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from Dr. Ma's lecture notes from MAT 5932." }}{PARA 0 "" 0 "" {TEXT -1 10 "Press the " }{TEXT 259 2 "+ " }{TEXT -1 46 "to expand sections and the - to collapse them." }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "Changing font sizes" }}{PARA 0 " " 0 "" {TEXT -1 44 "To alter the font size on the screen, press " } {TEXT 257 50 "ctrl + 1, ctrl + 2, ctrl + 3, ctrl + 4, ctrl + 5, " } {TEXT -1 3 "or " }{TEXT 258 11 "ctrl + 6. " }{TEXT -1 249 "Go ahead a nd experiment with those. You will notice that the smaller the number is, the smaller the font becomes. You can use a larger font size whi le doing your work, but I recommend that you use the smallest when pri nting in order to save paper." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "What is Maple?" }}{PARA 0 "" 0 "" {TEXT -1 250 "Maple is one of the m ost powerful mathematics software tools in existence. It is capable o f both symbolically and numerically arriving at solutions to mathemati cal expressions, as well as providing its own programming language. M aple is known as a " }{TEXT 260 23 "Computer Algebra System" }{TEXT -1 5 ", or " }{TEXT 261 3 "CAS" }{TEXT -1 182 ". The version of Maple that we will use is Maple 10. (NOTE: Maple 11 just released a few mo nths ago). There are several other softwars tools that work similarly as Maple, such as " }{TEXT 262 11 "Mathematica" }{TEXT -1 5 " and " } {TEXT 263 7 "Mathcad" }{TEXT -1 229 ". However, one might argue that \+ Maple is the most powerful and generalized of the bunch. Some of the \+ other programs are designed for specific areas or topics in mathematic s; Maple allows you to work in any field of mathematics." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "As I teach this co urse, I will be using " }{TEXT 264 26 "Maple 10 Classic Worksheet" } {TEXT -1 63 ". Classic Worksheet does not have all of the functionali ty of " }{TEXT 265 8 "Maple 10" }{TEXT -1 262 ", but it typically load s and runs faster, and provides (I think) an easier transition between problems. Note that if you save a file in Classic Worksheet, it migh t not open properly in Maple 10. Make sure that you use the correct f ile type. Files that end in " }{TEXT 266 4 ".cws" }{TEXT -1 52 " are \+ Classic Worksheet files, and files that end in " }{TEXT 267 4 ".mws" } {TEXT -1 30 " are for the regular Maple 10." }}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 19 "How do I use Maple?" }}{PARA 0 "" 0 "" {TEXT -1 314 "Yo u can use Maple as a simple calculator or graphing utility, like the o nes some of you may carry. But Maple offers much more than those tool s. However, in order to use Maple, you need to speak the Maple langua ge. We will first look at how Maple can be used as a calculator, and \+ then focus on the programming. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 29 "Notice that the text here is " }{TEXT 268 5 "black" }{TEXT -1 70 ". As I type this lecture, I am using Mapl e's text mode. By pressing " }{TEXT 269 8 "ctrl + j" }{TEXT -1 58 ", \+ I can insert an execution group after this line of text." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 183 "Notice that the text here is red. \+ Maple executes the code from these lines when you press \"Enter\". I f you press Enter anywhere in these sentences, you will receive an err or message." }}}{PARA 0 "" 0 "" {TEXT -1 17 "If I had pressed " } {TEXT 282 8 "ctrl + k" }{TEXT -1 110 ", then the execution group would have been inserted before the text line. Another way to do this is t o click " }{TEXT 283 25 "Insert -> Execution Group" }{TEXT -1 0 "" } {TEXT 284 3 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 272 41 "To see a list of all key shortcuts go to " }{TEXT 273 18 "Help, Topic Search" }{TEXT 272 14 " and type in " }{TEXT 273 13 " shortcut_keys" }{TEXT 272 91 ". Then click on the item for Macintosh, \+ Windows or Unix depending on what computer you have" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "In Engl ish class, you learned that sentences end with a period (usually). In Maple, " }{TEXT 271 75 "any lines of code that you want Maple to exec ute need to end in a semicolon" }{TEXT -1 8 " \";\" or " }{TEXT 270 5 "colon" }{TEXT -1 193 " \":\". If you use a semicolon, Maple will dis play the results of its computation on the screen. If you use a colon , Maple will still perform the operation, but it will not display the \+ results." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 253 "Below are a few simple exercises to familiarize you with how to i nput operations into Maple. Try to guess the answer before pressing e nter. Notice that non-executable text is black, executable code in an execution group is red, and the output is blue." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "5*2;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 9 "1276+424;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "(7+18-5)/5;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3^3;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "4^(3/2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "15/4;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "15./4;" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 300 "Notice the difference between the last two examples. The presenc e of the decimal told Maple to do the computation in floating point ar ithmetic. In this case, it will try to return an answer rounded to te n decimal places. If you do not specify otherwise, Maple will give ex act, not rounded answers." }}{PARA 0 "" 0 "" {TEXT 273 11 "IMPORTANT: \+ " }{TEXT 274 24 "Maple is case sensitive." }{TEXT 272 188 " So, for ex ample, ABC, ABc, AbC, Abc, aBc, Abc, etc, are all different so far as \+ Maple is concerned. \n\nBy this point of your mathematics careers, you 've undoubtedly encountered the number " }{XPPEDIT 18 0 "pi:" "6#%#piG " }{TEXT 272 14 ". Maple uses " }{TEXT 273 2 "Pi" }{TEXT 272 31 " (no t pi) to denote the number " }{XPPEDIT 18 0 "pi:" "6#%#piG" }{TEXT 272 44 ". We can get a floating point evaluation of " }{XPPEDIT 18 0 " pi;" "6#%#piG" }{TEXT 272 16 " by the command " }{TEXT 273 10 "evalf(P i) " }{TEXT 272 28 "as in the following examples" }{TEXT -1 1 ":" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "pi;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }{TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(pi);" }{TEXT -1 0 " " }}}{PARA 0 "" 0 "" {TEXT -1 10 "Note that " }{TEXT 275 2 "pi" } {TEXT -1 5 " and " }{TEXT 278 2 "Pi" }{TEXT -1 16 " both appear as " } {XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 35 ". This is an exception sin ce alpha" }{TEXT 276 2 ", " }{TEXT -1 11 "Alpha, beta" }{TEXT 277 2 " , " }{TEXT -1 79 "Beta, gamma, Gamma, delta, Delta, etc, appear in ou tput as the Greek letters, " }{XPPEDIT 18 0 "alpha,Alpha,beta,gamma,Ga mma,delta,Delta;" "6)%&alphaG%&AlphaG%%betaG%&gammaG%&GammaG%&deltaG%& DeltaG" }{TEXT -1 6 ", etc." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "alpha,Alpha;beta,Beta;gamma,Gamma;" }}}{PARA 0 "" 0 "" {TEXT -1 28 "Have you ever wondered what " }{XPPEDIT 18 0 "pi" "6#%#piG" } {TEXT -1 102 " was to 10,000 places. Execute the next line to find ou t. You can then remove the output by clicking" }{TEXT 279 40 " Edit - > Remove Output -> From Worksheet" }{TEXT -1 2 ". " }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "evalf[10000](Pi);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 126 "As I said earlier, Maple will only give a floa ting point number if you tell it to...or it's confused. Here's anothe r example." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "cos(Pi/4);" } {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 280 193 "We may get a floating \+ point evaluation of the previous output as follows. Note that % indica ted the previous output. %% indicates the output before that. The one \+ before that is indicated by %%%" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 46 "Here are some illustrations of % and %% below:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "12;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "sqrt(15);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 62 "What do you predict will appear when we execute the follo wing?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(%%%);" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf((%%)^ 2);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 29 "Here are a few mor e examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sqrt(Pi/6);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "sqrt(Pi/22 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(25);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(13);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{PARA 0 "" 0 "" {TEXT -1 148 "Remember, Maple will \+ always try to be as precise as possible. This can cause problems, bec ause if you're not careful, you can easily crash Maple. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "#353^10000000;" }}}{PARA 0 "" 0 "" {TEXT -1 209 "The # will keep Maple from actually executing the code. \+ If you remove it and press enter, you might crash Maple. If you're l ucky, you will get an error message saying that the number is too larg e to display." }}{PARA 0 "" 0 "" {TEXT -1 96 "If you're afraid that yo u've executed some code that might be causing Maple to crash, press th e " }{TEXT 281 4 "STOP" }{TEXT -1 229 " sign at the top of the screen. This sometimes work to interrupt the computation and return Maple to its normal operations. Don't count too heavily on this working thoug h...trust me...I've had several bad experiences with this." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 34 "More of Maple's built-in functions" }} {PARA 0 "" 0 "" {TEXT -1 23 "So far, you've seen the" }{TEXT 285 7 " e valf " }{TEXT -1 3 "and" }{TEXT 286 5 " sqrt" }{TEXT -1 98 ". These a re just two of the thousands of functions that Maple has to offer. He re are a few more." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve( 2*x+5=11);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(3*x^2+4 *y^2+x*y=3*x^2*y);" }}}{PARA 0 "" 0 "" {TEXT -1 165 "Notice that the o utput for the previous example gave solutions for both x and y. If we wanted just an expression of x in terms of y, then make the following change:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(3*x^2+4*y^ 2+x*y=3*x^2*y,x);" }}}{PARA 0 "" 0 "" {TEXT -1 48 "Here are some more \+ fun things that Maple can do." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x^2+3*x+6=0,x);" }}}{PARA 0 "" 0 "" {TEXT -1 57 "Note that Maple uses \"I\" to denote the square root of -1." }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "eval(I^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ifactor(15);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ifactor(126);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expa nd((x+1)^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((x+1 )^3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "seq((x+1)^n,n=1..1 0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "seq(expand((x+1)^n), n=1..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "factor(x^4+13* x^3+52*x^2+60*x);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Right-clic king the output" }}{PARA 0 "" 0 "" {TEXT -1 213 "You will find that wh en Maple executes a command, it will allow you to manipulate the outpu t. The manipulations it allows will depend in what type of output it \+ is. After executing each of the following commands " }{TEXT 287 11 "r ight click" }{TEXT -1 8 " on the " }{TEXT 288 6 "output" }{TEXT -1 211 " and try several of the options that appear in the little pop-up window. Note that this will also cause the appropriate command to be \+ typed in red. We will see later the significance of the colon equals s ymbol " }{TEXT 289 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 20 "Try this expression:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 31 "Pi*sin(x)*cos(2*x) + sqrt(2)*x;" }}}{PARA 0 "" 0 "" {TEXT -1 24 "Now look at an equation:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "3*x^2+2*x+6=2*x^2+5*x+11;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "The basics of gr aphing" }}{PARA 0 "" 0 "" {TEXT -1 98 "As I mentionied earlier, Maple \+ is more than capable of plotting graphs. Here are a few examples. " } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{PARA 0 " " 0 "" {TEXT -1 76 "Let's start with something basic, like a quadratic . We'll have Maple graph " }{XPPEDIT 18 0 "y = x^3+x^2+x+1" "6#/%\"yG ,**$%\"xG\"\"$\"\"\"*$F'\"\"#F)F'F)F)F)" }{TEXT -1 35 " for x in [-3,3 ] and y in [-15,15]." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot (x^3+x^2+x+1,x=-3..3, y=-15..15);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 3 "1. " }{TEXT 292 10 "Left click" }{TEXT -1 180 " on the plo t with the cursor. Then drag the lower right corner of the frame upwar d 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 291 11 "Right click" }{TEXT -1 73 " on the plot and when the lit tle window pops up try the various options: " }{TEXT 290 19 "style, le gend, axes" }{TEXT -1 5 ", etc" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 126 "Now, you might be thinking to yourself, \+ \"That's nice, but my TI-83 can do that. What makes Maple so special? \" Try these out:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot3d ((cos(x^2+y^2), x=-Pi/2..Pi/2,y=-Pi/2..Pi/2));" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 87 "spacecurve([cos(t),sin(t),t],t=0..8*Pi,color=b lue,style=line, thickness=1,axes=normal);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 193 "spacecurve(\{[t*cos(2*Pi*t),t*sin(2*Pi*t),2+t],[2+ t,t*cos(2*Pi*t),t*sin(2*Pi*t)],[t*cos(2*Pi*t),2+t,t*sin(2*Pi*t)]\},t=0 ..20,numpoints=400,orientation=[30,50],style=line, thickness=2,axes=bo xed);" }}}{PARA 0 "" 0 "" {TEXT -1 125 "1. Before continuing make thes e plots smaller also as you did the previous one to save paper when y ou print this worksheet. " }}{PARA 0 "" 0 "" {TEXT -1 3 "2. " }{TEXT 293 11 "Right click" }{TEXT -1 67 " on the picture. Then using the mo use you can rotate the surface. " }}{PARA 0 "" 0 "" {TEXT -1 136 "3. A lso when you click on the plot you will see a new row 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 294 15 "r ight clicking " }{TEXT -1 120 "on the plot and trying some of the opti ons that appear there. Many of these are the same ones you found in it em 3 above." }}{PARA 0 "" 0 "" {TEXT -1 123 "Later We will have lots m ore to say about piloting curves and surfaces. So don't try to learn a ll the options at this time." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 132 "Let's go back to something more basic now. Yo u all should be familiar with the natural logarithm curve. Let's have Maple graph it." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(ln( x),x=-1..5);" }}}{PARA 0 "" 0 "" {TEXT -1 73 "You'll have plenty of ti me to play with Maple's graphing abilities later." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Maple for " }{XPPEDIT 18 0 "e^x;" "6#)%\"eG%\"xG " }{TEXT -1 7 " and " }{XPPEDIT 18 0 "e;" "6#%\"eG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 63 "In many scientific and mathematical fie lds, the number we call " }{TEXT 295 1 "e" }{TEXT -1 174 " (which appr oximately equals 2.72) appears with widespread application, along with its inverse function, the natural logarithm. Maple has its own way o f handling the number " }{TEXT 296 1 "e" }{TEXT -1 3 ". " }{TEXT 272 13 "One must use " }{TEXT 273 6 "exp(x)" }{TEXT 272 5 " for " } {XPPEDIT 18 0 "exp(x)" "6#-%$expG6#%\"xG" }{TEXT 272 5 " and " }{TEXT 273 5 "exp(1" }{TEXT 272 7 ") for " }{XPPEDIT 18 0 "exp(1)" "6#-%$exp G6#\"\"\"" }{TEXT 272 49 ", as in the following. Note the output DOES \+ give " }{XPPEDIT 18 0 "exp(1);" "6#-%$expG6#\"\"\"" }{TEXT 272 5 " and " }{XPPEDIT 18 0 "exp(x);" "6#-%$expG6#%\"xG" }{TEXT 272 51 ". Execu te the following commands and you 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 21 "plot(exp(x),x=-2..2);" }}} {PARA 0 "" 0 "" {TEXT -1 30 "Note that the following fails:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(e);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(e^x,x=-2..2);" }}}{PARA 0 "" 0 "" {TEXT -1 106 "One way to make this code work is to assign the value of e to the letter. Assignments are done using the " }{TEXT 297 2 ":=" }{TEXT -1 9 " command." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "e:=evalf( exp(1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(e);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(e^x,x=-2..2);" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "Basic Worksheet Handling" }} {PARA 0 "" 0 "" {TEXT -1 316 "As you type your homework for this class , there is a simple format I would like you to adhere to. This sectio n walks you through the steps of how to create a new worksheet, give i t a proper heading, insert standard math, switch between text and exec ution groups, and save. Just follow the steps and you'll be fine." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "1. Under \+ " }{TEXT 299 4 "File" }{TEXT 300 20 " on the menu choose " }{TEXT 301 3 "New" }{TEXT 298 17 " or click on the " }{TEXT 302 16 "blank page ic on " }{TEXT 303 40 "on the menu bar. This opens a new page." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 "2. " }{TEXT 304 26 "Next go to the menu named " }{TEXT 305 6 "Window" }{TEXT 306 18 " \+ and pull down to " }{TEXT 307 8 "Vertical" }{TEXT 308 189 ". This will allow you to read this worksheet while following these directions in \+ the new worksheet. Click on the blank worksheet to make sure the curs or is there and not in this worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 2 "3." }{TEXT 326 6 " Press" }{TEXT 327 1 " " }{TEXT 328 8 "crtl + t" }{TEXT 329 1 " " }{TEXT 313 16 "or click on the " }{TEXT 310 1 "T" }{TEXT 314 76 " icon on the menu bar. Then, on the left side of the menu bar where it says " }{TEXT 309 8 "P Norm al" }{TEXT 315 45 " pull down the menu at that point and select " } {TEXT 311 7 "P Title" }{TEXT 319 2 ". " }{TEXT 316 18 "Type in the wor ds " }{TEXT 324 12 "Sample Title" }{TEXT 325 14 " and then hit " } {TEXT 330 6 "Return" }{TEXT 331 23 ". This will put you in " }{TEXT 312 8 "P Author" }{TEXT 317 34 " mode. Type your name and the hit " } {TEXT 322 6 "Return" }{TEXT 323 2 ". " }{TEXT 318 19 "You will now be \+ in " }{TEXT 320 8 "P Normal" }{TEXT 321 57 " text mode. Type the word s \"Some sample Maple commands.\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 3 "4. " }{TEXT 337 14 "Next click on " } {TEXT 332 2 "[>" }{TEXT 338 1 " " }{TEXT 334 9 "or press " }{TEXT 339 8 "ctrl + j" }{TEXT 343 5 " (or " }{TEXT 344 8 "ctrl + k" }{TEXT 340 56 "). [Sometimes you may want to insert an execution group " }{TEXT 333 6 "before" }{TEXT 336 11 " the cursor" }{TEXT 335 65 "--especially if you are at the top of the page. Then you may use " }{TEXT 341 8 "c trl + k" }{TEXT 342 36 ".]. When you see the prompt, i.e., " }{TEXT 346 1 ">" }{TEXT 347 48 ", then type in some mathematical command such as" }{TEXT 2 1 " " }{TEXT 19 6 "2^100;" }{TEXT -1 2 ". " }{TEXT 345 70 "Then hit return to execute this command. Try a few more such comma nds." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "5 .Go back to the text mode by repeating clicking on the " }{TEXT 348 1 "T" }{TEXT -1 32 " in the menu bar or by pressing " }{TEXT 349 8 "ctrl + t" }{TEXT -1 63 ". Type in the words \"We now compute the radical \". Next press " }{TEXT 350 8 "ctrl + r" }{TEXT -1 36 ". You will se e a \"?\". Now type in " }{TEXT 352 10 "sqrt(1296)" }{TEXT -1 64 ", a nd you will see this appear in a box under the menu bar. Now " }{TEXT 351 8 "ctrl + t" }{TEXT -1 136 " again or click on the T to go back in to ordinary text mode and continue to type the words \"as follows\". \+ You should see the following:\n" }}{PARA 0 "" 0 "" {TEXT -1 27 "We now compute the radical " }{XPPEDIT 18 0 "sqrt(1296);" "6#-%%sqrtG6#\"%'H \"" }{TEXT -1 11 " as follows" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 14 "6. Then press " }{TEXT 353 8 "ctrl + j" } {TEXT -1 13 " or click on " }{TEXT 354 2 "[>" }{TEXT -1 79 " to go ba ck into execution mode. When the cursor comes up type in the command \+ " }{TEXT 362 11 "sqrt(1296);" }{TEXT -1 44 " then execute the command \+ by hitting return." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "7. To save your new worksheet go under " }{TEXT 355 4 " File" }{TEXT -1 12 " and choose " }{TEXT 356 4 "Save" }{TEXT -1 137 " \+ (or click on the icon that looks like a floppy disk on the menu bar). \+ The first time you will be prompted to give a name. For example, " } {TEXT 357 15 "YourName01.mws " }{TEXT -1 116 "would be a possible name for a Maple file. If you look at the top of this page you will see t he name of this file: " }{TEXT 358 13 "Lecture 1.mws" }{TEXT -1 47 ". \+ That's the name 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 keeping what you already have in a named worksheet use \+ " }{TEXT 359 8 "Save As " }{TEXT -1 12 "instead of " }{TEXT 360 5 "Sa ve " }{TEXT 361 132 "and give the worksheet a new name. This way you c an keep your old worksheet and experiment with changes without losing \+ what you did." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Averting disast er" }}{PARA 0 "" 0 "" {TEXT -1 325 "Although Maple is a wonderful prog ram, it can crash..... a lot, actually. In many cases these crashes w ill be your fault (don't take it personally...I've crashed Maple many \+ times...it's a little fun, as long as it's not your homework or a test that crashing). To keep from losing your work, follow these three si mple steps." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "1. Click " }{TEXT 363 7 "Save as" }{TEXT -1 35 " shortly after beginning your work." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "2. Every time you complete a problem or part of a pro gram, click " }{TEXT 364 4 "Save" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "3. Even if you haven't f inished any major part of your program, press " }{TEXT 365 8 "ctrl + s " }{TEXT -1 20 " on a regular basis." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "In other words: SAVE, SAVE, SAVE!!!!!" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 35 "Using multiple worksheets at a time" }}{PARA 0 "" 0 "" {TEXT -1 29 "As you saw in the section on " } {TEXT 366 24 "Basic Worksheet Handling" }{TEXT -1 66 ", it is possible to view several worksheets at a time. Press the " }{TEXT 367 10 "Bla nk Page" }{TEXT -1 56 " a few times to make several new documents. Th en click " }{TEXT 368 7 " Window" }{TEXT -1 26 ", and try to four opti ons " }{TEXT 273 41 "Cascade, Tile, Horizontal, and Vertical. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 370 15 "Important Fact:" }{TEXT -1 142 " If you are working with sever al worksheets at once, any assignments you make in one will apply to t he others. Execute the following command:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "x:=5;" }}}{PARA 0 "" 0 "" {TEXT 273 0 "" }{TEXT 369 0 "" }{TEXT -1 36 "Now open a new document by pressing " }{TEXT 371 8 "ctrl + n" }{TEXT -1 33 ", and on the execution line type " }{TEXT 19 2 "x;" }{TEXT -1 36 ". You'll notice that the output is " }{TEXT 20 1 "5" }{TEXT -1 257 ", even though we made that assignment in this wor ksheet. I emphasize this point to make you sure you are aware of the \+ potential hazards of using several worksheets at once. Though it can \+ be a great tool, one worksheet can have drastic effects on others. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 115 "If you want to undo all of the assignments you have made and erase everythin g out of the computers memory, then use" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 246 "Executing t his will clear all of the memory. Go back to that other worksheet you opened earlier and ask Maple to evaluate x again. You'll notice that it does not return 5 again. This is because the memory was cleared f or all of the worksheets." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 372 28 "Cutting, Copying and Pasting" }{TEXT -1 115 ": Yo u may cut, copy and paste from a worksheet to itself or from one works heet to another using the commands under " }{TEXT 373 5 "Edit " } {TEXT -1 38 "as you would in most word processors." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Maple's built-in help" }}{PARA 0 "" 0 "" {TEXT -1 54 "If you not sre how to do something in Maple, then get " }{TEXT 374 4 "Help" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT 377 13 "Getting \+ Help:" }{TEXT 375 37 " Perhaps the easiest way is to use a " }{TEXT 382 13 "question mark" }{TEXT 383 73 " as follows: Here we suppose we \+ forgot the command for solving. We guess " }{TEXT 378 11 "that it is \+ " }{TEXT 376 3 "sol" }{TEXT 379 57 ". Type and execute the following \+ command by hitting the " }{TEXT 380 6 "Return" }{TEXT 381 4 " key" } {TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?sol" }}} {PARA 0 "" 0 "" {TEXT 385 45 "This will bring up several options inclu ding " }{TEXT 386 5 "solve" }{TEXT 387 1 "." }{TEXT -1 1 " " }{TEXT 384 23 " Now, you can click on " }{TEXT 389 5 "solve" }{TEXT 390 31 " \+ or go back and add the extra \"" }{TEXT -1 3 "ve\"" }{TEXT 388 351 " t o ?sol and re-execute. In any event you will be led to the help page f or solve. If you scroll down you will see a number of examples. This \+ will often be enough. 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 "?" }}}{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 ta ke you directly to the examples at the bottom of the help page. Here's an example:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "???solve" }}} {PARA 0 "" 0 "" {TEXT -1 112 "For another example: Suppose that you wa nt to know how to factor an integer or a polynomial: Then you could tr y:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?factor" }}}{PARA 0 "" 0 "" {TEXT -1 50 "Notice that the help page that comes up says that " }{TEXT 391 6 "factor" }{TEXT -1 67 " is used to factor polynomials and not integers. It tells you that " }{TEXT 392 7 "ifactor" }{TEXT -1 52 " is used to factor integers. Here are some examples:" }}{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 19 "ifactor(123456789);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 400 24 "Other ways to get help: " } {TEXT -1 37 "You may do a full text search of the " }{TEXT 399 16 "Map le Help Files" }{TEXT -1 13 " by going to " }{TEXT 394 4 "Help" } {TEXT -1 34 " on the menu bar and pull down to " }{TEXT 393 17 "Full T ext Search " }{TEXT 401 2 "or" }{TEXT 402 16 " Topic Search.\n\n" } {TEXT 395 59 "Another way is to select a word of interest and then go \+ to " }{TEXT 396 4 "Help" }{TEXT 397 34 " on the menu bar and pull down to " }{TEXT 398 17 "Help on Context. " }{TEXT 403 43 "Instead you may select the word and execute" }{TEXT 404 10 " ctrl + f1" }{TEXT -1 1 " ." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 "The Use of := , = , : , and ;" }}{PARA 0 "" 0 "" {TEXT -1 217 "If you've had any experience with \+ computer programming, you know that computers can manipulate variables similarly to what we do when solving an algebra problem. Let's say t hat we want to know what the value of x is." }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 2 "x;" }}}{PARA 0 "" 0 "" {TEXT -1 76 "So Maple does no t view x as a number, but only as a letter here. Using the " }{TEXT 405 2 ":=" }{TEXT -1 228 ", we can assign in the computer's memory any value we want for x. Note that the colon is necessary to make an ass ignment. Using only an equal sign does not make an assignment in the \+ computer's memory. Here are some examples: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "y =3;" }}}{PARA 0 "" 0 "" {TEXT -1 31 "Now let's see what x and y are:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{PARA 0 "" 0 "" {TEXT -1 25 "Now let's do \+ it with the " }{TEXT 406 2 ":=" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "y:=3;" }}}{PARA 0 "" 0 "" {TEXT -1 34 "Again, let's see what x and \+ y are:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{PARA 0 "" 0 "" {TEXT -1 95 " So as far a Maple is concerned, x means 5 and y means 3. So, if you t ry 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 21 "solve(x^2+x+1 = 0,x);" }}} {PARA 0 "" 0 "" {TEXT -1 57 "We can clear the value of 5 from x two wa ys. We can use " }{TEXT 407 8 "restart;" }{TEXT -1 76 ", which will c lear all assignments from memory, or we can use the following:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x:='x';" }}}{PARA 0 "" 0 "" {TEXT -1 67 "Now we see that x is just x, not 5. Now we can solve the equation." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x^2+x+1 \+ = 0,x);" }}}{PARA 0 "" 0 "" {TEXT 272 16 "Note the use of " }{TEXT 273 1 "=" }{TEXT 272 15 " as opposed to " }{TEXT 273 2 ":=" }{TEXT 272 17 " in the equation " }{TEXT 273 15 "x^2 + x + 1 = 0" }{TEXT 272 35 ". We can even assign a name, say, " }{TEXT 273 4 "eqn " }{TEXT 272 16 "to this equation" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eqn:=x^2+x+1 = 0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(eqn,x);" }}}{PARA 0 "" 0 "" {TEXT -1 209 "We ca n assign values to several variables at a time as in the following com mand. Actually, the parentheses in this line are not necessary, but ar e included for clarity. Notice they do not appear in the output." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "(x,y,z):=(4,18,t^2+7);" }}} {PARA 0 "" 0 "" {TEXT -1 45 "We can see the values of the variables be low:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x;y;z;" }}}{PARA 0 " " 0 "" {TEXT -1 18 "Compare with this:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x,y,z;" }}}{PARA 0 "" 0 "" {TEXT -1 32 "As we noted be fore, the command " }{TEXT 408 7 "restart" }{TEXT -1 50 " is useful fo r clearing all of the memory at once:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "(x,y):=45,8674;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " x,y;" }}}{PARA 0 "" 0 "" {TEXT -1 46 "As I mentioned earlier, if a lin e ends with a " }{TEXT 409 1 ":" }{TEXT -1 12 " instead of " }{TEXT 410 1 ";" }{TEXT -1 7 ", then " }{TEXT 411 56 "the command will be exe cuted but no output will be shown" }{TEXT -1 22 ". Here is an example :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "y:=Pi^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{PARA 0 "" 0 "" {TEXT -1 79 " Here's what happens if you forget the semi-colon or colon at the end o f a line:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x:=6" }}}{PARA 0 "" 0 "" {TEXT -1 101 "You can correct this by simply inserting the s emicolon at the end of that line above and hitting the " }{TEXT 413 5 "Enter" }{TEXT -1 10 " key again" }{TEXT 412 1 "." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 41 "Functions (Procedures) versus Expressions" }} {PARA 0 "" 0 "" {TEXT -1 62 "Maple has a large number of built-in func tions (also known as " }{TEXT 415 10 "procedures" }{TEXT -1 17 ") . Fo r example: " }{TEXT 414 113 "sin, cos, tan, cotan, sec, csec, arcsin, \+ ln, exp, int, diff, solve, factor, plot, abs, sqrt, tan, factorial, d et" }{TEXT -1 136 ", and many more. These functions behave pretty muc h as you would expect. You can also make your own functions (that we w ill often call " }{TEXT 416 10 "procedures" }{TEXT -1 28 ") which we i llustrate below." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "First, let's ask the question: What is a " }{TEXT 417 10 "procedure " }{TEXT -1 21 "and why is it useful?" }}{PARA 0 "" 0 "" {TEXT -1 391 "Let's say that you're writing a program that is required to perform the same operation several times. Instead of copying and \+ pasting essentially the same code many times in your program, it is be tter to create one block of code that you can call repeatedly whenever you need it. This saves on the space that your program takes up, and also makes it look neater. Here's a practical example:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "Let's say that a pro gram you are writing requires you to evaluate the sine of some number \+ " }{TEXT 418 3 "x. " }{TEXT -1 168 " Let's also assume that you're usi ng a programming language that does not have the sine function built-i n to help you evaluate it (e.g. in Maple, you only have to type " } {TEXT 419 7 "sin(x);" }{TEXT -1 130 ", and Maple will evaluate it for \+ you). How then do you evaluate the sine of a number. If you've studi ed calculus, you know that " }{XPPEDIT 18 0 "sin(x) = x-x^3/3!+x^5/5!- x^7/7!+x^9/9!-x^11/11!+x^13/13!-x^15/15!;" "6#/-%$sinG6#%\"xG,2F'\"\" \"*&F'\"\"$-%*factorialG6#F+!\"\"F/*&F'\"\"&-F-6#F1F/F)*&F'\"\"(-F-6#F 5F/F/*&F'\"\"*-F-6#F9F/F)*&F'\"#6-F-6#F=F/F/*&F'\"#8-F-6#FAF/F)*&F'\"# :-F-6#FEF/F/" }{TEXT -1 103 " (approximately). Instead of re-using th e same code over and over, you can call a procedure like this:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "sine:=proc(x)\n evalf(x-x^3 /3!+x^5/5!-x^7/7!+x^9/9!-x^11/11!+x^13/13!-x^15/15!);\nend proc:" }}} {PARA 0 "" 0 "" {TEXT -1 54 "Let's compare the accuracy of my procedur e to Maple's:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf(sin(P i/4));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sine(Pi/4);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf(sin(Pi/3));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sine(Pi/3);" }}}{PARA 0 "" 0 "" {TEXT -1 152 "You see that my procedure is accurate to nine decim al places!! Which would you rather do: copy that expression over and \+ over again, or simply call the " }{TEXT 422 4 "sine" }{TEXT -1 251 " p rocedure? In case you're wondering, yes, I can write a procedure that will return a value as accurately as Maple's. However, it would req uire notation you are (probably) not familiar with, so I chose this si mpler procedure which works quite well." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Let's say that you wanted to make a \+ function. " }{TEXT 421 38 "The obvious way actually does not work" } {TEXT -1 118 ". Suppose we want to define a new function f satisfying f(x) = x^2 + x + 1 for all x. Execute the following command: " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "f(x):=x^2+x+1;" }}}{PARA 0 "" 0 "" {TEXT 420 38 "This is not the way to make a function" }{TEXT -1 47 ". Note \+ what happens in the following commands:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ev alf(f(3));" }}}{PARA 0 "" 0 "" {TEXT 272 11 "The object " }{TEXT 273 11 "x^2 + x + 1" }{TEXT 272 22 " is what is called an " }{TEXT 273 20 "algebraic expression" }{TEXT 272 139 ". We may plot it, solve it, fac tor it, integrate it, differentiate it, and so forth, but it is NOT a function so far as Maple is concerned" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "plot(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "int(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(f(x)=0,x);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "What we would like is for f(2) to give us 7. " } {TEXT 424 54 "Here are three correct ways to define such a function." }{TEXT -1 2 " " }{TEXT 423 30 "You should learn each of these" } {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 425 15 "Arrow notation:" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "f:=x->x^2+x+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 426 15 "Use of unapply:" }{TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{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):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 427 21 "Creating a procedure:" }} {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);" }}}{PARA 0 "" 0 "" {TEXT -1 207 "We will use these ideas repeatedly in this course. You s hould make absolutely sure you understand each of these three methods \+ for constructing a function. Now is a good time to experiment with the se methods." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Instructions for \+ Printing" }}{PARA 0 "" 0 "" {TEXT -1 159 "I recommend that you print o ut these pages and keep them in your notebook. If you have closed any section, open them now. You may accomplish this by going to " }{TEXT 429 4 "View" }{TEXT -1 35 " on the top menu and going down to " } {TEXT 431 20 "Expand All Sections." }{TEXT -1 8 " Go to " }{TEXT 428 4 "File" }{TEXT -1 12 " and select " }{TEXT 430 5 "Print" }{TEXT -1 22 ". If you would like a " }{TEXT 432 17 "Table of Contents" }{TEXT -1 8 ", go to " }{TEXT 433 6 "View, " }{TEXT -1 7 " click " }{TEXT 434 21 "Collapse All Sections" }{TEXT -1 16 ", and the click " }{TEXT 435 5 "Print" }{TEXT -1 58 " again. This will help you to be a little more organized." }}}}{MARK "3" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }