its value. \n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$,$*$)%\"nG\"\"#\"\"\"$\"+++++5!#=/F );F+\"%+5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++]LQL!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(x^2,x=0..1); #this is the exa ct value of the integral" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "Pi;exp(1);evalf(Pi);evalf(exp(1));infinity; \n #some import ant numbers" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 309 22 "4b) Saving your file:" } {TEXT -1 416 " It is always a good idea to save your Maple file period ically. Do this now using the tool bar, using the \"save\" option und er 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 f ile and say where you want to keep it. You name it in the left part o f the box, being careful to keep the suffix \".mws\" so that Maple kno ws this file is a " }{TEXT 308 1 "M" }{TEXT -1 5 "aple " }{TEXT 306 1 "W" }{TEXT -1 4 "ork " }{TEXT 307 1 "S" }{TEXT -1 371 "heet. If your \+ directory is new you probably haven't made any subdirectories yet (uni x 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, which you can follow in the right side of your savin g box. If you need more help saving your file see the instructions i n the " }{TEXT 305 59 "Introduction to Maple V.4 in the Undergraduate \+ 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 M aple long after your last save. This will not make you feel happy. \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 311 19 "4c) \+ Text editing: " }{TEXT -1 1 " " }{TEXT 310 760 "First, scroll to some where in your worksheet and add some text with the ``T'' menu item. M aybe scroll to the top and put the title ``My first Maple worksheet'' \+ (center it with the menu option on the right side of the toolbar), as \+ well as your name and today's date. When you are doing your Maple proj ects 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 doi ng. You can highlight text with the mouse, and then delete it or copy it elsewhere. Sometimes if you are having trouble adding text in a p articular place you can use the Maple command button \"[>\" first to g et a command field, and then turn it into a text field by putting your cursor into it and using the \"T\" button." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 26 "4d) Printing your file: " } {TEXT 312 960 "Go to the file menu option and choose the print option. You get a little printer setup box. If you then click on the print \+ command diamond, followed by ``enter'' or by a click on the print 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. Alternately, if you wa nt to use a different printer, you can use the output to file diamond \+ to create a postscript file which you can then print anywhere, using t he appropriate unix commands. 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. Yo u do not put in the quote marks, but you should be careful to leave sp aces exactly as indicated. The lpr stands for line printer, the -P st ands for print, and the 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 272 3 "5) " }{TEXT -1 1 " " }{TEXT 262 47 "Linear Algebra, and using Maple's help windows" }{TEXT -1 315 ": So, it looks like Maple might be interesti ng to use in Calculus, but how do we find out what it can do for us in that subject, or in another subject, say linear algebra? It is inst ructive to use the Help directory located at the upper right-hand corn er 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 273 4 "5a) " }{TEXT -1 1 " " }{TEXT 271 66 "In mapleV6 and V5 (but not in \+ mapleV4) there's an online tutorial!" }{TEXT -1 1011 " Click on the ` `Help'' box, and then on the choice ``New User's Tour''. Probably th is tour will superimpose onto your current Maple session. Or maybe yo u can't see the new tour because it's hidden behind your current windo w. In the latter case use the ``window'' menu option to change window s. The tutorial give examples from many areas of mathematics, includ ing linear algebra, which you can peruse at your leisure. In this tour you will be able to put your cursor onto any command line, type retur n, and see what the command does. If you wish you can explore now, or you can continue with these notes below and come back to the tour lat er. There are not very many examples in the subheading ``linear algeb ra'', and they might not all make sense to you this early in our cours e, but you might want to look at them anyway. To close the new tour ( or any other top window), use the ``close'' option inside the ``file'' menu item, or use an option in the ``window'' box to return to your c urrent session." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 274 55 "5b) Getting an on-line copy of this Math 2270 project: " }{TEXT -1 68 " This xeroxed project has been saved \+ in two different formats, at " }{TEXT 269 53 "http:/www.math.utah.edu/ ~korevaar/2270fall00proj1.txt" }{TEXT -1 5 " and " }{TEXT 313 54 "http :/www.math.utah.edu/~korevaar/2270fall00proj1.mws " }{TEXT 315 1 "." } {TEXT 314 2 " " }{TEXT 320 655 "The first file is in \"Maple text\" f ormat, and will be easier to read from your browser. The second file \+ is in \"Maple work sheet\" format, and will look ugly in your browser, but if you're lucky (or working in the computer lab) your own Maple w ill be able to open it directly once you save it from the internet. \+ The advantage of the second (\".mws\") format is that plots, formattin g and output are reproduced exactly as in your xerox copy. The disadv antage is that some computers may not be able to understand it. The a dvantage of the first (\".txt\") format is that it is more universal. \+ The disadvantage is that Maple output and formatting often lost. " } {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 24 " For now, go to the " }{TEXT 321 6 "second" }{TEXT -1 362 " web address (\"....mws\") usi ng your browser window. Then, if you're using netscape as your brow ser, pick the ``file'' menu option, choosing ``save as''. Unless you give another name for it you will now save this document with the sa me name it has on the web, namely ``2270fall00proj1.mws''. It creates a copy of this file in your home directory. Do it. " }}{PARA 0 "" 0 "" {TEXT -1 107 " Now return to your Maple window and use the `` file'' menu item to open``2270fall00proj1.mws'': Choose" }{TEXT 324 6 " open " }{TEXT -1 9 "from the " }{TEXT 325 4 "file" }{TEXT -1 14 " \+ menu option. " }{TEXT -1 174 "The default expectation of Maple is Mapl e Worksheet Documents, so \"2270proj1.mws\" should appear as a choice \+ in the central box. (If you don't see this file, make sure that i" } {TEXT -1 6 "n the " }{TEXT 322 9 "open file" }{TEXT -1 17 " dialog box the " }{TEXT 323 9 " filetype" }{TEXT -1 365 " at the bottom is \"Ma ple Worksheet\".) Click on \"2270proj1.mws\" with the mouse to highl ight it and then click ``OK'' or type ``return''. A copy of this proj ect should then appear in your Maple window, as a Maple document that \+ you can work in. Possibly Maple has hidden it behind another file, in which case you can use the \"Window\" menu item to bring it forward. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 311 " \+ (Only follow the directions in this paragraph if you could not open t he \".mws\" file: Save \"2270fall00proj1.txt\" from the internet. T hen return to your Maple window and use the ``file'' menu item to ope n``2270fal00proj1.txt''. In order to open a ``Maple text'' document, \+ which this is, you must chose " }{TEXT 316 4 "open" }{TEXT -1 10 " fr om the " }{TEXT 317 4 "file" }{TEXT -1 32 " menu option. In the resul ting " }{TEXT 318 9 "open file" }{TEXT -1 22 " dialog box go to the " }{TEXT 319 9 " filetype" }{TEXT -1 599 " box at the bottom, click on t he triangle to see the list of choices, and use your mouse to choose ` `Maple text.'' At this point ``2270fall00proj1.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 project \+ should then appear in your Maple window, as a Maple document that you \+ can work in. The copy is not as pretty as your xerox (the execution g roups are all single lines, and the text formatting is not as neat, an d some output may be lost), but it is O.K. It has text and it has Map le input.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 276 28 "5c) Using help, an example :" }{TEXT -1 220 " You may proceed whether or not you created a copy of 2270fall00proj1.mws in your own \+ directory and opened from Maple. In future projects you will want to \+ be able to work off of the web, however, as indicated in (5b). " } {TEXT 275 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 163 " Let's illustrate some material from chapter 1, and the usefulness of help windows. Can Maple do matrix operations, or e ven define matrices???? Of course!!!" }}{PARA 0 "" 0 "" {TEXT -1 37 " Let's try to find the right commands:" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 133 " Click on the Help option at the upper right corner of your Maple window. A little window opens with \+ further choices. Pick the " }{TEXT 278 10 "Using Help" }{TEXT -1 183 " choice, click on it, and a help window should appear. (If it doesn' t, it's hidden behind your worksheet; use the ``window'' option in you r menu to bring it to the front.) Click on " }{TEXT 279 11 "Mathemati cs" }{TEXT -1 137 " from your choices at the top left of the help win dow (use scroll bar if necessary), then make successive choices so tha t you've done: " }{TEXT 280 44 "Mathematics/Linear Algebra/linalg.../ matrix." }{TEXT -1 447 " At this point you should get a help window a bout the matrix command. It is often helpful to skim to the bottom of such windows to look at examples, and then to return to the detailed \+ instructions above as necessary. At the bottom of this window you wi ll see that there are at least two ways to enter matrices, and that ma trix operations are a subset of a library of commands from the package ``linalg''. We load this package with the command" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "with(lina lg); #to hide the list of commands in this\n #package use a colo n instead of a semicolon" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 91 "And now we copy the commands from the help window: (For long ones we would use our mouse!)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "matrix(2,2,[5,4,6,3]); #a 2 by 2 matrix with\n # successive entries as indicated" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"AG-%'matrixG6#7$7$\"\"&\"\"%7$\"\"'\"\"$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "matrix([[5,4],[6,3]]); #same matrix" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"&\"\"%7$\"\"'\"\"$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "So that's how to make a matrix. T o find out more about the help windows, click on " }{TEXT 277 26 "Help /Using Help/Help Guide" }{TEXT -1 83 ". You can use the index, as we \+ did above, or you can do various key-word searches." }}}{PARA 0 "" 0 " " {TEXT -1 62 " To close the help files after you've used them use the ``" }{TEXT 261 11 "file/close " }{TEXT -1 222 "'' sequence in the toolbar, or the equivalent key stroke given next to it, which is simu ltaneous ``control-F4'' on my work station. Or you can keep them arou nd and return to your worksheet with the ``window'' menu option." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 281 3 "5d)" } {TEXT -1 1 " " }{TEXT 282 36 " Some Linear Algebra computations: " } {TEXT -1 430 " Can you figure out the syntax of the commands and their meanings? Some of these commands will be useful in part 6 below, whe re you are to do actual problems. Use the help windows for more detai ls about the commands. This example is worked on page 55 of the text, \+ by hand. Of course, the computer could work much larger systems almos t as easily as this one. When systems get too large, working them by \+ hand becomes cumbersome." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "A:=matrix([[1,2,3],[2,-1,1],[3,0,-1]]);\n #coefficient matrix fo r a linear system,\n #``:='' is used to define the object on\n \+ #its left by the construction on its right" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A[2,3]; #o ne of the entries of A" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "b:=vector([9,8,3]); #the right-han d side for\n #a linear system Ax=b" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "augAb:=augment(A,b); #the augmented matrix" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "C:=rref(augAb); #compute the reduc ed row echelon form\n #of the augmented matrix" }}{PARA 11 "" 1 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "x:=col(C, 4); #read off the solution vector to Ax=b " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 192 "evalm(A&*x)=evalm(b); #check your answer\n \+ #NOTE to do matrix operations use the evalm\n #command. Addition is +, but matrix multiplication\n #is &*. (Scalar times matrix \+ is *.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "x:=linsolve(A,b); another way to solve linear systems." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Ainv:=inverse(A) ; #the inverse matrix (it it exists)!" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "x:=evalm(Ainv &* b); \+ #yet another way, for nonsingular matrices,\n #to solve Ax=b" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "evalm(A&*Ainv); evalm(Ainv&* A); #just checking!" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "evalm(A^3); evalm(A&*A&*A), evalm( A+3*A); \n transpose(A); \n #matrix powers, multiplicatio ns, addition,\n #transpose " }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 270 36 "6) Your actual homework on Mapl e: " }{TEXT -1 57 "(These are modified from problems on page 27 of t he text " }{TEXT 284 36 "Multivariable Mathematics with Maple" }{TEXT -1 315 ", by J.A. Carlson and J.M Johnson.) You are to create a docum ent in which you answer the following questions, via a mixture of Mapl e computations and textual insertions. You are to print out a copy of this document to hand in, as your first Maple project. Don't forget \+ to put your name and section number on it! " }}{PARA 0 "" 0 "" {TEXT -1 15 " Define " }{TEXT 283 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'7%\"\"(\" \")\"\"*" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7%7%\"\"#\"\"\"\"\"!7%F+F*F+7%F,F+F* " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 43 "1a) Compute AB and BA. Are they the sam e?" }}{PARA 0 "" 0 "" {TEXT -1 45 "1b) Compute A+B and B+A. Are they the same?" }}{PARA 0 "" 0 "" {TEXT -1 235 "1c) Define C to be A+B. \+ Compute C^2 and compare it to A^2 + 2AB + B^2. Are they the same? Ca n you think of a small change you could make in the expression ``A^2 + 2AB + B^2'' in order to make it equal to C^2? Justify your answers! " }}{PARA 0 "" 0 "" {TEXT -1 169 "1d) Compute the transpose of AB and \+ compare it to the product of the transpose of A with the transpose of \+ B, multiplied in the correct order so that you expect equality." }} {PARA 0 "" 0 "" {TEXT -1 93 "1e) Define v=(1,2,3) to be a vector. Co mpute Av. What does Maple give you when you try vA?" }}{PARA 0 "" 0 " " {TEXT -1 236 "1f) Solve Bx=v for x, where v is the vector in (1d). \+ Get your solution all three ways that were indicated in section (5d): by row-reducing the augmented matrix, by using the command ``linsolv e'', and by using the inverse matrix to B." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 136 "2a) Solve Ax=v for x, where A \+ and v are as indicated above. Verify, with Maple, that your solution \+ x actually solves the equation Ax=v." }}{PARA 0 "" 0 "" {TEXT -1 91 "2 b) Repeat your work above in order to solve Ax=w, where w=(-1,4,1). \+ Explain your answer." }}}{MARK "68 1" 43 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }