{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "Blue Emphasis" -1 256 "Times" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Green Emphasis" -1 257 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Maroon Emphasis" -1 258 "Times" 1 12 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 261 "Geneva" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 262 "Ge neva" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE " " -1 266 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 267 "Geneva " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "Geneva" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "Geneva" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 } {CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 } {CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 280 "Geneva" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "Geneva" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 } {CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "Purple \+ Emphasis" -1 287 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "Red Emphasis" -1 288 "Times" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 289 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 297 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 300 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 301 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 302 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 303 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 304 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 305 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 306 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 307 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 308 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 309 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 310 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 } {CSTYLE "" -1 311 "" 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 }{CSTYLE "" -1 312 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 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 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal " -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 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 }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "Getting started with Maple II" }} {PARA 0 "" 0 "" {TEXT -1 73 "Adapted from a worksheet by A. Kluge, T he University of Texas at Austin" }}{PARA 0 "" 0 "" {TEXT -1 40 "http: //www-math.cc.utexas.edu/math/Maple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 18 "Version: 13.7.2004" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart: #to begin press [RETURN]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 "Introduction" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 159 "This d ocument was prepared as a Maple worksheet so that you can load it into Maple and work through the examples it contains. In Maple a document is called a " }{TEXT 287 9 "worksheet" }{TEXT -1 74 ". Worksheets ca n contain text, Maple commands, Maple output or graphics. " }{TEXT 287 80 "Maple is a large and full-featured program for doing mathemati cs on the computer" }{TEXT -1 163 ". This worksheet will touch on onl y a few of its more basic features. This will provide you with an intr oduction to Maple and allow you to learn more on your own." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 270 "No prior knowled ge of Maple or any symbolic mathematical software is assumed. This wor ksheet will cover the basic aspects of Maple such as statement syntax, mathematical operations and graphics, as well as some system interact ions such as saving and printing your files." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 152 "You are encouraged to edit the Maple commands contained in this worksheet, and to try out some of yo ur own. The best way to learn Maple is by using it." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "Launching Mapl e" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 287 20 "O n a Windows machine" }}{PARA 0 "" 0 "" {TEXT -1 460 "Maple can be star ted by double-clicking on Maple or, on some machines, by double-clicki ng on a Maple worksheet. Under Microsoft Windows you will have to use the file association option under the file manager to associate files that have the .mws extension with Maple. If you double-click on Mapl e, then Maple will start up with an empty worksheet. If you start Mapl e by double-clicking on a worksheet, Maple will start up with the cont ents of that worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 " " 0 "" {TEXT 287 14 "On a Macintosh" }}{PARA 0 "" 0 "" {TEXT -1 281 "M aple is started by double-clicking on Maple or by double-clicking on a Maple worksheet. If you double-click on Maple, then Maple will start up with an empty worksheet. If you start Maple by double-clicking on a worksheet, Maple will start up with the contents of that worksheet. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "Loading and saving worksheets" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 63 "You can load an existing worksheet into M aple by selecting the " }{TEXT 259 4 "Open" }{TEXT -1 28 " option from the File menu. " }}{PARA 0 "" 0 "" {TEXT -1 253 "\nIf they are instal led on your system, the Maple example worksheets provide a number of e xamples of interesting things you can do with Maple. The Example work sheets are usually in the examples directory within the directory in w hich Maple is installed." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 60 "It is a good idea to save your work frequently. C hoose the " }{TEXT 290 10 "Save As..." }{TEXT -1 99 " option from the File menu to choose a new location to store your copy of the workshee t. Choosing " }{TEXT 292 4 "Save" }{TEXT -1 137 " will overwrite the c opy on disk with the changed version. This is not a good thing to do \+ with example worksheets, so make sure you use " }{TEXT 291 10 "Save As ..." }{TEXT -1 56 " at least the first time you save an example works heet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 "How to use this worksheet" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 224 "In this worksheet the Maple input is red and appears afer a command line prompt [ >. Maple does not evalua te your input until you type either [ENTER] or [RETURN]. Which of thes e you type depends on the system you are using. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 205 "You can evaluate the Map le commands in this worksheet by placing the cursor on the command lin e and pressing [ENTER/RETURN]. Try it out below: just put the cursor \+ on the next line and type [ENTER/RETURN]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 124 "Maple should have produced a new line wi th a 4 on it. If it didn't, then something is wrong, and you will nee d to get help." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "Simple uses of Maple" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 92 "You can use Maple as a desktop calcul ator. Just enter an expression followed by a semicolon " }{TEXT 0 1 "; " }{TEXT -1 25 " and type [ENTER/RETURN]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "1.29 + 4.50;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 504 "To change the calculation slig htly, or to correct a mistake, use the mouse to position the cursor in the input region and edit its contents. Then typing [ENTER/RETURN] w ill cause the input to be re-evaluated. This ability to edit and re-e valuate Maple expressions becomes more and more useful as you deal wit h more and more sophisticated aspects of Maple.\n\nComplicated express ions can be broken into multiple lines with a [SHIFT-RETURN]. Maple wo n't evaluate your expression until you type a semicolon " }{TEXT 0 1 " ;" }{TEXT -1 138 ". Since there is no semicolon on the first line of \+ this expression, Maple recognizes that the second line is a continuati on of the first." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 "2 * 3 * (7+42)\n + 7 * 9 * (110 + 795);" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Maple per forms exact arithmetic unless told otherwise." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sqrt(40)*3; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#\"#5\"\"\"\"\"'" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 0 4 "sqrt" } {TEXT -1 34 " denotes the square root function." }}{PARA 0 "" 0 "" {TEXT -1 67 "If you want a decimal value you can just force the issue \+ by giving " }{TEXT 0 4 "sqrt" }{TEXT -1 17 " a decimal input." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "sqrt(40.)*3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+'fmt*=!\")" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Alternat ively, you can use " }{TEXT 0 5 "evalf" }{TEXT -1 49 " which will \"ev aluate as a floating point number\"" }}{PARA 0 "" 0 "" {TEXT -1 40 " ( or, roughly speaking , . . a decimal)." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf(sqrt(40)*3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+'fmt*=!\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "You can also use hundreds of mathematical functions like . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ln(2.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1=ZJp!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "The constant " }{XPPEDIT 18 0 "Pi" "6#%#PiG" } {TEXT -1 24 " is denoted in Maple by " }{TEXT 0 2 "Pi" }{TEXT -1 1 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "We ca n get 30 digits in the decimal expansion of " }{XPPEDIT 18 0 "Pi" "6#% #PiG" }{TEXT -1 10 " by using " }{TEXT 0 5 "evalf" }{TEXT -1 60 " with the number of required digits as the second argument. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(P i,30);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "When used in connection with trigonometric functions, exact value s can be obtained in many familiar circumstances." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "cos(Pi/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sin(Pi/3);\n evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#!\"\"\"\"$#\"\" \"F%F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+SSDg')!#5" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "The symbol " } {TEXT 0 1 "%" }{TEXT -1 112 " refers to the last result generated by M aple (in terms of time, and not in terms of position in the worksheet) ." }}{PARA 0 "" 0 "" {TEXT -1 36 "It is probably a good policy to use \+ " }{TEXT 0 1 "%" }{TEXT -1 100 " sparingly, possibly restricting its u se to consecutive commands asociated with a single prompt [ >." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Defining functions" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "This defi nes a function that squares its argument (or input parameter):" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f := x -> x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6 \"6$%)operatorG%&arrowGF(*$)9$\"\"#\"\"\"F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "This can be tested with a few examples." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f(a+b);\nexpand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"a G\"\"\"%\"bGF'\"\"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"aG\" \"#\"\"\"F(*&F&F(%\"bGF(F'*$)F*F'F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 0 6 "expand" }{TEXT -1 57 " gives the expans ion of the previous expression f(a + b)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 0 4 "eval" }{TEXT -1 45 " will display th e definition of the function." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"xG6\"6$%)operatorG%&arrowGF&*$)9$\"\"#\"\"\"F&F& F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Si nce no arguments are given to f, " }{TEXT 0 4 "eval" }{TEXT -1 73 " \+ stops once it has expanded the definition of the function. In general " }{TEXT 0 4 "eval" }{TEXT -1 126 " works by recursively replacing e ach occurrence of a variable in a Maple expression with its value. Thi s recursion ends when " }{TEXT 0 4 "eval" }{TEXT -1 62 " can find no f urther values to substitute into the expression." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "Maple plots" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 129 "One of the most useful feature s of Maple is its ability to generate plots. We can plot our function f from the previous section:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(x),x=-2..2);" }} {PARA 13 "" 1 "" {GLPLOT2D 271 241 241 {PLOTDATA 2 "6%-%'CURVESG6$7S7$ $!\"#\"\"!$\"\"%F*7$$!3MLLL$Q6G\">!#<$\"3A!e4#)QZ)eOF07$$!3bmm;M!\\p$= F0$\"3'*[e7a'***!#=$\"3mq \"))\\%))R#***Fbo7$$!3E++++0\"*H\"*Fbo$\"3ND5!QdEbL)Fbo7$$!35++++83&H) Fbo$\"3yo4Oxt$3)oFbo7$$!3\\LLL3k(p`(Fbo$\"3[Bt(zL,1o&Fbo7$$!3Anmmmj^Nm Fbo$\"3%37I_u2IS%Fbo7$$!3)zmmmYh=(eFbo$\"39$[s$3d(yW$Fbo7$$!3+,++v#\\N )\\Fbo$\"3W.`jPjd$[#Fbo7$$!3commmCC(>%Fbo$\"3'*4!*RKWoh6\"Fbo7$$!3t*****\\#=/8DFbo$\"3CH$*>9#z`J'!#>7$ $!3=mmm;a*el\"Fbo$\"38sw$4j*)>u#Fbr7$$!3komm;Wn(o)Fbr$\"37a/+x'ova(!#? 7$$!3IqLLL$eV(>F]s$\"3gBHSG34)*Q!#B7$$\"3)Qjmm\"f`@')Fbr$\"3[xsBc\")3L uF]s7$$\"3%z****\\nZ)H;Fbo$\"3)*)*GqVMScEFbr7$$\"3ckmm;$y*eCFbo$\"3SBo $=Oul/'Fbr7$$\"3f)******R^bJ$Fbo$\"3+&>/'3\")G*4\"Fbo7$$\"3'e*****\\5a `TFbo$\"3q1NSD.>D$)Fbo$\"3$*4F1'4 l>#pFbo7$$\"3M*******pfa<*Fbo$\"3:3Cjqg!*=%)Fbo7$$\"39HLLeg`!)**Fbo$\" 3))y\"p6+56'**Fbo7$$\"3w****\\#G2A3\"F0$\"3EMgH-EF0$\"3?')3\"\\D2*fOF07$$\"\"#F*F +-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fa[l-%+AXESLABELSG6$Q\"x6\"Q!Ff[l-%% VIEWG6$;F(Fhz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "; " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "The \+ first argument passed to " }{TEXT 0 4 "plot" }{TEXT -1 49 " in this ex ample is the function to be plotted. " }{TEXT 0 4 "plot" }{TEXT -1 81 " is not limited to predefined functions; it can plot anything Mapl e can evaluate." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "plot(t^3-4*t+1,t=-3..3);" }}{PARA 13 "" 1 "" {GLPLOT2D 360 270 270 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"$\"\"!$!#9F*7 $$!1+++vq@pG!#:$!1o2CN$pV6\"F,7$$!1++D^NUbFF0$!1l*4lWq%)*))F07$$!1++]K 3XFEF0$!17Ti9zzGmF07$$!1++]F)H')\\#F0$!1sxMLS![g%F07$$!1++D'3@/P#F0$!1 [u%Q^lu$GF07$$!1++Dr^b^AF0$!1hXQ2)R!39F07$$!1++D,kZG@F0$!1s>.%z*o*G\"! #;7$$!1++Dh\")=,?F0$\"1fqfzB'[!**FQ7$$!1++DO\"3V(=F0$\"1h+Fy*HF\">F07$ $!1+++NkzV/En#F07$$!1++]d;%)G;F0$\"1Pb#4(e%Q>$F07$$!1+++0) H%*\\\"F0$\"1i[QtlcEOF07$$!1+++vl[p8F0$\"1W`')eJ[4RF07$$!1+++&>iUC\"F0 $\"1Hl\"3Z'p]SF07$$!1++DhkaI6F0$\"1()\\S.X>xSF07$$!1+++]XF`**FQ$\"1MQ) *e?E&*RF07$$!1++++Az2))FQ$\"1;wl#*H$)RQF07$$!1++]7RKvuFQ$\"1-?Lp\\SsNF 07$$!1-+++P'eH'FQ$\"1!4_fm!zoKF07$$!1****\\7*3=+&FQ$\"19TZZyevGF07$$!1 )***\\PFcpPFQ$\"1(=UT5hUX#F07$$!1)****\\7VQ[#FQ$\"1T$*yPK@y>F07$$!1)** *\\i6:.8FQ$\"1;&[)\\u/>:F07$$!1b+++v`hH!#=$\"1I_-Ch%=,\"F07$$\"1++](QI KH\"FQ$\"1!QA[,2([[FQ7$$\"1****\\7:xWCFQ$\"1#='fzoNqO!#<7$$\"1,++vuY)o $FQ$!19>Xg:1_UFQ7$$\"1)******4FL(\\FQ$!1qMA[l?j')FQ7$$\"1)****\\d6.B'F Q$!16wz\")RG]7F07$$\"1++](o3lW(FQ$!1B'Gt!4pl:F07$$\"1*****\\A))oz)FQ$! 1RJ'>'f+Q=F07$$\"1+++Ik-,5F0$!1hHCoK-,?F07$$\"1+++D-eI6F0$!1*>;14+s2#F 07$$\"1++v=_(zC\"F0$!1'y)Qr;D[?F07$$\"1+++b*=jP\"F0$!15/z=$y\")*=F07$$ \"1++v3/3(\\\"F0$!1M`wU0*Hj\"F07$$\"1++vB4JB;F0$!1)Hmu\"[f:7F07$$\"1++ +DVsYw7#F0$\"1YcqQ1v?@F07$$\"1++v)Q?QD#F0$ \"1u%\\O$[FF0$\"1R<%zf\\l2 \"F,7$$\"1++D6EjpGF0$\"1='*QG&H_J\"F,7$$\"\"$F*$\"#;F*-%'COLOURG6&%$RG BG$\"#5!\"\"F*F*-%+AXESLABELSG6$Q\"t6\"%!G-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 151 "The second argument in our exa mples is the range of values over which to plot the function. In the f irst example, x= -2..2 means to plot the graph as " }{TEXT 306 1 "x" }{TEXT -1 82 " varies from -2 to 2. In the second example, t= -3..3 m eans to plot the graph as " }{TEXT 307 1 "t" }{TEXT -1 21 " varies fro m -3 to 3." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 12 "Getting help" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 0 1 "?" }{TEXT -1 76 " returns help about a particular topic or Maple function. For example, the " } {TEXT 0 1 "?" }{TEXT -1 39 " operator can return information about " } {TEXT 0 4 "plot" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 287 23 "Under Microsoft Windows" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 65 "For the Microsoft Windows version of Maple, sel ect, for example, " }{TEXT 295 10 "Using Help" }{TEXT -1 10 " from the " }{TEXT 293 4 "Help" }{TEXT -1 271 " menu. At the top of the resulti ng help page is a browser for accessing specific topics. Clicking on a topic that is followed by three dots will open a list of related topi cs. Double-clicking on a topic that is not marked in this fashion will open the relevant help page." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 48 "The Microsoft Windows version of Maple al so has " }{TEXT 296 15 "Topic Search..." }{TEXT -1 6 " and " }{TEXT 297 19 "Full Text Search..." }{TEXT -1 37 " items in its Help menu. \+ Selecting " }{TEXT 294 19 "Full Text Search..." }{TEXT -1 200 " opens a dialog box with which you can carry out a keyword or phrase search \+ through the Maple online help files. This search provides links to hel p pages which contain the relevant keyword or phrase." }}{PARA 0 "" 0 "" {TEXT -1 102 "The Topic Search is useful if you are familiar with t he name of a topic available through the browser." }}{PARA 0 "" 0 "" {TEXT -1 33 "For more information consult the " }{TEXT 301 10 "Using H elp" }{TEXT -1 11 " help page." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 256 "" 0 "" {TEXT 287 14 "On a Macintosh" }}{PARA 0 "" 0 "" {TEXT -1 60 "To access an index to help pages on a Macintosh, select t he " }{TEXT 299 10 "Using Help" }{TEXT -1 63 " option from the standar d Macintosh help menu. Clicking on the " }{TEXT 17 17 "Table of Conten ts" }{TEXT -1 84 " hyperlink near the top of this help page gives an i ndex to the various help topics." }}{PARA 0 "" 0 "" {TEXT 302 15 "Topi c Search..." }{TEXT -1 6 " and " }{TEXT 303 19 "Full Text Search..." }{TEXT -1 46 " are also available as for Microsoft Windows." }}{PARA 0 "" 0 "" {TEXT -1 33 "For more information consult the " }{TEXT 300 10 "Using Help" }{TEXT -1 11 " help page." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 31 "Differentiation and integ ration" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Maple can do a lot more than simply plot the function " }{XPPEDIT 18 0 "f(x)=x^2" "6#/-%\"fG6#%\"xG*$F'\"\"#" }{TEXT -1 39 ". You can integ rate it with respect to " }{TEXT 308 1 "x" }{TEXT -1 27 " as an indefi nite integral:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "int(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,$*&\"\"$!\"\"%\"xGF%\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "or as a definite integral:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "int(f(x),x = -1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#G\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "Maple does different iation as well." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"xG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "is the partial (as opposed to total) derivative of " } {XPPEDIT 18 0 "f(x);" "6#-%\"fG6#%\"xG" }{TEXT -1 17 " with respect to " }{TEXT 312 1 "x" }{TEXT -1 38 ". Maple can even plot the derivativ e:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(diff(f(x),x),x=-2..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 225 252 252 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"#\"\"!$!\"%F* 7$$!1LLL$Q6G\">!#:$!1nmmmFiDQF07$$!1nm;M!\\p$=F0$!1LLLo!)*Qn$F07$$!1LL L))Qj^1DBF07$$!1LLLQW*e3\"F0$!1nmmw))yr@F07$$!1,+++()>'***! #;$!1+++S(R#**>F07$$!1++++0\"*H\"*Fbo$!1++++@)f#=F07$$!1++++83&H)Fbo$! 1+++gi,f;F07$$!1LLL3k(p`(Fbo$!1nmm\"G&R2:F07$$!1nmmmj^NmFbo$!1LLLtK5F8 F07$$!1ommm9'=(eFbo$!1MLL$HsV<\"F07$$!1,++v#\\N)\\Fbo$!1-++]&)4n**Fbo7 $$!1pmmmCC(>%Fbo$!1PLLL\\[%R)Fbo7$$!1*****\\FRXL$Fbo$!1)*****\\&y!pmFb o7$$!1+++D=/8DFbo$!1******\\O3E]Fbo7$$!1mmm;a*el\"Fbo$!1KLLL3z6LFbo7$$ !1pmm;Wn(o)!#<$!1MLL$)[`P!#=$!1Tnmmmr[RF`s7$$\"1Mmm; f`@')Fjr$\"1FLL$=2Vs\"Fbo7$$\"1)****\\nZ)H;Fbo$\"1'*****\\`pfKFbo7$$\" 1lmm;$y*eCFbo$\"1HLLLm&z\"\\Fbo7$$\"1*******R^bJ$Fbo$\"1(******z-6j'Fb o7$$\"1'*****\\5a`TFbo$\"1#******4#32$)Fbo7$$\"1(****\\7RV'\\Fbo$\"1%* ****\\#y'G**Fbo7$$\"1'*****\\@fkeFbo$\"1******H%=H<\"F07$$\"1JLLL&4Nn' Fbo$\"1mmm1>qM8F07$$\"1*******\\,s`(Fbo$\"1++++.W2:F07$$\"1lmm\"zM)>$) Fbo$\"1LLLep'Rm\"F07$$\"1*******pfa<*Fbo$\"1+++S>4N=F07$$\"1HLLeg`!)** Fbo$\"1mmm6s5'*>F07$$\"1++]#G2A3\"F0$\"1+++lXTk@F07$$\"1LLL$)G[k6F0$\" 1mmmmd'*GBF07$$\"1++]7yh]7F0$\"1+++DcB,DF07$$\"1nmm')fdL8F0$\"1MLLt>:n EF07$$\"1nmm,FT=9F0$\"1LLL.a#o$GF07$$\"1LL$e#pa-:F0$\"1nmm^Q40IF07$$\" 1+++Sv&)z:F0$\"1+++!3:(fJF07$$\"1LLLGUYo;F0$\"1nmmc%GpL$F07$$\"1nmm1^r ZF0$\" 1+++:o " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "Solving equations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "We can set up an equation using the function " }{XPPEDIT 18 0 "f(x)=x^2" "6#/-%\"fG6#%\"xG*$F' \"\"#" }{TEXT -1 26 " which can then be solved:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(f(x)=4 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#!\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "This produces the two sol utions to " }{XPPEDIT 18 0 "x^2 = 4" "6#/*$%\"xG\"\"#\"\"%" }{TEXT -1 9 ". Since " }{TEXT 304 1 "x" }{TEXT -1 150 " is the only unknown her e Maple knows to solve for it. If there are more unknowns, you will h ave to specify which one or ones Maple should solve for." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve (a*x^2+b*x+c=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&,&%\"bG!\"\" *$-%%sqrtG6#,&*$)F&\"\"#\"\"\"F0*&%\"aGF0%\"cGF0!\"%F0F0F0F2F'#F0F/,$* &,&F&F'F(F'F0F2F'F5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 45 "The second argument tells Maple to solve for " }{TEXT 305 1 "x" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 60 "Solve can work with a set of simultaneous equation s as well." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 40 "solve(\{x+y+z=0, x+y=0, x-y =1\},\{x,y,z\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"zG\"\"!/%\"xG#\"\"\"\"\"#/%\"yG# !\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "This illustrates a g eneral Maple principle of using " }{TEXT 0 3 "\{ \}" }{TEXT -1 183 " t o group together separate elements into a single argument for a Maple \+ function. Both the list of equations and the list of variables to solv e for are treated as single arguments to " }{TEXT 0 5 "solve" }{TEXT -1 109 ". Each of these arguments is itself a list consisting of sever al members. These equations need not be linear." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "Matrices and lin ear equations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "A system of linear equations can be represented in matrix form as " }{XPPEDIT 18 0 "M*`.`*u = b;" "6#/*(%\"MG\"\"\"%\".GF&%\"uG F&%\"bG" }{TEXT -1 58 ". Maple has matrix operations to solve such a \+ system. If " }{TEXT 309 1 "u" }{TEXT -1 28 " is taken to be the vector " }{XPPEDIT 18 0 "u=matrix([[x], [y], [z]])" "6#/%\"uG-%'matrixG6#7% 7#%\"xG7#%\"yG7#%\"zG" }{TEXT -1 12 ", and . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "M := Matrix( [[1,1,1],[1,1,0],[1,-1,0]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG -%'RTABLEG6$\")'*e=8-%'MATRIXG6#7%7%\"\"\"F.F.7%F.F.\"\"!7%F.!\"\"F0" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 " . . . while . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "b := Vector([0,0,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'RTABLEG6$\")3n>8-%'MATRIXG6#7%7#\"\"!F-7#\"\" \"" }}}{PARA 0 "" 0 "" {TEXT 0 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "We can solve the system of linear equations " }{XPPEDIT 18 0 "M*`.`*u = b" "6#/*(%\"MG\"\"\"%\".GF&%\"uGF&%\"bG" }{TEXT -1 5 " for " }{TEXT 298 1 "u" }{TEXT -1 12 " as follows." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "u := LinearA lgebra[LinearSolve](M,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG-%' RTABLEG6$\")3oN8-%'MATRIXG6#7%7##\"\"\"\"\"#7##!\"\"F07#\"\"!" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "This uses the procedure " }{TEXT 0 11 "LinearSolve" }{TEXT -1 25 " from the lin ear algebra " }{TEXT 0 13 "LinearAlgebra" }{TEXT -1 225 " package. A p ackage in Maple is a collection of functions written in Maple. Maple c omes with several standard packages, and you can write additional pack ages of your own. You can get a list of the standard Maple packages wi th" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "?index,package" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 59 "We can check this solution vector by matr ix multiplication." }}{PARA 0 "" 0 "" {TEXT -1 40 "The symbol for matr ix multiplication is " }{TEXT 0 1 "." }{TEXT -1 1 "." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "M.u;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\")_ETN-%'MATRIXG6#7%7#\" \"!F+7#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "Row vectors are generated by using " }{TEXT 0 11 "Vector[ row]" }{TEXT -1 44 " while column vectors are obtained by using " } {TEXT 0 14 "Vector[column]" }{TEXT -1 9 " or just " }{TEXT 0 6 "Vector " }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "v := Vector[row]([1,2,3]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"vG-%'RTABLEG6$\")cxXN-%'VECTORG6#7%\"\"\"\"\"#\" \"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "The matrix product " }{XPPEDIT 18 0 "v*`.`*M" "6#*(%\"vG \"\"\"%\".GF%%\"MGF%" }{TEXT -1 18 " now makes sense." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "v.M;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\")g(Hc$-%'VECTORG6#7%\"\" '\"\"!\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "Closi ng thoughts" }}{PARA 0 "" 0 "" {TEXT -1 316 "It is important to keep t he purpose of Maple in perspective. Maple is just a tool. Maple cannot replace your understanding of mathematics, but it can help you apply \+ that understanding in new and creative ways. If you don't exercise you r judgment while using Maple, you may find yourself led astray. Take t he integral" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "int(x^n,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)% \"xG,&%\"nG\"\"\"F(F(F(F&!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 231 "Maple applies its rules for doing integr als and quickly produces a result. Maple lacks the insight to ask, \" Does this result make sense?\" If you ask yourself the same question, you find that it clearly does not. What happens if " }{XPPEDIT 18 0 "n = -1" "6#/%\"nG,$\"\"\"!\"\"" }{TEXT -1 30 "? Maple can do that in tegral." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(x^(-1),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%# lnG6#%\"xG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 201 "This looks nothing like the result Maple gave earlier. Similar situations arise frequently with this type of software. So don't neg lect your knowledge and insight expecting Maple to do it all for you. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 "Glossary of Maple symbols" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 0 1 "?" }{TEXT -1 86 " Que ry Maple for information on one of its symbols or procedures" }}{PARA 0 "" 0 "" {TEXT 0 1 "+" }{TEXT 267 1 " " }{TEXT -1 29 " \+ Addition" }}{PARA 0 "" 0 "" {TEXT 0 1 "-" }{TEXT 268 23 " \+ " }{TEXT -1 11 "Subtraction" }}{PARA 0 "" 0 "" {TEXT 0 1 "*" }{TEXT -1 37 " Multiplication" }}{PARA 0 "" 0 "" {TEXT 0 2 "/ " }{TEXT -1 28 " Division" } }{PARA 0 "" 0 "" {TEXT 0 1 "^" }{TEXT 269 1 " " }{TEXT -1 35 " \+ Exponentiation" }}{PARA 0 "" 0 "" {TEXT 0 1 ";" }{TEXT 280 2 " " }{TEXT -1 97 " Signifies the end of a Ma ple statement - - output, if any, will be displayed." }}{PARA 0 "" 0 " " {TEXT 0 1 ":" }{TEXT 282 1 " " }{TEXT -1 85 " Si gnifies the end of a Maple statement - - output, if any, will " } {TEXT 281 3 "not" }{TEXT -1 14 " be displayed." }}{PARA 0 "" 0 "" {TEXT 0 1 "," }{TEXT -1 69 " Separates terms in a n expression sequence e.g. " }{TEXT 0 11 "2,3,4,hello" }}{PARA 0 "" 0 "" {TEXT 0 3 "( )" }{TEXT -1 74 " Surrounds the argum ents (input parameters) to a function" }}{PARA 0 "" 0 "" {TEXT 0 3 "( \+ )" }{TEXT 270 46 " Mathematically group symbols" }} {PARA 0 "" 0 "" {TEXT 0 3 "\{ \}" }{TEXT 271 96 " Sur round a Maple set - - order of terms is unimportant, no repetitions ap pear." }}{PARA 0 "" 0 "" {TEXT 0 3 "[ ]" }{TEXT 272 98 " \+ Surround a Maple list - - order of terms is important, repetitions are possible." }}{PARA 0 "" 0 "" {TEXT 0 1 "%" }{TEXT 273 57 " \+ The last result generated by Maple." }}{PARA 0 "" 0 "" {TEXT 0 2 "%%" }{TEXT 274 63 " The next to last res ult generated by Maple." }}{PARA 0 "" 0 "" {TEXT 0 3 "%%%" }{TEXT 275 43 " The third to last result." }}{PARA 0 "" 0 "" {TEXT 0 3 ":= " }{TEXT 276 67 " Assignment; calculate s the right side and assigns" }{TEXT 261 1 " " }{TEXT 266 55 "it to th e left hand side. " }}{PARA 0 "" 0 "" {TEXT 0 1 "=" }{TEXT 277 75 " \"equals\" - - com pares the right- and left-hand sides" }{TEXT 262 1 " " }{TEXT 263 17 " of an expression," }}{PARA 0 "" 0 "" {TEXT 265 100 " \+ returns true if they are the same, false if not. This is freque ntly used in" }}{PARA 0 "" 0 "" {TEXT 260 25 " \+ " }{TEXT 0 5 "solve" }{TEXT 264 24 " and related functions." }} {PARA 0 "" 0 "" {TEXT 0 2 "<>" }{TEXT 285 95 " \"n ot equals\" - - compares the right- and left-hand sides of an expressi on," }}{PARA 0 "" 0 "" {TEXT 286 74 " returns false if they are the same, true if not." }}{PARA 0 "" 0 "" {TEXT 0 2 "< " }{TEXT 279 59 " Comparison for numbers: is less than." }}{PARA 0 "" 0 "" {TEXT 0 2 "<=" }{TEXT 311 72 " \+ Comparison for numbers: \"is less than or equal to\"." }} {PARA 0 "" 0 "" {TEXT 0 1 ">" }{TEXT 278 65 " Co mparison for numbers: \"is greater than\"." }}{PARA 0 "" 0 "" {TEXT 0 2 ">=" }{TEXT 310 75 " Comparison for numbers: \"i s greater than or equal to\"." }{TEXT -1 11 " " }}{PARA 0 " " 0 "" {TEXT 0 2 "->" }{TEXT -1 92 " The arrow oper ator (subtract - - greater than) defines a function as in " }{TEXT 0 13 "f := x -> x^2" }}{PARA 0 "" 0 "" {TEXT 0 2 ".." }{TEXT -1 76 " \+ Used to define a range of values, e.g. for use with th e " }{TEXT 0 4 "plot" }{TEXT -1 7 " as in " }{TEXT 0 17 "plot(x^2,x=-2 ..2)" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT 0 1 "@" }{TEXT -1 54 " \+ Composition of functions: e.g. " }{TEXT 0 12 "(s in@exp)(x)" }{TEXT -1 16 " is the same as " }{TEXT 0 11 "sin(exp(x))" }{TEXT 283 1 "." }}{PARA 0 "" 0 "" {TEXT 0 1 "$" }{TEXT -1 57 " \+ Form an expression sequence: e.g. " }{TEXT 0 6 "$ 2..5 " }{TEXT -1 16 " is the same as " }{TEXT 0 7 "2,3,4,5" }{TEXT 284 1 ". " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 0 1 "." }{TEXT -1 54 " \+ Used for matrix multiplication." }}{PARA 0 "" 0 "" {TEXT 0 2 "# " }{TEXT -1 56 " Maple ignores anythi ng typed after " }{TEXT 0 1 "#" }{TEXT -1 43 " on a given line. Used f or making comments." }}{PARA 0 "" 0 "" {TEXT 0 1 "`" }{TEXT -1 72 " \+ Enclosing any group of symbols within back quotes " }{TEXT 0 4 " ` `" }{TEXT -1 21 " allows the resulting" }}{PARA 0 "" 0 "" {TEXT -1 76 " object to be used as the na me of a variable, as in " }{TEXT 0 12 "`7*?#w`:= 5;" }}{PARA 0 "" 0 " " {TEXT -1 1 " " }{TEXT 0 1 "'" }{TEXT -1 76 " En closing any expression within a pair forward quotes " }{TEXT 0 3 "' ' " }{TEXT -1 20 " delays evaluation, " }}{PARA 0 "" 0 "" {TEXT -1 30 " \+ e.g. " }{TEXT 0 10 "cos(3*Pi);" }{TEXT -1 29 " gives the output -1, while " }{TEXT 0 12 "'cos(3*Pi)';" }{TEXT -1 19 " gives the output " }{XPPEDIT 18 0 "cos(3*Pi)" "6#-%$cosG6#*&\"\" $\"\"\"%#PiGF(" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 0 1 "\"" } {TEXT -1 128 " Used to define a string by enclos ing any sequence of characters within a pair of double quote character s " }{TEXT 0 4 "\" \"" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 86 " For example, strings are used in error me ssages. The command " }{TEXT 0 4 "1/0;" }{TEXT -1 29 " produces the er ror message. " }}{PARA 8 "" 0 "" {TEXT -1 68 " \+ Error, numeric exception: division by zero" }}{PARA 0 "" 0 "" {TEXT -1 127 " The actual error string \"Error, nume ric exception: division by zero\" can be accessed via the variable " } {TEXT 0 9 "lasterror" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT 0 2 "|| " }{TEXT -1 55 " Concatenation operator for strings ." }}{PARA 0 "" 0 "" {TEXT 0 5 "< , >" }{TEXT -1 52 " Cons tructs a Matrix or Vector by rows. " }}{PARA 0 "" 0 "" {TEXT 0 5 "< | \+ >" }{TEXT -1 55 " Constructs a Matrix or Vector by columns . 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