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0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 263 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Author" -1 264 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 8 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 265 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 260 "" 0 "" {TEXT -1 10 "Lecture 1 " }}{PARA 264 "" 0 "" {TEXT -1 12 "Click on a " }{TEXT 406 1 "+" }{TEXT -1 41 " to open a section. You may click on the" }{TEXT 435 2 " -" }{TEXT -1 72 " to close the section. This will be useful for clearing up some space . " }}{PARA 264 "" 0 "" {TEXT -1 178 "As you read this worksheet, exp eriment with the commands. Use the mouse to change symbols. Re-execut e the commands by placing the cursor on the line of interest and hitti ng the " }{TEXT 392 6 "Return" }{TEXT -1 84 " key again. From time to \+ time try your hand at typing in and executing new commands." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 26 "Controlling the Font Size " }}{PARA 0 " " 0 "" {TEXT -1 215 "The size of the fonts in this worksheet may be ad justed to by clicking on one of the three magnifying glasses on the m enu at the top of this worksheet. For a wider selection of font sizes \+ use one of the following " }{TEXT 501 60 "ctrl + 1, ctrl + 2, ctrl + \+ 3, ctrl + 4, ctrl + 5, ctrl + 6. " }{TEXT -1 10 "[Note that" }{TEXT 502 10 " ctrl + i " }{TEXT -1 19 "means to press the " }{TEXT 504 4 "c trl" }{TEXT -1 5 " and " }{TEXT 505 2 "i " }{TEXT -1 23 "keys at the s ame time.]" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 122 "You may wish to use a larger font size while working on the wo rksheet and a smaller size, for example, the smallest size (" }{TEXT 503 8 "ctrl + 1" }{TEXT -1 61 ") when printing to save paper and make \+ your notebook thinner." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "What is Maple?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 260 5 "Maple" }{TEXT -1 4 " is \+ " }{TEXT 256 17 "what is called a " }{TEXT 437 24 "Computer Algebra S ystem" }{TEXT 438 13 " (for short: " }{TEXT 439 3 "CAS" }{TEXT 436 2 " )." }{TEXT -1 37 " That is, it manipulates information " }{TEXT 257 12 "symbolically" }{TEXT -1 4 " or " }{TEXT 258 13 "algebraically" } {TEXT -1 122 " as opposed to just numerically. Nevertheless, it does \+ have numerical manipulation abilities. In this course we will use " } {TEXT 259 9 "Maple 8. " }{TEXT -1 1 " " }{TEXT 324 7 "Maple 7" }{TEXT -1 84 " was the previous version of Maple and it uses essentially the \+ same syntax. Before " }{TEXT 335 5 "Maple" }{TEXT -1 8 " 7 were " } {TEXT 336 8 "Maple 6 " }{TEXT -1 3 "and" }{TEXT 506 8 " Maple V" } {TEXT -1 49 ". Significant changes were made when going from " } {TEXT 326 7 "Maple V" }{TEXT -1 4 " to " }{TEXT 327 7 "Maple 6" } {TEXT -1 124 ", so you should be sure of the version you are using. So me differences in syntax will be pointed out as we proceed. See the " }{URLLINK 17 "Maple Links" 4 "http://www.math.usf.edu/~eclark/maple_li nks.html" "" }{TEXT -1 122 " on the course webpage or my homepage for \+ more information about the history of Maple and Maple resources on the internet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "For those who are interested, the kernel of Maple is written in the " }{TEXT 261 2 "C " }{TEXT -1 150 "language. But most of the func tions in Maple are written in Maple and can be viewed and manipulated \+ by the user. We will discuss how to do this later." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Perhaps the program most \+ similar to " }{TEXT 337 5 "Maple" }{TEXT -1 4 " is " }{TEXT 338 11 "Ma thematica" }{TEXT -1 176 ". However, there are many other such program s available. Some like Maple and Mathematica are quite general and som e are more specialized. For a more comprehensive list see the " } {URLLINK 17 "List of Computer Algebra Systems" 4 "http://sal.kachinate ch.com/A/1/ " "" }{TEXT -1 21 " by Herng-Jeng Jou. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Maple as a Calculator" }}{PARA 0 "" 0 "" {TEXT -1 30 "Maple may be us ed as simply a " }{TEXT 263 10 "calculator" }{TEXT -1 108 " with graph ing capabilities: We illustrate this capability first. Later we will \+ show how to use Maple as a " }{TEXT 264 22 "programming language.\n" } }{PARA 0 "" 0 "" {TEXT -1 100 "To start Maple on most platforms just d ouble click on the Maple icon. (In Unix systems one may type " }{TEXT 328 6 "xmaple" }{TEXT -1 83 " from a command line to open Maple). When Maple opens, you are in what is called a " }{TEXT 323 15 "Maple works heet" }{TEXT -1 45 ". Names of Maple worksheets usually end in " } {TEXT 325 4 ".mws" }{TEXT -1 71 ". I am now typing this lecture in a M aple worksheet which I have named " }{TEXT 339 15 "fall2002_01.mws" } {TEXT -1 2 ".\n" }}{PARA 0 "" 0 "" {TEXT -1 355 "\"Execute\" each of t he commands (in red) below by placing the cursor anywhere on the line, then hitting the return key. If you have done this correctly you sho uld see the answer in blue. Also the cursor will move to the next line . Hit the return key again to execute the next line. Continue to do th is. The first commands show how to do simple arithmetic." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 48 "Note that each c ommand ends with a semi-colon. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 82 "Try to guess the output, before executing a command when possible. Note that this " }{TEXT 442 3 "tex" }{TEXT -1 5 "t is " }{TEXT 440 5 "black" }{TEXT -1 6 ", the " }{TEXT 443 5 "i nput" }{TEXT -1 4 " is " }{TEXT 441 3 "red" }{TEXT -1 9 " and the " } {TEXT 444 6 "output" }{TEXT -1 48 " is blue. One can enter the text mo de by either " }{TEXT 452 6 "ctrl-T" }{TEXT -1 18 ", clicking on the \+ " }{TEXT 453 1 "T" }{TEXT -1 35 " in the menu above, or by going to " }{TEXT 454 6 "Insert" }{TEXT -1 27 " on the menu and selecting " } {TEXT 455 4 "Text" }{TEXT -1 14 ". Look under " }{TEXT 456 6 "Insert " }{TEXT -1 62 " again to see the other options. See the section below titled " }{TEXT 458 36 "Inserting prompts and shortcut keys." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3*4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2^5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "2^(1/3);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "12/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "1 1/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "11.0/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 179 "Notice the effect of changing 11 to 11.0. Generally Maple uses exact arithmetic unless you use numbers containing decimal points and then it switches to floating point arithmetic." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "3-4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3+4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 330 11 "IMPORTANT: " }{TEXT 445 24 "Maple is cas e sensitive." }{TEXT -1 114 " So, for example, ABC, ABc, AbC, Abc, aBc , Abc, etc, are all different so far as Maple is concerned. \n\nMaple \+ uses " }{TEXT 329 2 "Pi" }{TEXT -1 31 " (not pi) to denote the number \+ " }{XPPEDIT 18 0 "pi:" "6#%#piG" }{TEXT -1 44 ". We can get a floating point evaluation of " }{XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 16 " b y the command " }{TEXT 341 10 "evalf(Pi) " }{TEXT -1 29 "as in the fol lowing examples:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalf(pi); #pi is not equal to Pi" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Note " }{TEXT 446 1 "#" }{TEXT -1 63 " may be used for co mments as we just did. Everything following " }{TEXT 447 1 "#" }{TEXT -1 89 " on a line is ignored by Maple. However, it looks better to use the text mode. Note that " }{TEXT 448 2 "pi" }{TEXT -1 5 " and " } {TEXT 451 2 "Pi" }{TEXT -1 16 " both appear as " }{XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 35 ". This is an exception since alpha" }{TEXT 449 2 ", " }{TEXT -1 11 "Alpha, beta" }{TEXT 450 2 ", " }{TEXT -1 79 " Beta, gamma, Gamma, delta, Delta, etc, appear in output as the Greek \+ letters, " }{XPPEDIT 18 0 "alpha,Alpha,beta,gamma,Gamma,delta,Delta;" "6)%&alphaG%&AlphaG%%betaG%&gammaG%&GammaG%&deltaG%&DeltaG" }{TEXT -1 6 ", etc." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "We can get 1000 decimal digits of " } {XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 12 " as follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf[1000](Pi);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(Pi), evalf[10](Pi);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "No te that " }{MPLTEXT 1 0 9 "evalf[10]" }{TEXT -1 22 " is the same thing as " }{MPLTEXT 1 0 5 "evalf" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Maple does not give a floating point number unless y ou specifically ask for it. For example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 195 "W e may get a floating point evaluation of the previous output as follow s. Note that % indicated the previous output. %% indicates the output \+ before that. The one before that is indicated by %%%. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 40 "We illustrate the use of % and %% below:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "1;" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "See if you can predict what will \+ be the output when the next line is executed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "%%;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "More \+ examples:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/5);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sin(Pi/37);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(16);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 684 "Maple has very high precision \+ arithmetic. However, if you push it too far, you will cause Maple to c rash or, if you are lucky, just to say, \" The object you asked for is too large.\" When I attempted to execute the following commands with Maple 6 on my Mac G-4 the first came back with a warning that I had u sed too much memory and should quit and restart Maple. The second cau sed Maple to crash. I would have lost everything if I had not saved th e worksheet before executing these two commands. I will place # before them to guard against accidental execution. (Maple ignores everything on a line after a #.) I'm not going to try it with Maple 8 since I \+ don't feel like rebooting." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "# 353^10000000;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# 353^1000;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Clicking on the " }{TEXT 457 4 "STOP" }{TEXT -1 173 " sig n on the menu bar will sometimes cause Maple to terminate the current \+ computation. It depends on the type of computation. We will see examp les later where it does work." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 262 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 35 "Inserting Prompts and Shortcut Keys" }}{EXCHG {PARA 264 " " 0 "" {TEXT -1 88 "You may insert new prompts before or after the cur sor by clicking on the button labeled " }{TEXT 407 2 "[>" }{TEXT -1 46 " on the menu bar or by going to the menu item " }{TEXT 408 6 "Inse rt" }{TEXT -1 19 " and going down to " }{TEXT 409 15 "Execution Group " }{TEXT -1 21 " and choosing either " }{TEXT 410 13 "Before Cursor" } {TEXT -1 4 " or " }{TEXT 411 12 "After Cursor" }{TEXT -1 71 ". If you do this a lot you may want to learn the keyboard short cuts. " }} {PARA 264 "" 0 "" {TEXT -1 16 "Using Windows, " }{TEXT 412 8 "ctrl + \+ j" }{TEXT -1 43 " will insert a prompt after the cursor and " }{TEXT 413 8 "ctrl + k" }{TEXT -1 47 " will insert one before the cursor. (No te that " }{TEXT 459 8 "ctrl + j" }{TEXT -1 38 " means to hold down t he keys labeled " }{TEXT 460 4 "ctrl" }{TEXT -1 5 " and " }{TEXT 461 1 "j" }{TEXT -1 19 " at the same time.)" }}{PARA 264 "" 0 "" {TEXT -1 41 "To see a list of all key shortcuts go to " }{TEXT 414 18 "Help, To pic Search" }{TEXT -1 14 " and type in " }{TEXT 415 13 "shortcut_keys " }{TEXT -1 92 ". Then click on the item for Macintosh, Windows or Uni x depending on what computer you have." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 32 "Removing Output from a Worksheet" }}{PARA 0 "" 0 "" {TEXT -1 89 "Sometimes one want to cle ar the output from the worksheet when it becomes too cluttered. " }} {PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 416 110 "YOU DO NOT WANT TO DO \+ THAT NOW SINCE YOU WILL HAVE TO PRINT OUT THE OUTPUT IN THIS WORKSHEET FOR YOUR NOTEBOOK" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 29 "This can be done by going to " }{TEXT 417 4 "Edit" }{TEXT -1 48 " on the menu at the top. Drag the mouse dow n to " }{TEXT 418 13 "Remove Output" }{TEXT -1 43 " and with the mouse still held down select " }{TEXT 419 16 "From Worksheet. " }{TEXT -1 68 "When you release the mouse button all of the output will be remove d." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT 265 31 "More Use of Built-in Functions:" }{TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 143 "The following commands should be self e xplanatory. Execute each in turn. In some cases you may guess the out put. Note the different effect of " }{TEXT 462 4 "Diff" }{TEXT -1 4 " \+ vs " }{TEXT 463 4 "diff" }{TEXT -1 8 " and of " }{TEXT 464 3 "Int" } {TEXT -1 4 " vs " }{TEXT 465 3 "int" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(sin(x),x);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 42 "Diff(arctan(2*x),x) = diff(arctan(2*x),x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Diff(arctan(a*x),x) = diff(a rctan(a*x),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Note that in t his case Maple uses the symbol for partial derivative because of the p resence of the variable " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT -1 16 " in the formula." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "int(x^3 ,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(x^3,x=1..2);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Int(x^3,x=1..2) = int(x^3,x=1..2);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "An alternative way to achieve this is via the following two commands." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Int(x^3,x=1..2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "%=value(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "T he following can be used to solve an equation." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "solve(2*x^3+x^2+x-1=0,x);" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 34 "Here I denotes the complex number " }{XPPEDIT 18 0 "sqrt(-1);" "6#-%%sqrtG6#,$\"\"\"!\"\"" }{TEXT -1 79 ". These three solutions can be converted to floating point numbers as follows:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Next we solve a differential equation. First we d efine the equation. We call it ODE." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ODE := diff(y(x),x)-y(x) = sin(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "dsolve(ODE);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "We will discuss the various uses of " }{TEXT 340 13 "solv e, dsolve" }{TEXT -1 87 " and other Maple commands for solving various kinds of equations in more detail later. " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 28 "Right Clicking on the Output" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Af ter executing each of the following commands " }{TEXT 469 11 "right cl ick" }{TEXT -1 8 " on the " }{TEXT 470 6 "output" }{TEXT -1 211 " and \+ try several of the options that appear in the little pop-up window. N ote that this will also cause the appropriate command to be typed in r ed. We will see later the significance of the colon equals symbol " } {TEXT 471 2 ":=" }{TEXT -1 65 " . All of these commands will be gone \+ into in more detail later." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "First we have a simple expression." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Pi*sin(x)*cos(x) + sqrt(2)*x;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Next we have an equation." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "x^2+2*x+2=3*x^2+5*x+7;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 19 "Elementary Plotting" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 98 "This is a brief introduction to the Maple plotting functions. We will go into more details later. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "First we plot the \+ graph of " }{XPPEDIT 18 0 "y = x^3+x^2+x+1;" "6#/%\"yG,**$%\"xG\"\"$\" \"\"*$F'\"\"#F)F'F)F)F)" }{TEXT -1 28 " for x in the range [-1,1] ." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(x^3+x^2+x+1,x=-1..1); \n" }{TEXT -1 26 "After executing thi s line " }}{PARA 0 "" 0 "" {TEXT -1 3 "1. " }{TEXT 468 10 "Left click " }{TEXT -1 180 " on the plot with the cursor. Then drag the lower rig ht corner of the frame upward to the left to make the size of the plot smaller. This will help to save space in the worksheet. " }}{PARA 0 " " 0 "" {TEXT -1 3 "2. " }{TEXT 467 11 "Right click" }{TEXT -1 73 " on \+ the plot and when the little window pops up try the various options: \+ " }{TEXT 466 19 "style, legend, axes" }{TEXT -1 6 ", etc." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Now we plot the graph of the surface " } {XPPEDIT 18 0 "z = cos(x^2+y^2);" "6#/%\"zG-%$cosG6#,&*$%\"xG\"\"#\"\" \"*$%\"yGF+F," }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plot3d(cos(x^2+y^2), x=-Pi/2 ..Pi/2,y=-Pi/2..Pi/2);\n" }}{PARA 0 "" 0 "" {TEXT -1 123 "1. Before co ntinuing make this plot smaller also as you did the previous one to sa ve paper when you print this worksheet. " }}{PARA 0 "" 0 "" {TEXT -1 3 "2. " }{TEXT 472 11 "Right click" }{TEXT -1 67 " on the picture. Th en using the mouse you can rotate the surface. " }}{PARA 0 "" 0 "" {TEXT -1 136 "3. Also when you click on the plot you will see a new ro w on the menu bar. Click on some of the icons to see the effect on the picture. " }}{PARA 0 "" 0 "" {TEXT -1 23 "4. You should also try " } {TEXT 473 15 "right clicking " }{TEXT -1 120 "on the plot and trying s ome of the options that appear there. Many of these are the same ones \+ you found in item 3 above." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "La ter We will have lots more to say about piloting curves and surfaces. \+ So don't try to learn all the options at this time." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Here are some m ore self-explanatory built-in functions. Execute these." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "ln(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(ln(x), x=.3..4);\n" }{TEXT -1 51 "After executing this comman d make the plot smaller." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 11 " Maple for " }{XPPEDIT 18 0 "e^x;" "6#)%\"eG%\"xG " }{TEXT -1 7 " and " }{XPPEDIT 18 0 "e;" "6#%\"eG" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Note that Maple does not recogni ze the symbols " }{XPPEDIT 18 0 "exp(1);" "6#-%$expG6#\"\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "exp(x);" "6#-%$expG6#%\"xG" }{TEXT -1 67 " as having the usual meaning from calculus. Instead one must use " }{TEXT 434 6 "exp(x)" }{TEXT -1 5 " for " }{XPPEDIT 18 0 "exp(x)" "6#- %$expG6#%\"xG" }{TEXT -1 5 " and " }{TEXT 474 5 "exp(1" }{TEXT -1 7 ") for " }{XPPEDIT 18 0 "exp(1)" "6#-%$expG6#\"\"\"" }{TEXT -1 49 ", as in the following. Note the output DOES give " }{XPPEDIT 18 0 "exp(1); " "6#-%$expG6#\"\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "exp(x);" "6# -%$expG6#%\"xG" }{TEXT -1 51 ". Execute the following commands and yo u will see." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(exp(x), x=-1..2);\n" }{TEXT -1 51 "After executi ng this command make the plot smaller." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Shrink the above plot before continuing.\n\nBut note the \+ failure of the following commands:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(e);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(e^x,x=-1..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 157 "This i s because Maple does not know what e^x is. It considers e to be some u nknown number. However, is we replace e by a specific number there is \+ no trouble:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "diff(2^x,x); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(2^x,x=-1..2);\n" } {TEXT -1 55 "Make the plot smaller after executing the plot command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "Basic \+ Worksheet Handling" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 256 "" 0 "" {TEXT 279 70 "Here I indicate how to start a new worksheet , make a title, indicate " }{TEXT 278 102 "author, insert Standard Ma th (that is, a mathematical formula) in text, and how to save a works heet. " }{TEXT 280 1 " " }{TEXT -1 2 "\n\n" }{TEXT 272 9 "1. Under " } {TEXT 274 4 "File" }{TEXT 275 20 " on the menu choose " }{TEXT 276 3 " New" }{TEXT 273 17 " or click on the " }{TEXT 277 16 "blank page icon \+ " }{TEXT 281 42 "on the menu bar. This opens a new page. " }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 342 30 "2. Next g o to the menu named " }{TEXT 343 6 "Window" }{TEXT 344 18 " and pull d own to " }{TEXT 345 8 "Vertical" }{TEXT 346 194 ". This will allow you to read this worksheet while following these directions in the new wo rksheet. Click on the blank worksheet to make sure the cursor is ther e and not in this worksheet.\n\n3. " }{TEXT 475 5 "Press" }{TEXT 476 10 " crtl + t " }{TEXT 282 16 "or click on the " }{TEXT 267 1 "T" } {TEXT 283 76 " icon on the menu bar. Then, on the left side of the men u bar where it says " }{TEXT 266 8 "P Normal" }{TEXT 284 45 " pull dow n the menu at that point and select " }{TEXT 268 7 "P Title" }{TEXT 318 2 ". " }{TEXT 285 18 "Type in the words " }{TEXT 347 12 "Sample Ti tle" }{TEXT 348 43 " and then hit return. This will put you in " } {TEXT 269 8 "P Author" }{TEXT 286 34 " mode. Type your name and the hi t " }{TEXT 331 6 "Return" }{TEXT 332 2 ". " }{TEXT 287 19 "You will no w be in " }{TEXT 319 8 "P Normal" }{TEXT 320 57 " text mode. Type the words \"Some sample Maple commands.\"" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 322 17 "4. Next click on " }{TEXT 270 2 "[>" }{TEXT 349 1 " " }{TEXT 288 9 "or press " }{TEXT 477 6 "ctrl + " }{TEXT 478 56 " . [Sometimes you may want to insert an execution gro up " }{TEXT 271 6 "before" }{TEXT 321 11 " the cursor" }{TEXT 289 65 " --especially if you are at the top of the page. Then you may use " } {TEXT 479 8 "ctrl + k" }{TEXT 480 4 ".]\n " }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 351 81 "When you see the prompt, i.e., >, then type \+ in some mathematical command such as " }{MPLTEXT 1 0 6 "2^100;" } {TEXT -1 2 ". " }{TEXT 350 70 "Then hit return to execute this command . Try a few more such command. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 57 "5. Go back to the text mode by repeating \+ clicking on the " }{TEXT 352 1 "T" }{TEXT -1 32 " in the menu bar or b y pressing " }{TEXT 481 8 "ctrl + t" }{TEXT -1 65 ". Type in the word s \"We now compute the integral\" .\n\nNext press " }{TEXT 482 8 "ctrl + r" }{TEXT -1 104 ". You will see a ?. Now type in int(x^2,x=1..2) you will see this appear in a box under the menu bar. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "Now " }{TEXT 483 8 "c trl + t" }{TEXT -1 165 " again or click on the T to go back into ordin ary text mode and continue to type the words \"as follows\". You shou ld see the following:\n\nWe now compute the integral " }{XPPEDIT 18 0 "int(x^2,x = 1 .. 2);" "6#-%$intG6$*$%\"xG\"\"#/F';\"\"\"F(" }{TEXT -1 14 " as follows. \n" }}{PARA 0 "" 0 "" {TEXT -1 14 "6. Then press \+ " }{TEXT 484 8 "ctrl + j" }{TEXT -1 13 " or click on " }{TEXT 485 2 "[ >" }{TEXT -1 79 " to go back into execution mode. When the cursor com es up type in the command " }{MPLTEXT 1 0 16 "int(x^2,x=1..2);" } {TEXT -1 45 " then execute the command by hitting return. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "7. To save your \+ new worksheet go under " }{TEXT 290 4 "File" }{TEXT -1 12 " and choose " }{TEXT 291 4 "Save" }{TEXT -1 172 " (or click on the icon that look s like a floppy disk on the menu bar). The first time you will be prom pted to give a name. Use a single word with no spaces and end it with \+ " }{TEXT 293 4 ".mws" }{TEXT -1 16 ". For example, " }{TEXT 292 15 "Y ourName01.mws " }{TEXT -1 116 "would be a possible name for a Maple fi le. If you look at the top of this page you will see the name of this file: " }{TEXT 333 15 "fall2002_01.mws" }{TEXT -1 47 ". That's the n ame I originally gave this file." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 95 "8. If you want to start a new worksheet k eeping what you already have in a named worksheet use " }{TEXT 294 8 " Save As " }{TEXT -1 12 "instead of " }{TEXT 295 5 "Save " }{TEXT 353 133 "and give the worksheet a new name. This way you can keep your old worksheet and experiment with changes without losing what you did. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Averting Disaster" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "After a worksheet has been named , you should still save it frequently by clicking on the icon of the f loppy disk which is on the menu bar or using " }{TEXT 420 4 "Save" } {TEXT -1 7 " under " }{TEXT 421 4 "File" }{TEXT -1 22 " or easiest: pr essing " }{TEXT 486 8 "ctrl + s" }{TEXT -1 136 "--to guard against los ing work if Maple crashes. Note that you will not need to change the n ame after you have saved it the first time. " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 35 "Using Several Worksheets at a Time." }}{PARA 0 "" 0 "" {TEXT -1 26 "Under the menu item named " }{TEXT 354 6 "Window" } {TEXT -1 33 " you will find the three options " }{TEXT 355 41 "Cascade , Tile, Horizontal, and Vertical. " }{TEXT -1 268 "To see the effect o f these first open several different worksheet in succession. An easy way to do this is just by clicking on the blank page icon on the menu bar. But you may also open any worksheets. Then select each of these options. You will see what they do. \n\n" }{TEXT 356 15 "Important Fa ct:" }{TEXT -1 219 " Assignments made in one open worksheet are recogn ized by all open worksheets. When switching worksheets be sure you hav e clicked with the cursor in the worksheet you want to work in before \+ continuing in that worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 357 28 "Cutting, Copying and Pasting" }{TEXT -1 115 ": You may cut, copy and paste from a worksheet to itself or from \+ one worksheet to another using the commands under " }{TEXT 422 5 "Edit " }{TEXT -1 38 "as you would in most word processors." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Maple's Built-in Help" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 257 "" 0 "" {TEXT 300 13 "Getti ng Help:" }{TEXT 296 129 " Perhaps the easiest way is to use a questio n mark as follows: Here we suppose we forgot the command for different iate. We guess " }{TEXT 302 11 "that it is " }{TEXT 297 71 "dif. Type and execute the following command by hitting the Return key." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?dif" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 423 45 "This will bring u p several options including " }{TEXT 424 4 "diff" }{TEXT 425 1 "." } {TEXT -1 1 " " }{TEXT 334 23 " Now, you can click on " }{TEXT 428 4 "d iff" }{TEXT 429 30 " or go back and add and extra " }{MPLTEXT 1 0 1 "f " }{TEXT 427 4 " to " }{MPLTEXT 1 0 4 "?dif" }{TEXT 426 340 " and re-e xecute. In any event you will be led to the help page for diff. If yo u scroll down you will see a number of examples. This will often be en ough. In some cases however you may need to read the entire help page \+ carefully. If you execute a single question mark (as follows) you will bring up some general information on getting help." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 208 "Usually you would just like to see some examples of how a command is \+ used in this case use three question marks and it will take you direct ly to the examples at the bottom of the help page. Here's an example: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "???diff" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "\nFor another example: Suppose that you \+ want to know how to factor an integer or a polynomial: Then you could \+ try:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?factor" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Notice that the help page that comes up says that " }{TEXT 298 6 "factor" } {TEXT -1 67 " is used to factor polynomials and not integers. It tells you that " }{TEXT 299 7 "ifactor" }{TEXT -1 53 " is used to factor in tegers. Here are some examples.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factor(t^2-t-2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(123456789);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ifactor(123456789);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 430 24 "Other ways to get help: " }{TEXT -1 37 "You may do a ful l text search of the " }{TEXT 308 16 "Maple Help Files" }{TEXT -1 13 " by going to " }{TEXT 303 4 "Help" }{TEXT -1 34 " on the menu bar and \+ pull down to " }{TEXT 301 17 "Full Text Search " }{TEXT 431 2 "or" } {TEXT 432 16 " Topic Search.\n\n" }{TEXT 304 59 "Another way is to sel ect a word of interest and then go to " }{TEXT 305 4 "Help" }{TEXT 306 34 " on the menu bar and pull down to " }{TEXT 307 17 "Help on Con text. " }{TEXT 487 43 "Instead you may select the word and execute" } {TEXT 488 11 " ctrl + f1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 29 "The Use of := , = , : , and ;" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "The expression " } {TEXT 316 4 "x:=2" }{TEXT -1 54 " means \"assign 2 to the variable x. \" The expression " }{TEXT 489 5 "x:=2 " }{TEXT 490 37 "is called an \+ \"assignment statement\". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Here are some examples: We make two assignments: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "x:=2; \ny:=3;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Now let's see what the values of x and y are:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 88 "Now x is 2 and y is 3 so far as Maple is concerned. So \+ if you try to solve the equation " }{XPPEDIT 18 0 "x^2+x+1 = 0;" "6#/, (*$%\"xG\"\"#\"\"\"F&F(F(F(\"\"!" }{TEXT -1 20 " Maple is confused:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+x+1=0,x);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Clearing x of the value 2 may be a ccomplished as follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x :='x';" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Now you see that x is j ust x. It no longer stands for the number 2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "We can now solve the equation:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+x+1=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Note the \+ use of " }{TEXT 363 1 "=" }{TEXT -1 15 " as opposed to " }{TEXT 364 2 ":=" }{TEXT -1 17 " in the equation " }{TEXT 365 15 "x^2 + x + 1 = 0" }{TEXT -1 35 ". We can even assign a name, say, " }{TEXT 366 4 "eqn \+ " }{TEXT -1 17 "to this equation:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eqn:=x^2+x+1=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(eqn,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 208 "We can assign values to several variables at a time as in the fol lowing command. Actually the parentheses in this line are not necessar y, but are included for clarity. Notice they do not appear in the outp ut." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "(x,y,z):=(2,3,w+8); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "We can see the values of the \+ variables as follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x,y ,z;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Compare the above with:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x; y; z; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "The command " }{TEXT 317 9 "restart; " }{TEXT -1 74 " as noted above, is useful for clearing all variables and start ing afresh." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "(x,y):=45,86 74;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x,y;" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT 309 29 "Note that if a line en ds with" }{TEXT 312 3 " : " }{TEXT 315 12 " instead of " }{TEXT 313 3 " ; " }{TEXT 314 12 "the command " }{TEXT 310 39 "is executed, but the output is not show" }{TEXT -1 2 ". " }{TEXT 311 11 "Here is an " } {TEXT -1 8 "example:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "y:=14:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "t:=12; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "See what happens if you forge t the semi-colon at the end of the line:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "t:=2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 173 "You can \+ go back to the line t:=2 with the cursor and add the semi-colon or you may add it on the second line, where the cursor has moved to, before \+ re-executing the command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 41 "Functions (Procedures) versus Expressions" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Ma ple has a large number of built-in functions (also known as " }{TEXT 360 10 "procedures" }{TEXT -1 17 ") . For example: " }{TEXT 358 81 "si n, cos, tan, cotan, sec, csec, arcsin, ln, exp, abs, sqrt, tan, facto rial, det" }{TEXT -1 151 " (determinant), and many more. These functi ons behave pretty much as you would expect. You can also make your ow n functions (that we will often call " }{TEXT 491 10 "procedures" } {TEXT -1 28 ") which we illustrate below." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 183 "The \"obvious\" way to make a fun ction, however, does not work. Suppose we want to define a new funct ion f satisfying f(x) = x^2 + x + 1 for all x. Try execute the followi ng command.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f(x):=x^2+x+1;\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 361 68 "This is NOT the way to do it. Not e what happens in the next command:" }{TEXT -1 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(%);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "T he object " }{TEXT 367 11 "x^2 + x + 1" }{TEXT -1 22 " is what is call ed an " }{TEXT 362 20 "algebraic expression" }{TEXT -1 141 ". We may p lot it, solve it, factor it, integrate it, differentiate it, and so f orth, but it is NOT a function so far as Maple is concerned. " }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "\nWhat we would like is for f(2) t o give us 7. " }{TEXT 493 54 "Here are three correct ways to define su ch a function." }{TEXT -1 2 " " }{TEXT 492 31 "You should learn each \+ of these." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 27 "Use of the arrow notation:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->x^2+x+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(a);" }}} {EXCHG {PARA 257 "" 0 "" {TEXT -1 17 "\nUse of unapply:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart: " }{TEXT -1 178 "(It is a g ood idea to restart after finishing one problem and starting on anoth er. This clears the internal memory. In this case, it let's us clear t he above definition of f. )\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=unapply(x^2+x+1,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(a);" }}} {EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 22 "Creating a procedure: " }{TEXT 359 103 "(This is very useful for c reating very complicated functions as we shall see as the course progr esses.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f:=proc(x)\n x^2+x+1;\nend proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(a );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 210 "We will use these ideas re peatedly in this course. So you should make absolutely sure you unders tand each of these three methods for constructing a function. Now is a good time to experiment with these methods." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 41 " Instructions for Printing this Worksheet" }}{EXCHG {PARA 0 "" 0 "" {TEXT 393 82 "If you have closed any section open them now. You may accomplish this by going to " }{TEXT 494 4 "View" } {TEXT 495 35 " on the top menu and going down to " }{TEXT 496 19 "Expa nd All Sections" }{TEXT 497 3 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 500 6 "Go to " }{TEXT 397 4 "File" }{TEXT 398 24 " on the menu and select " }{TEXT 399 5 "print" }{TEXT 400 51 ". Pr int this worksheet before you start working on " }{TEXT 401 12 "Assign ment 1" }{TEXT 402 8 " below. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 403 147 "Keep a loose-leaf notebook with all the printouts of the executed worksheets. The homework assignments must b e printed out separately and handed in" }{TEXT 404 151 ". After they a re returned they should also be kept in the note book together with th e solutions provided. I will check the notebooks from time to time." } {TEXT 396 1 " " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 265 "" 0 "" {TEXT -1 47 "After you have printed out the workshee t go to " }{TEXT 394 4 "View" }{TEXT -1 16 " and go down to " }{TEXT 395 21 "Collapse All Sections" }{TEXT -1 77 ". Then print again. This \+ will give you a printout of just the section names. " }{TEXT 405 108 " You should place this before the executed worksheet in your notebook \+ to serve as a rough table of contents." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 "Assignment 1 (Due Tuesday, September 3)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 368 10 "Problem 1." } {TEXT -1 50 " \n\n(a) Start a new worksheet. Make a title called " } {TEXT 371 12 "Assignment 1" }{TEXT -1 11 " using the " }{TEXT 372 1 "P " }{TEXT -1 1 " " }{TEXT 369 11 "Title style" }{TEXT -1 44 ". Follow t he heading by your name using the " }{TEXT 370 14 "P Author style" } {TEXT -1 34 ". [Look back at the above section " }{TEXT 373 24 "Basic \+ Worksheet Handling" }{TEXT -1 108 " if you don't recall how to do this .] \n \n(b) Still using the methods described above type in the follo wing " }{TEXT 433 8 "verbatim" }{TEXT -1 7 " using " }{TEXT 374 11 "In sert Text" }{TEXT -1 4 " or " }{TEXT 498 8 "ctrl + t" }{TEXT -1 5 " an d " }{TEXT 375 20 "Insert Standard Math" }{TEXT -1 4 " or " }{TEXT 499 9 "ctrl + r " }{TEXT -1 98 "to type in the comment containing the \+ integral: [Also execute each of the three Maple commands.]\n\n" } {TEXT 376 1 ">" }{MPLTEXT 1 0 9 " restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "It is easy to compute " }{MPLTEXT 1 0 0 "" }{XPPEDIT 18 0 "Int(x^2*sqrt(1-x^2),x = 0 .. 1);" "6#-%$IntG6$*&%\"xG\"\"#-%%sqrtG6 #,&\"\"\"F-*$F'F(!\"\"F-/F';\"\"!F-" }{TEXT -1 42 " using Maple. One s imply types the command" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " int(x^2*sqrt(1-x^2),x=0..1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "T o find the approximate floating point value of the integral we apply e valf as follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 377 11 "\nProblem 2." }{TEXT -1 1 " " }{TEXT 378 3 " \n\n" }{TEXT -1 25 "(a) Show using Maple that" } {TEXT 379 1 " " }{XPPEDIT 18 0 "sqrt(2)+sqrt(3) = pi;" "6#/,&-%%sqrtG6 #\"\"#\"\"\"-F&6#\"\"$F)%#piG" }{TEXT -1 39 " is correct to three dec imals digits, " }{TEXT 382 33 "but is not correct to more than 3" } {TEXT -1 6 ". Use " }{TEXT 388 11 "evalf[3](x)" }{TEXT -1 33 " to obta in x to 3 decimal digits." }}{PARA 0 "" 0 "" {TEXT -1 25 "\n(b) Assign the equation " }{XPPEDIT 18 0 "x^3-4*x^2-4*x-5 = 0" "6#/,**$%\"xG\"\" $\"\"\"*&\"\"%F(*$F&\"\"#F(!\"\"*&F*F(F&F(F-\"\"&F-\"\"!" }{TEXT -1 17 " to the variable " }{TEXT 389 3 "Eqn" }{TEXT -1 1 "." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "(c) Use " }{TEXT 387 5 "solve" }{TEXT -1 10 " to solve " }{TEXT 390 3 "Eqn" }{TEXT -1 18 " for the variable " }{TEXT 391 1 "x" }{TEXT -1 2 ". " }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 380 9 "Problem 3" }{TEXT -1 63 ". \n\nUse Maple to find the value of each of the following:\n\n (a) " }{XPPEDIT 18 0 "int(sin(x)*cos(x)^2,x);" "6#-%$intG6$*&-%$sinG6# %\"xG\"\"\"*$-%$cosG6#F*\"\"#F+F*" }{TEXT -1 28 " [indefinite integral ]\n\n(b) " }{XPPEDIT 18 0 "int(sin(x)*cos(x)^2,x = 1 .. 3);" "6#-%$int G6$*&-%$sinG6#%\"xG\"\"\"*$-%$cosG6#F*\"\"#F+/F*;F+\"\"$" }{TEXT -1 106 " [definite integral exact value]\n\n(c) The floating point value of the integral in (b) to 10 digits.\n\n(d) " }{XPPEDIT 18 0 "diff(x* exp(x)*sin(x),x);" "6#-%%diffG6$*(%\"xG\"\"\"-%$expG6#F'F(-%$sinG6#F'F (F'" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 381 10 "P roblem 4." }{TEXT -1 46 " \n\nLet f be the function defined by the ru le " }}{PARA 0 "" 0 "" {TEXT -1 18 "\n " }{XPPEDIT 18 0 "f(x) = sin(x)*(exp(x)+x^2+x+1);" "6#/-%\"fG6#%\"xG*&-%$sinG6#F'\"\" \",*-%$expG6#F'F,*$F'\"\"#F,F'F,F,F,F," }{TEXT -1 3 ". \n" }}{PARA 0 " " 0 "" {TEXT -1 54 "Use each of the three methods described in Lecture 1 (" }{TEXT 383 14 "arrow, unapply" }{TEXT -1 5 " and " }{TEXT 384 4 "proc" }{TEXT -1 124 ") to define this function in Maple and find the \+ value of f(x) to 10 digits for each of the following values of x: 0, \+ 1. " }{TEXT 385 36 "After each case execute the command " } {MPLTEXT 1 0 8 "restart;" }{TEXT 386 27 "before doing the next case." }{TEXT -1 0 "" }}}}{MARK "17" 0 }{VIEWOPTS 0 0 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 1 1 2 33 1 1 }