{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 "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 "Purple Emphasis" -1 259 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 260 "T imes" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Red Emphasis" -1 261 "Times" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 124 1 100 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 266 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 258 270 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 258 272 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 258 273 "" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 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 "Time s" 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 "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 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 Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 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 "Bullet Item" -1 15 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 3 3 1 0 1 0 2 2 15 2 }{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 } {PSTYLE "Normal" -1 257 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" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 1 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 42 "A short introduction to the Maple language" }}{PARA 0 "" 0 "" {TEXT -1 88 "Based on a worksheet by Carl Eberhart,\nDepartment of Mathematics, University of Kentucky" }} {PARA 0 "" 0 "" {TEXT -1 27 "http://www.ms.uky.edu/~carl" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "Version: 5.2.2004 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "This \+ worksheet contains an introduction to some of the Maple language. " }} {PARA 0 "" 0 "" {TEXT -1 62 "It is not meant to cover everything, just some of the basics. " }}{PARA 0 "" 0 "" {TEXT -1 61 "Read it through \+ quickly, to get an overview of the language. " }}{PARA 0 "" 0 "" {TEXT -1 63 "Then you can come back and read with more understanding l ater. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " ;" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Arithmetic" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 295 "First, there is arith metic: addition, subtraction, multiplication, division and exponentiat ion. These can be combined, just as on a calculator. The order of pre cedence is the the usual one: exponentiation first, then multiplicati on and division, then addition and subtraction. So entering . ." }} {PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "2-3+4/5*6^7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"(R(>6\"\"&" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 " . . is the same as entering . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(2-3)+(4/5)*(6^7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"(R(>6\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 152 "You will notice that Maple works with fr actions whenever possible, changing to decimal numbers only on demand. So typing and pressing the enter key . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1/3 + 1/2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"&\"\"'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 ". . w ill get a return of " } {XPPEDIT 18 0 "5/6" "6#*&\"\"&\"\"\"\"\"'!\"\"" }{TEXT -1 100 ". If y ou put a decimal point in one of the numbers, that forces Maple to re turn a decimal answer. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "1/3. + 1/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLL$)!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "evalf" {TEXT -1 53 "Another way to get decimals is to us e the maple word " }{TEXT 0 5 "evalf" }{TEXT -1 37 " to convert a resu lt to decimal form." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(1/2+1/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLL$)!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 49 "Maple does arithmetic with complex number s too. " }{TEXT 0 1 "I" }{TEXT -1 36 " is a Maple constant standing \+ for " }{XPPEDIT 18 0 "sqrt(-1)" "6#-%%sqrtG6#,$\"\"\"!\"\"" }{TEXT -1 19 " . So entering . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "(3+2*I)*(2-I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\")\"\"\"%\"IGF%" }}}{PARA 0 "" 0 "" {TEXT -1 1 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 75 " . . causes complex multiplication to be performed giving the output 8 + I." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "Maplese" {TEXT -1 13 "The name for " }{XPPEDIT 18 0 "pi" "6#%#piG" }{TEXT -1 54 ", the area of the circle of radius 1, in \+ \"Maplese\" s " }{TEXT 0 2 "Pi" }{TEXT -1 73 ". So to calculate the area of a circle of radius 3, you would enter . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Pi*3^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 48 "Expressions, names, statements, and as signments" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "expressions " {TEXT -1 31 "Quantities to be computed like " }{TEXT 0 9 "1/2 + 1/3 " }{TEXT -1 13 " are called " }{TEXT 259 11 "expressions" }{TEXT -1 4 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "name" {TEXT -1 2 "A " }{TEXT 259 4 "name" }{TEXT -1 84 " is a string of characters which can be used to store the result of a computation. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "statement" {TEXT -1 2 "A " } {TEXT 259 9 "statement" }{TEXT -1 169 " in Maple is a string of names \+ and expressions terminated with a semicolon, or a colon if you don't w ant to see the output, which when entered will produce some action. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "assignment" {TEXT -1 4 "The " }{TEXT 259 10 "assignment" }{TEXT -1 67 " statement is one of the most common statements. It is of the form" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 0 19 "name := expression;" }{TEXT -1 3 " " }} {PARA 0 "" 0 "" {TEXT -1 32 "For example, the assignment . ." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "area := Pi*3^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%areaG,$%#PiG \"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 " . . stores " }{XPPEDIT 18 0 "9*Pi" "6#*&\"\"*\"\"\"%#PiGF%" } {TEXT -1 40 " in a location marked by the name area." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "A more useful assignme nt for the area of a circle is " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "area := Pi*r^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%areaG*&%#PiG\"\"\"%\"rG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "subs" {TEXT -1 30 "In this case, th e expression " }{TEXT 0 6 "Pi*r^2" }{TEXT -1 15 " is stored in " } {TEXT 0 4 "area" }{TEXT -1 141 " and with this assignment, the area of a circle of any given radius can be computed using the Maple word sub s. So to calculate the area when " }{TEXT 274 1 "r" }{TEXT -1 19 " is \+ 3, we enter . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 15 "subs(r=3,area);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 95 "Here, it is convenient to think of the assignment as de fining area as a function of the radius " }{TEXT 275 1 "r" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Functions \+ " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "funct ion" {TEXT -1 267 "A function is a rule f (possibly very complicated) for assigning to each argument x in a given set, a unique value f(x) \+ in a set. In calculus the arguments and values of a function are alwa ys real numbers, but the notion of function is much more flexible than that." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 58 " Functions can be defined in several useful ways in Maple." }} {PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 259 17 "As an e xpression:" }}{PARA 0 "" 0 "" {TEXT -1 21 "The assignment . . . " }} {PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "area := Pi*r^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%areaG*&%#PiG \"\"\"%\"rG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 127 " . . . defines the area of a circle as a function of it' s radius. The area function defined as an expression is evaluated with " }{TEXT 0 4 "subs" }{TEXT -1 122 ". Since this function assigns rea l numbers to real numbers, its values can be plotted on a graph with t he Maple procedure" }{TEXT 0 5 " plot" }{TEXT -1 26 ". So the stateme nt . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(area,r=0..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 213 155 155 {PLOTDATA 2 "6%-%'CURVESG6$7S7$\"\"!F(7$$\"1mmmm;')=()!#<$\"1: tGVJ>)Q#F,7$$\"1LLLe'40j\"!#;$\"1M<4]!=@N)F,7$$\"1nmm;6m$[#F2$\"1BrC=U \"z$>F27$$\"1nmm;yYULF2$\"1BD@Mf\")4NF27$$\"1LLLeF>(>%F2$\"1g$o/yjV`&F 27$$\"1mmm\">K'*)\\F2$\"10b\"H(RW@yF27$$\"1*****\\Kd,\"eF2$\"1o'*[!fO0 1\"!#:7$$\"1mmm\"fX(emF2$\"1(G,1SZHR\"FN7$$\"1*****\\U7Y](F2$\"1`b2!4? $p!3DEF N7$$\"1+++I,Q+5FN$\"1LqxM:)R9$FN7$$\"1+++]*3q3\"FN$\"1F=F<'p?r$FN7$$\" 1+++q=\\q6FN$\"1s9oSG9/VFN7$$\"1nm;fBIY7FN$\"1Ibhr-uz[FN7$$\"1LLLj$[kL \"FN$\"1GE&[]!=6cFN7$$\"1LLL`Q\"GT\"FN$\"1X(>`(RvqiFN7$$\"1++]s]k,:FN$ \"1Flf:k4%3(FN7$$\"1LLL`dF!e\"FN$\"1`**)>m4a%yFN7$$\"1++]sgam;FN$\"1k% *\\YMQD()FN7$$\"1++]FN$\"15+djc$)\\6Fdr7$$\"1nmmTc-)*>FN$\"1ZI?Ms:a7F dr7$$\"1mm;f`@'3#FN$\"1rUa]OJn8Fdr7$$\"1++]nZ)H;#FN$\"1T'p#)4&zp9Fdr7$ $\"1mmmJy*eC#FN$\"17&HOEPYe\"Fdr7$$\"1+++S^bJBFN$\"1(=JFp;yq\"Fdr7$$\" 1+++0TN:CFN$\"1!y@f([yK=Fdr7$$\"1++]7RV'\\#FN$\"1/Z]1y*y&>Fdr7$$\"1+++ :#fke#FN$\"1&[syi`;5#Fdr7$$\"1LLL`4NnEFN$\"1/>(H7o^B#Fdr7$$\"1+++],s`F FN$\"11,%)\\$GFN$\"1.6!GG)f>DFdr7$$\"1+++qfaLFdr7$$\"1nmm')fdLLFN$\"1q%RWtm6\\$Fdr7$$\"1nmm,FT=MFN$\"1^C%yNA6n $Fdr7$$\"1LL$e#pa-NFN$\"1)o')4-aS&QFdr7$$\"1+++Sv&)zNFN$\"10%*>o.2ESFd r7$$\"1LLLGUYoOFN$\"1$[K(*3RyA%Fdr7$$\"1nmm1^rZPFN$\"1T5" }{TEXT -1 22 ". For e xample, . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "areafunction := r -> Pi*r^2;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%-areafunctionGf*6#%\"rG6\"6$%)operatorG%&arrowGF(*& %#PiG\"\"\")9$\"\"#F.F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 " . . . defines the area function also." }} {PARA 0 "" 0 "" {TEXT -1 82 "Now to find the area of a circle of radiu s 3, we simply enter the statement . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "areafunction(3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "To plot this function ove r the domain given by the interval " }{XPPEDIT 18 0 "0<=r" "6#1\"\"!% \"rG" }{XPPEDIT 18 0 "``<=4" "6#1%!G\"\"%" }{TEXT -1 13 ", type . . . \+ " }}{PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(areafunction(r),r=0..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 252 252 252 {PLOTDATA 2 "6%-%'CURVESG6$7S7$\"\"!F(7$$\"1mmmm;')=()!#<$ \"1:tGVJ>)Q#F,7$$\"1LLLe'40j\"!#;$\"1M<4]!=@N)F,7$$\"1nmm;6m$[#F2$\"1B rC=U\"z$>F27$$\"1nmm;yYULF2$\"1BD@Mf\")4NF27$$\"1LLLeF>(>%F2$\"1g$o/yj V`&F27$$\"1mmm\">K'*)\\F2$\"10b\"H(RW@yF27$$\"1*****\\Kd,\"eF2$\"1o'*[ !fO01\"!#:7$$\"1mmm\"fX(emF2$\"1(G,1SZHR\"FN7$$\"1*****\\U7Y](F2$\"1`b 2!4?$p! 3DEFN7$$\"1+++I,Q+5FN$\"1LqxM:)R9$FN7$$\"1+++]*3q3\"FN$\"1F=F<'p?r$FN7 $$\"1+++q=\\q6FN$\"1s9oSG9/VFN7$$\"1nm;fBIY7FN$\"1Ibhr-uz[FN7$$\"1LLLj $[kL\"FN$\"1GE&[]!=6cFN7$$\"1LLL`Q\"GT\"FN$\"1X(>`(RvqiFN7$$\"1++]s]k, :FN$\"1Flf:k4%3(FN7$$\"1LLL`dF!e\"FN$\"1`**)>m4a%yFN7$$\"1++]sgam;FN$ \"1k%*\\YMQD()FN7$$\"1++]FN$\"15+djc$)\\6Fdr7$$\"1nmmTc-)*>FN$\"1ZI?M s:a7Fdr7$$\"1mm;f`@'3#FN$\"1rUa]OJn8Fdr7$$\"1++]nZ)H;#FN$\"1T'p#)4&zp9 Fdr7$$\"1mmmJy*eC#FN$\"17&HOEPYe\"Fdr7$$\"1+++S^bJBFN$\"1(=JFp;yq\"Fdr 7$$\"1+++0TN:CFN$\"1!y@f([yK=Fdr7$$\"1++]7RV'\\#FN$\"1/Z]1y*y&>Fdr7$$ \"1+++:#fke#FN$\"1&[syi`;5#Fdr7$$\"1LLL`4NnEFN$\"1/>(H7o^B#Fdr7$$\"1++ +],s`FFN$\"11,%)\\$GFN$\"1.6!GG)f>DFdr7$$\"1+++qf aLFdr7$$\"1nmm')fdLLFN$\"1q%RWtm6\\$Fdr7$$\"1nmm,FT=MFN$\"1^ C%yNA6n$Fdr7$$\"1LL$e#pa-NFN$\"1)o')4-aS&QFdr7$$\"1+++Sv&)zNFN$\"10%*> o.2ESFdr7$$\"1LLLGUYoOFN$\"1$[K(*3RyA%Fdr7$$\"1nmm1^rZPFN$\"1T5 " 0 "" {MPLTEXT 1 0 24 "plot(areafunction,0..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 230 168 168 {PLOTDATA 2 "6%-%'CURVESG6$7S7$\"\"!F(7$$\"1mmmm ;')=()!#<$\"1:tGVJ>)Q#F,7$$\"1LLLe'40j\"!#;$\"1M<4]!=@N)F,7$$\"1nmm;6m $[#F2$\"1BrC=U\"z$>F27$$\"1nmm;yYULF2$\"1BD@Mf\")4NF27$$\"1LLLeF>(>%F2 $\"1g$o/yjV`&F27$$\"1mmm\">K'*)\\F2$\"10b\"H(RW@yF27$$\"1*****\\Kd,\"e F2$\"1o'*[!fO01\"!#:7$$\"1mmm\"fX(emF2$\"1(G,1SZHR\"FN7$$\"1*****\\U7Y ](F2$\"1`b2!4?$p!3DEFN7$$\"1+++I,Q+5FN$\"1LqxM:)R9$FN7$$\"1+++]*3q3\"FN$\"1F= F<'p?r$FN7$$\"1+++q=\\q6FN$\"1s9oSG9/VFN7$$\"1nm;fBIY7FN$\"1Ibhr-uz[FN 7$$\"1LLLj$[kL\"FN$\"1GE&[]!=6cFN7$$\"1LLL`Q\"GT\"FN$\"1X(>`(RvqiFN7$$ \"1++]s]k,:FN$\"1Flf:k4%3(FN7$$\"1LLL`dF!e\"FN$\"1`**)>m4a%yFN7$$\"1++ ]sgam;FN$\"1k%*\\YMQD()FN7$$\"1++]FN$\"15+djc$)\\6Fdr7$$\"1nmmTc-)*>F N$\"1ZI?Ms:a7Fdr7$$\"1mm;f`@'3#FN$\"1rUa]OJn8Fdr7$$\"1++]nZ)H;#FN$\"1T 'p#)4&zp9Fdr7$$\"1mmmJy*eC#FN$\"17&HOEPYe\"Fdr7$$\"1+++S^bJBFN$\"1(=JF p;yq\"Fdr7$$\"1+++0TN:CFN$\"1!y@f([yK=Fdr7$$\"1++]7RV'\\#FN$\"1/Z]1y*y &>Fdr7$$\"1+++:#fke#FN$\"1&[syi`;5#Fdr7$$\"1LLL`4NnEFN$\"1/>(H7o^B#Fdr 7$$\"1+++],s`FFN$\"11,%)\\$GFN$\"1.6!GG)f>DFdr7$$ \"1+++qfaLFdr7$$\"1nmm')fdLLFN$\"1q%RWtm6\\$Fdr7$$\"1nmm,FT=M FN$\"1^C%yNA6n$Fdr7$$\"1LL$e#pa-NFN$\"1)o')4-aS&QFdr7$$\"1+++Sv&)zNFN$ \"10%*>o.2ESFdr7$$\"1LLLGUYoOFN$\"1$[K(*3RyA%Fdr7$$\"1nmm1^rZPFN$\"1T5 " 0 "" {MPLTEXT 1 0 20 "pol := x^2 + 4*x -1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,(* $%\"xG\"\"#\"\"\"F'\"\"%!\"\"F)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 34 " . . . then the assignment . . . " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pol := unapply(pol,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polGf *6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$9$\"\"#\"\"\"F.\"\"%!\"\"F0F(F(6 \"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 " . . . turns " }{TEXT 0 3 "pol" }{TEXT -1 48 " into a function defined b y an arrow operator. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "proc" {TEXT 259 15 "As a procedure:" }}{PARA 0 "" 0 "" {TEXT -1 15 "The Maple word " }{TEXT 0 4 "proc" }{TEXT -1 53 " can be used to defi ne functions. For example, . . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " area := proc(r) Pi*r^2 end; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%areaGf*6#%\"rG6\"F(F(*&%#PiG\" \"\"9$\"\"#F(F(6\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "E RROR" {TEXT -1 340 " . . . defines the area function too. It is evalu ated and plotted as in the arrow operator definition. One advantage of this way of defining a function is that the domain can be specified. \+ For example, the domain of the area function for a circle is all posi tive real numbers. This can be inserted into the procedure, with the M aple word " }{TEXT 0 5 "error" }{TEXT -1 63 ". The message must be enc losed in backquotes \" . . . \". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "areaproc := proc(r) \n if r > 0 then\n Pi*r^2\n else\n error \"radius must b e positive\" \n end if\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%)areaprocGf*6#%\"rG6\"F(F(@%2\"\"!9$*&%#PiG\"\"\")F,\"\"#F/YQ8radiu s~must~be~positiveF(F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ar eaproc(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ar eaproc(-3);" }}{PARA 8 "" 1 "" {TEXT -1 45 "Error, (in areaproc) radiu s must be positive\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "if..then..fi" {TEXT -1 9 "Note the " }{TEXT 0 20 "if .. then .. end if" }{TEXT -1 26 " control statement h ere. " }}{PARA 0 "" 0 "?if" {TEXT -1 47 "You can learn more about the \+ word if by typing " }{TEXT 0 3 "?if" }{TEXT -1 18 " in an input cell. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 190 "Func tions of two variables can be defined and plotted just as easily in Ma ple as functions of one variable. For example, the volume V of a cylin der of height h and radius r is defined by . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "V := (r,h) - > Pi*r^2*h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VGf*6$%\"rG%\"hG6\" 6$%)operatorG%&arrowGF)*(%#PiG\"\"\")9$\"\"#F/9%F/F)F)F)" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "plot3d" {TEXT -1 43 "To see what \+ the graph of V looks like, use " }{TEXT 0 6 "plot3d" }{TEXT -1 5 ". \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot3d(V(r,h),r=0..4,h=0..4,axes=boxed);" }}{PARA 13 "" 1 "" {GLPLOT3D 377 377 377 {PLOTDATA 3 "6%-%%GRIDG6%;\"\"!$\"\"%F'F &X,%)anythingG6\"6\"[gl'!%\"!!#\\bm\":\":00000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000 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LEG6#%$BOXG" 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 0 " Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 224 "Which way of defining a function is the preferred way? That real ly depends on the situation. The expression method works well for func tions which have only one rule of evaluation, but eventually you canno t avoid using an " }{TEXT 0 2 "->" }{TEXT -1 8 " or " }{TEXT 0 4 "proc" }{TEXT -1 13 " definition." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 259 28 "Piecewise defined functions:" }} {PARA 0 "" 0 "piecewise" {TEXT -1 111 "Many functions can only be desc ribed by stating various rules for various parts of the domain. The M aple word " }{TEXT 0 9 "piecewise" }{TEXT -1 40 " will help with defin ing such functions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 27 "Here is an example to show " }{TEXT 0 9 "piecewise" } {TEXT -1 9 " is used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "fx := piecewise(x<=-1,x^3+8, x<=2,3+2*x, \+ x<=4,11-cos(x),20-3*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fxG-%*PI ECEWISEG6&7$,&*$)%\"xG\"\"$\"\"\"F.\"\")F.1F,!\"\"7$,&F-F.F,\"\"#1F,F4 7$,&\"#6F.-%$cosG6#F,F11F,\"\"%7$,&\"#?F.F,!\"$%*otherwiseG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "As it stands, f x is an expression in the variable x. We can use " }{TEXT 0 7 "unappl y" }{TEXT -1 28 " to make it into a function." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := unapply (fx,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)opera torG%&arrowGF(-%*piecewiseG6)19$!\"\",&*$)F0\"\"$\"\"\"F6\"\")F61F0\" \"#,&F5F6F0F91F0\"\"%,&\"#6F6-%$cosG6#F0F1,&\"#?F6F0!\"$F(F(F(" }}} {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 "" }}{PARA 0 "" 0 "" {TEXT -1 121 "It is sometimes useful t o add various \"options\" to the plot procedure, which usually take th e form of equations such as \"" }{TEXT 0 11 "color=green" }{TEXT -1 2 "\"." }}{PARA 0 "" 0 "" {TEXT -1 12 "The option \"" }{TEXT 0 12 "disco nt=true" }{TEXT -1 100 "\" prevents the various curve segments being j oined by vertical line segments at the discontinuities." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot(f( x),x=-2.5..6,color=green,thickness=2,discont=true);" }}{PARA 13 "" 1 " " {GLPLOT2D 332 332 332 {PLOTDATA 2 "6(-%'CURVESG6%7S7$$!0+++'******** !#:$\"1+++3+++5F*7$$!1sPuO`3Y$*!#;$\"1Y7lKHyI6F*7$$!1>5^>x6x()F0$\"1'z (4ckdW7F*7$$!1BtYFTDP\")F0$\"1Nl]u\"\\DP\"F*7$$!1N\\=/\"\\J\\(F0$\"18I ;z,P,:F*7$$!1'QW'*R0@&oF0$\"1B62?*y&H;F*7$$!1l#Hi#exdiF0$\"1ZTvM[W[QUcF0$\"1PfU/O_r=F*7$$!1#\\n&z2%f+&F0$\"1-l3W=\"))*>F*7$$!1 D#filS:P%F0$\"1b\"[(o=pD@F*7$$!1#Q\\<:#)*=PF0$\"1C,lpN?cAF*7$$!17@yl#3 U9$F0$\"1xN%oMe6P#F*7$$!1.w+0!\\r\\#F0$\"1![)**)>q0]#F*7$$!1!=Sn&GVZ=F 0$\"1k>lGM^IEF*7$$!1Q)4%e4J@7F0$\"1K!=$3ytbFF*7$$!1![g<\"HKFl!#<$\"1!z kK5FQFOB!#=$\"12UlZDn/IF*7$$\"1GsV<\"R5'fFap$\"1W([By?# >JF*7$$\"1(4/b&4*\\#F0$\"1:Q35\">)*\\$F*7$$\"1%3wij=_6$F0$\"1<_DFP/BOF*7 $$\"1\"z63Wy!ePF0$\"1eB;)o:;v$F*7$$\"1Mv[?WU[VF0$\"12v4%)[opQF*7$$\"1& [RDJ#>&)\\F0$\"1(*y]i%Qq*RF*7$$\"1\"pD?>:mk&F0$\"1Q^SQIKHTF*7$$\"1,.*H v&QAiF0$\"1g!)f]rZWUF*7$$\"1U?eKPBWoF0$\"13k^Yn%)oVF*7$$\"1$*)oLajm[(F 0$\"1yPn3FL(\\%F*7$$\"19H>zd::\")F0$\"1$eQe:JIi%F*7$$\"1>8#QLaKs)F0$\" 1kUwm3lWZF*7$$\"193x+TW)R*F0$\"1jT:?))oz[F*7$$\"1)HlO@80+\"F*$\"1&fItU E5+&F*7$$\"1fD*46!Hl5F*$\"1=^)>A!eI^F*7$$\"1L5r2w)R7\"F*$\"1l?U:_(zC&F *7$$\"13\\mv%f\")=\"F*$\"1;)H8&*=jP&F*7$$\"1#*)yB?S&[7F*$\"1%ydZS!3(\\ &F*7$$\"1&e5(fal68F*$\"1q6U>4JBcF*7$$\"1M5=+:F*$\"1'plY(RO+gF*7$$\"1uJTB& 4Qc\"F*$\"1[j#o/>w7'F*7$$\"11*p8>5pi\"F*$\"17)RFQ?QD'F*7$$\"1&GS=:$*[o \"F*$\"1p0o.jypjF*7$$\"1rI\"z;[8v\"F*$\"1Uh#eL'p-lF*7$$\"1pX]Ejy5=F*$ \"1R\"4Ils:i'F*7$$\"1u0r+)fT(=F*$\"1Z6U,'>$[nF*7$$\"1B))z,j\"[$>F*$\"1 Ywf.EjpoF*7$$\"1+++'*******>F*$\"1*****>*******pF*-%'COLOURG6&%$RGBG\" \"!$\"*++++\"!\")F^[l-%*THICKNESSG6#\"\"#-F$6%7S7$$\"1+++3+++?F*$\"1_@ Q%o9;9\"!#97$$\"1zX)fJ%fV?F*$\"1D#z2\"z`X6F^\\l7$$\"1jWE!\\D:3#F*$\"1) GY!\\8))[6F^\\l7$$\"1p)RG1$=C@F*$\"1\"eL,:dD:\"F^\\l7$$\"1Yj\\(RBr;#F* $\"1&[Assgh:\"F^\\l7$$\"1!zPUkf)4AF*$\"1z%QqQW'f6F^\\l7$$\"1\"[(e:;[\\ AF*$\"1e@t>qxi6F^\\l7$$\"1Pf#>(y]!H#F*$\"1&*=Dyn\"f;\"F^\\l7$$\"1N)>\\ GPHL#F*$\"1(oc3+DF*$\"1:w?Nd7!=\"F^\\l7$$\"1k>lyW]VDF*$\"1__Ng8k#=\"F^\\l7$$\" 1L!=$QfC&e#F*$\"19(=F+>\\=\"F^\\l7$$\"1C\")f#=^Ji#F*$\"1'4]FDfo=\"F^\\ l7$$\"1t3K%=C#oEF*$\"1lA%*pP+*=\"F^\\l7$$\"17a,HpS1FF*$\"1u\"Rg\"F ^\\l7$$\"1?MCQD#3v#F*$\"1#=o'*fhC>\"F^\\l7$$\"1jbMyy8!z#F*$\"1L^(zG()Q >\"F^\\l7$$\"1;QePIFLGF*$\"19Z2%[%G&>\"F^\\l7$$\"1<_v4zMuGF*$\"1,r1:-X '>\"F^\\l7$$\"1D!H)H_?\"F^\\l7$$\"1uTEG;ccHF*$\"11cJa IH)>\"F^\\l7$$\"1J7%3#G,**HF*$\"1>2Nq_)*)>\"F^\\l7$$\"1s%Q#zw5VIF*$\"1 K*[tU:&*>\"F^\\l7$$\"1h!)4$Q#\\\"3$F*$\"1w'HAX>)*>\"F^\\l7$$\"1U(\\[\" *[H7$F*$\"1$p`5i#)**>\"F^\\l7$$\"1zPnovxlJF*$\"1\"f>fvq**>\"F^\\l7$$\" 1$eQ30xw?$F*$\"1?q2A\"F^\\l7$$\"1kUEap@[KF*$\"1ddD,@V*>\"F^\\l7$$ \"1jT:0'HKH$F*$\"1@+.8D&))>\"F^\\l7$$\"1js*RZvOL$F*$\"1^0iu3;)>\"F^\\l 7$$\"1>^)>2goP$F*$\"1Ki+/_C(>\"F^\\l7$$\"1*Rbit\"*fT$F*$\"1G86?)ei>\"F ^\\l7$$\"1;)H8)HxeMF*$\"1*=/='=,&>\"F^\\l7$$\"1_W#*)zE!*\\$F*$\"1$GQEw zO>\"F^\\l7$$\"1r6#pj.6a$F*$\"1tDfJ^7#>\"F^\\l7$$\"1N(3qVTAe$F*$\"1&HO I^Z/>\"F^\\l7$$\"1HvC,*3`i$F*$\"1jOgrs_)=\"F^\\l7$$\"1H!**z)zymOF*$\"1 &*o4-E_'=\"F^\\l7$$\"1#of^M1#4PF*$\"1Ef`I'=V=\"F^\\l7$$\"1zk!pXt7v$F*$ \"12![L3$)>=\"F^\\l7$$\"1q0oj(G**y$F*$\"1fZ'f'*3(z6F^\\l7$$\"14G\\2@BM QF*$\"17t)>Kcp<\"F^\\l7$$\"1tCMYv&Q(QF*$\"1aeT5iOu6F^\\l7$$\"1[6#*Gl5; 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For example, " }{TEXT 0 4 "sqrt " }{TEXT -1 33 " is the square root function and " }{TEXT 0 3 "abs" } {TEXT -1 73 " is the absolute value function. The trig and inverse tri g functions are " }{TEXT 0 3 "sin" }{TEXT -1 3 ", " }{TEXT 0 6 "arcsi n" }{TEXT -1 3 ", " }{TEXT 0 3 "cos" }{TEXT -1 60 ", etc., the natura l logarithm and exponential functions are " }{TEXT 0 2 "ln" }{TEXT -1 7 " and " }{TEXT 0 3 "exp" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 54 "For a complete list of built in functions, type . . . " }} {PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "?inifcns " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "@" {TEXT -1 57 "The operation of composition of functions, is denoted by \+ " }{TEXT 0 1 "@" }{TEXT -1 53 ". Thus the function defined by the assi gnment . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "g := x -> sin(cos(x^2+3));\ng(x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%$sinG 6#-%$cosG6#,&*$)9$\"\"#\"\"\"F7\"\"$F7F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#-%$cosG6#,&*$)%\"xG\"\"#\"\"\"F.\"\"$F." }}} {PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 50 " . . . c ould also be defined by the assignment . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "g := sin@cos@(x->x ^2+3);\ng(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG-%\"@G6%%$sinG% $cosGf*6#%\"xG6\"6$%)operatorG%&arrowGF-,&*$)9$\"\"#\"\"\"F6\"\"$F6F-F -F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#-%$cosG6#,&*$)%\"xG\" \"#\"\"\"F.\"\"$F." }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 42 "Using Maple as a fancy graphing calculator" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 160 "It is conveni ent to think of Maple as a fancy graphing calculator for many purposes . For example, suppose you want to find the real solutions of the equa tion " }{XPPEDIT 18 0 "x^5-3*x-1 = 0;" "6#/,(*$%\"xG\"\"&\"\"\"*&\" \"$F(F&F(!\"\"F(F+\"\"!" }{TEXT -1 18 " in the interval " }{XPPEDIT 18 0 "-2<=x" "6#1,$\"\"#!\"\"%\"xG" }{XPPEDIT 18 0 "``<=2" "6#1%!G\"\" #" }{TEXT -1 102 ". Then we can just plot the right hand side of the \+ equation and look for where the graph crosses the " }{TEXT 281 1 "x" } {TEXT -1 6 "-axis." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 40 "f := x -> x^5-3*x+1;\nplot(f(x),x=-2..2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arro wGF(,(*$)9$\"\"&\"\"\"F1F/!\"$F1F1F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 294 209 209 {PLOTDATA 2 "6%-%'CURVESG6$7W7$$!\"#\"\"!$!#DF*7 $$!1nmm\"p0k&>!#:$!1nv*Rt*>z@!#97$$!1LLL$Q6G\">F0$!1eQ=%foo)=F37$$!1++ v3-)[(=F0$!1o[rLVAa;F37$$!1nm;M!\\p$=F0$!1`[.J&[0W\"F37$$!1LLL))Qj^?w#oF07$$!1nm;C2G!e\"F0$!1wLV'z) [9TF07$$!1LL$3yO5]\"F0$!17=zv%>p6#F07$$!1++]nU)*=9F0$!1uGgUYhf\\!#;7$$ !1LL$3WDTL\"F0$\"1l/xsT_exFfn7$$!1++]d(Q&\\7F0$\"1_a(zq%[-'***Ff n$\"155c:)e2+$F07$$!1++++0\"*H\"*Ffn$\"1uFw3yh/JF07$$!1++++83&H)Ffn$\" 1>zP4hy&4$F07$$!1LLL3k(p`(Ffn$\"1t%4b[!)y,$F07$$!1nmmmj^NmFfn$\"1cr@Bc ,iGF07$$!1ommm9'=(eFfn$\"1(*R')\\Yv\"p#F07$$!1,++v#\\N)\\Ffn$\"1R&Qf\\ DVY#F07$$!1pmmmCC(>%Ffn$\"1^x_jk9YAF07$$!1*****\\FRXL$Ffn$\"1h**o1\"Ri *>F07$$!1+++D=/8DFfn$\"1K6`X-\"Hv\"F07$$!1mmm;a*el\"Ffn$\"1I\\QETk'\\ \"F07$$!1pmm;Wn(o)!#<$\"1\"Q(\\$GD1E\"F07$$!1qLLL$eV(>!#=$\"1q***\\2Bf +\"F07$$\"1Mmm;f`@')Fes$\"1u_nfoe8uFfn7$$\"1)****\\nZ)H;Ffn$\"1o3jtqg6 ^Ffn7$$\"1lmm;$y*eCFfn$\"1R&\\dLb?j#Ffn7$$\"1*******R^bJ$Ffn$\"1Cev'=1 7M*F[t7$$\"1'*****\\5a`TFfn$!1u``p?+PBFfn7$$\"1(****\\7RV'\\Ffn$!1*3'* ec.:f%Ffn7$$\"1'*****\\@fkeFfn$!1;6w*o[+!pFfn7$$\"1JLLL&4Nn'Ffn$!1m^\" p*Q)op)Ffn7$$\"1*******\\,s`(Ffn$!1%ekJp6z,\"F07$$\"1lmm\"zM)>$)Ffn$!1 \"4WY>F0$\"1K@63.k)3#F37$$\"1++v.Uac>F0$ \"1+J\\?H " 0 "" {MPLTEXT 1 0 24 "plot(f(x),x=-1.5..1.5); " }}{PARA 13 "" 1 "" {GLPLOT2D 306 264 264 {PLOTDATA 2 "6%-%'CURVESG6$7bo7$$!1+++++++:!#:$!1+++++v$4#F*7$$!1+ ]PM@l$[\"F*$!1/t(*e-\"zt\"F*7$$!1++voUIn9F*$!1&HmQsF&*R\"F*7$$!1+]7.k& 4X\"F*$!1AmY(oJ!y5F*7$$!1++]P&3YV\"F*$!1Yso'=S'Gx!#;7$$!1+Dcc,;19F*$!1 Pe&f*oH\"z#FA7$$!1+]ivF*7$$!1+ ]7V0@&=\"F*$\"1%>$e$R:p@#F*7$$!1+]i&exd7\"F*$\"1!e/@'R1pDF*7$$!1+]i+#Q U1\"F*$\"1frez5_FGF*7$$!1+]iShTK5F*$\"1)H^%pMJCHF*7$$!1+]i!3%f+5F*$\"1 )yMtI3))*HF*7$$!1***\\PuS()o*FA$\"1@e650'G0$F*7$$!1++D\"oS:P*FA$\"1;;P 04g)3$F*7$$!1+]7G9EX!*FA$\"1*z'G@.43JF*7$$!1+++v@)*=()FA$\"1LJDJD\"=6$ F*7$$!1++DJ_fJ%)FA$\"1pOWc?M.JF*7$$!1++](G3U9)FA$\"1DwE0X'\\3$F*7$$!1* ****\\-\\r\\(FA$\"1a@Q52H7IF*7$$!1+++vGVZoFA$\"1WP[mVp.HF*7$$!1+++v4J@ iFA$\"1*oZvl%>tFF*7$$!1++D1Bt_cFA$\"1])=0C/\"QEF*7$$!1+++vsjw\\FA$\"1u (\\nZkCY#F*7$$!1++++h*QS%FA$\"1gaRjSg/BF*7$$!1++Dc>mPPFA$\"1fN35S+9@F* 7$$!1,++]=$z9$FA$\"1kC`e$)GT>F*7$$!1***\\iX/4]#FA$\"1N-e1IH\\l:F*7$$!1****\\i:#>C\"FA$\"1c]kCpas8F*7$$!1!* **\\7ev:l!#<$\"1![`**\\ra>\"F*7$$!1G++](o2[\"!#=$\"1$**\\iIUW+\"F*7$$ \"1)***\\P>:mkF`v$\"1HY]l:JL'FA7$$\"1, +]PPBW=FA$\"1F.XCAVpWFA7$$\"1******\\Nm'[#FA$\"1wMPd$*G,ZFA7$$\"1,++D6!Hl &FA$!1$3WFni9Q'FA7$$\"1***\\P4w)RiFA$!1m'>+\"HltxFA7$$\"1-++vZf\")oFA$ !1ztOi;],\"*FA7$$\"1)**\\P/-a[(FA$!1BPB&R;1,\"F*7$$\"1++v=Yb;\")FA$!1K u-T-r#3\"F*7$$\"1+](=7)3D%)FA$!1pfG[<..6F*7$$\"1*****\\i@Ot)FA$!1X6>m* f>6\"F*7$$\"1**\\P4wic!*FA$!14'\\EN'o26F*7$$\"1***\\PfL'z$*FA$!19Eq.A! z3\"F*7$$\"1+](ouE2p*FA$!106lH4e_5F*7$$\"1+++!*>=+5F*$!1v6O()oN'***FA7 $$\"1++DE&4Q1\"F*$!1c6mrL#)*G)FA7$$\"1+]P%>5p7\"F*$!1![ErgsMj&FA7$$\"1 +++bJ*[=\"F*$!1T$R[#)H4>#FA7$$\"1+]7j17=7F*$\"1b!HD&4MfFF`v7$$\"1++Dr \"[8D\"F*$\"13bn\\+1UJFA7$$\"1+]i]s1\"G\"F*$\"1J#>K(Q?rgFA7$$\"1+++Ijy 58F*$\"114r)*e#=P*FA7$$\"1+v=nIZU8F*$\"1;bQKm*HL\"F*7$$\"1+]P/)fTP\"F* $\"1#Q]7;4ux\"F*7$$\"1+++b!)[/9F*$\"1MZ7%)o`^AF*7$$\"1+]i0j\"[V\"F*$\" 18X*=HUmx#F*7$$\"1](=#HA6^9F*$\"1U*zz>=53$F*7$$\"1+D\"G:3uY\"F*$\"1m2b (4C;S$F*7$$\"1]iSwSq$[\"F*$\"1/`%o\"H,RPF*7$$\"1+++++++:F*$\"1+++++v$4 %F*-%'COLOURG6&%$RGBG$\"#5!\"\"\"\"!Fjal-%+AXESLABELSG6$Q\"x6\"%!G-%%V IEWG6$;$F*Fial$\"#:Fial%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "fsolve" {TEXT -1 42 "The largest solution is between 1 a nd 1.5." }}{PARA 0 "" 0 "" {TEXT -1 61 "We can calculate this largest \+ solution more accurately using " }{TEXT 0 6 "fsolve" }{TEXT -1 118 ". \+ Note the syntax. There are two arguments, the equation to solve, and t he interval in which to search for a solution." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fsolve(f(x)= 0,x=1..1.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+V![Y@\"!\"*" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 63 "Data types: expression \+ sequences, lists, sets, arrays, tables " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Data types " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "types" {TEXT -1 173 "Maple expressions are classified into various data types. For exampl e, arithmetic expressions are classified by whether they are sums: typ e \"+\" or products: type \"*\" , etc." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "whattype" {TEXT -1 15 "The Maple word " }{TEXT 0 8 " whattype" }{TEXT -1 48 " will tell what type a particular expression i s." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "whattype(12345);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% (integerG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }{MPLTEXT 1 0 14 "whattype(1/2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#%)fractionG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "whattype(0.4 567);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&floatG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "The type " }{TEXT 0 5 "flo at" }{TEXT -1 70 " indicates a floating point number ( roughly speakin g . . a decimal )." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "whattype(a+b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"+G" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "whattype(sin(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)functionG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "whattype(sin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'symbolG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "whattype(a,b,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(exprseqG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 "Ex pression sequences and lists" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 "An " }{TEXT 259 19 "expression sequence" }{TEXT -1 9 " ( type: " }{TEXT 0 7 "exprseq" }{TEXT -1 72 " ), is any sequenc e of expressions separated by commas. For example, . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "junk := 1, 2, w*r+m, a=b+c, 1/2, (x+y)/z, `hello`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%junkG6)\"\"\"\"\"#,&*&%\"wGF&%\"rGF&F&%\"mGF&/%\"aG, &%\"bGF&%\"cGF&#F&F'*&,&%\"xGF&%\"yGF&F&%\"zG!\"\"%&helloG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 126 "is an assignme nt to \"junk\" of an expression sequence of 7 expressions. To refer to the sixth expression in this sequence, use " }{TEXT 0 9 "junk[6]; " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "junk[6];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"%\"yGF &F&%\"zG!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "A " }{TEXT 259 4 "list" }{TEXT -1 9 " ( type: " }{TEXT 0 4 "list" }{TEXT -1 68 " ) is an expression sequence enclosed by square brackets. So . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "junklist := [junk];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)junklistG7)\"\"\"\"\"#,&*&%\"wGF&%\"rGF&F&%\"mGF&/% \"aG,&%\"bGF&%\"cGF&#F&F'*&,&%\"xGF&%\"yGF&F&%\"zG!\"\"%&helloG" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 253 " . . . m akes a list whose terms are those in junk. As with expression sequence s, we can refer to particular terms of a list by appending to its name the number of the term enclosed in square brackets. Thus to get the \+ 5th term of \"junklist\", type . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "junklist[5];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "You can also reference the 3rd term \+ in this list by by using the Maple word " }{TEXT 0 2 "op" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "op(3,junklist);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,& *&%\"wG\"\"\"%\"rGF&F&%\"mGF&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 13 "In general, " }{TEXT 0 11 "op(n,alist)" }{TEXT -1 43 " returns the n th term in the list \"alist\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "If the first nu merical argument or input parameter for " }{TEXT 0 2 "op" }{TEXT -1 157 " is omitted, the output produced consists of all the terms of \"j unklist\" as a sequence. In other words, we return to the original exp ression sequence \"junk\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "op(junklist);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)\"\"\"\"\"#,&*&%\"wGF#%\"rGF#F#%\"mGF#/%\"aG,&%\"bGF#% \"cGF##F#F$*&,&%\"xGF#%\"yGF#F#%\"zG!\"\"%&helloG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "if op(junkli st)=junk then print(`they are the same`) end if;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2they~are~the~sameG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "nops" {TEXT -1 52 "To count how many terms are in a li st, use the word " }{TEXT 0 4 "nops" }{TEXT -1 24 ". So for example, . . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "nops(junklist);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 " \+ . . . tells us that there are 7 terms in the list \"junklist\". " } {TEXT 0 4 "nops" }{TEXT -1 24 " comes in handy when you" }}{PARA 0 "" 0 "" {TEXT -1 68 "don't want to (or aren't able to) count the terms in a list by hand." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 32 "You can't directly use the word " }{TEXT 0 4 "nops" } {TEXT -1 199 " to count the number of terms in an expression sequence. But you can put square brackets around the expression sequence and co unt the terms in the resulting list. This device is used again and aga in." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "nops(3,4,a);" }}{PARA 8 "" 1 "" {TEXT -1 60 "Error, w rong number (or type) of parameters in function nops" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 0 4 "nops" }{TEXT -1 61 " sim ply thinks that it has been given three input parameters." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "nops( [3,4,a]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 109 " A point in a plane is a list of two numbers. Points can be added and subtracted and multipl ied by a number. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 44 "p := [1,2]; q := [-3,1];\nw := 3*p + 2*q - p ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG7$\"\"\"\"\"#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"qG7$!\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG7$!\"%\"\"'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 39 "Using lists in connection with graphing" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 121 "One important use of l ists is to make lists of points to plot. For example, to draw a pictur e of the square with vertices" }{XPPEDIT 18 0 " ``(1,1), ``(3,1), ``(3 ,3), ``(1,3)" "6&-%!G6$\"\"\"F&-F$6$\"\"$F&-F$6$F)F)-F$6$F&F)" }{TEXT -1 31 ", make a list and then plot it." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "pts := [[1,1],[3,1],[3,3 ],[1,3],[1,1]];\nplot(pts);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ptsG 7'7$\"\"\"F'7$\"\"$F'7$F)F)7$F'F)F&" }}{PARA 13 "" 1 "" {GLPLOT2D 243 207 207 {PLOTDATA 2 "6%-%'CURVESG6$7'7$$\"\"\"\"\"!F(7$$\"\"$F*F(7$F,F ,7$F(F,F'-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F7-%+AXESLABELSG6$Q!6\"F;-%% VIEWG6$%(DEFAULTGF@" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 138 "Notice that the origin is not included in the fie ld of view. We can arrange for the origin to be included by specifying the ranges of the " }{TEXT 276 1 "x" }{TEXT -1 5 " and " }{TEXT 277 1 "y" }{TEXT -1 39 " coordinates to be used for the plot. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "pl ot(pts,x=0..4,y=0..4);" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 13 " " 1 "" {GLPLOT2D 299 261 261 {PLOTDATA 2 "6%-%'CURVESG6$7'7$$\"\"\"\" \"!F(7$$\"\"$F*F(7$F,F,7$F(F,F'-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F7-%+A XESLABELSG6$Q\"x6\"Q\"yF<-%%VIEWG6$;F7$\"\"%F*FA" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "Sequences can be construc ted using the word " }{TEXT 0 3 "seq" }{TEXT -1 65 ". For example, we can construct a list of points along the line " }{XPPEDIT 18 0 "y=x+2 " "6#/%\"yG,&%\"xG\"\"\"\"\"#F'" }{TEXT -1 26 " and plot them as follo ws." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "line := [seq([i,i+2],i=-5..5)];\nplot(line,style=poin t,symbol=circle);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%lineG7-7$!\"&! \"$7$!\"%!\"#7$F(!\"\"7$F+\"\"!7$F-\"\"\"7$F/\"\"#7$F1\"\"$7$F3\"\"%7$ F5\"\"&7$F7\"\"'7$F9\"\"(" }}{PARA 13 "" 1 "" {GLPLOT2D 280 209 209 {PLOTDATA 2 "6'-%'CURVESG6$7-7$$!\"&\"\"!$!\"$F*7$$!\"%F*$!\"#F*7$F+$! \"\"F*7$F0F*7$F3$\"\"\"F*7$F*$\"\"#F*7$F7$\"\"$F*7$F:$\"\"%F*7$F=$\"\" &F*7$F@$\"\"'F*7$FC$\"\"(F*-%'COLOURG6&%$RGBG$\"#5F4F*F*-%+AXESLABELSG 6$%!GFT-%&STYLEG6#%&POINTG-%'SYMBOLG6#%'CIRCLEG-%%VIEWG6$%(DEFAULTGFjn " 1 5 4 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }} }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "Lists a re useful when plotting more than one function at at time. In addition " }{TEXT 0 4 "plot" }{TEXT -1 65 " options can be directed to a parti cular graph by means of lists." }}{PARA 0 "" 0 "" {TEXT -1 62 "For exa mple, we can plot the graphs of the quadratic function " }{XPPEDIT 18 0 "x^2-2" "6#,&*$%\"xG\"\"#\"\"\"F&!\"\"" }{TEXT -1 25 " and the linea r function " }{XPPEDIT 18 0 "2*x+5" "6#,&*&\"\"#\"\"\"%\"xGF&F&\"\"&F& " }{TEXT -1 18 " over the domain " }{XPPEDIT 18 0 "x=-5..5 " "6#/%\"x G;,$\"\"&!\"\"F'" }{TEXT -1 24 " on the same axes by . ." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot( [x^2-2,2*x+5],x=-5..5,color=[red,blue],thickness=[1,2]);" }}{PARA 13 " " 1 "" {GLPLOT2D 257 224 224 {PLOTDATA 2 "6&-%'CURVESG6%7S7$$!\"&\"\"! $\"#BF*7$$!1LLLe%G?y%!#:$\"1))4j<'zn3#!#97$$!1mmT&esBf%F0$\"1c'Gjf))*3 >F37$$!1LL$3s%3zVF0$\"1&fB#*HQwr\"F37$$!1ML$e/$QkTF0$\"16CC:'3U`\"F37$ $!1nmT5=q]RF0$\"1`H[zW!3O\"F37$$!1LL3_>f_PF0$\"1gS)ej%>37F37$$!1++vo1Y ZNF0$\"1?Gj>xWe5F37$$!1LL3-OJNLF0$\"1*4UU#oJC\"*F07$$!1++v$*o%Q7$F0$\" 1A:f:%>%exF07$$!1mmm\"RFj!HF0$\"1o>b2*QnW'F07$$!1LL$e4OZr#F0$\"13/-q?z p`F07$$!1+++v'\\!*\\#F0$\"10w6y#\\_C%F07$$!1+++DwZ#G#F0$\"1Rci3Tq4KF07 $$!1+++D.xt?F0$\"101&3OB0I#F07$$!1LL3-TC%)=F0$\"1EeBOeP]:F07$$!1mmm\"4 z)e;F0$\"1X#)o2%)z=v!#;7$$!1mmmm`'zY\"F0$\"1,!Gt1vHs%*)*)Fip7$$!1$***\\(=[jL) Fip$!1cw'*))H008F07$$!1'***\\iXg#G'Fip$!1UD6*z)G0;F07$$!1emmT&Q(RTFip$ !1'Rm![ciG=F07$$!1lm;/'=><#Fip$!1Z(odpFG&>F07$$!1EMLLe*e$\\!#=$!1AB$pj v***>F07$$\"1sm;zRQb@Fip$!1;N-*>VN&>F07$$\"1-+](=>Y2%Fip$!1o&oZyuR$=F0 7$$\"1vmm\"zXu9'Fip$!1(>&Q-\"*3A;F07$$\"1,+++&y))G)Fip$!1xB7K\\%HJ\"F0 7$$\"1++]i_QQ5F0$!1a!GiYgv@*Fip7$$\"1,+D\"y%3T7F0$!1$Q'\\dc3(f%Fip7$$ \"1++]P![hY\"F0$\"195ly1!f\\\"Fip7$$\"1LLL$Qx$o;F0$\"1!y\"=K4$[$yFip7$ $\"1+++v.I%)=F0$\"1U^A.ze]:F07$$\"1mm\"zpe*z?F0$\"1$>R]=GiK#F07$$\"1,+ +D\\'QH#F0$\"1h_9%H;=E$F07$$\"1LLe9S8&\\#F0$\"1S2t]PpDUF07$$\"1,+D1#=b q#F0$\"1A-Nk(G)>`F07$$\"1LLL3s?6HF0$\"1d>&)4u7vkF07$$\"1++DJXaEJF0$\"1 !G*)eq!GvxF07$$\"1ommm*RRL$F0$\"1StL,d::\"*F07$$\"1om;a<.YNF0$\"1Me:?T Vd5F37$$\"1NLe9tOcPF0$\"1,q?S&H5@\"F37$$\"1,++]Qk\\RF0$\"1$G%=a'o*f8F3 7$$\"1NL$3dg6<%F0$\"1nuw]!e)R:F37$$\"1ommmxGpVF0$\"1+Vzev14V.Uu3#F37$$\"\"&F*F+ -%'COLOURG6&%$RGBG$\"*++++\"!\")F*F*-%*THICKNESSG6#\"\"\"-F$6%7S7$F(F( 7$F.$!1nmm;p0kXF07$F5$!1LL$3s%H%Fip7$F ao$\"1.0+++l+>F`s7$Ffo$\"1.+++vW]VFip7$F[p$\"1-+++NfC&)Fip7$F`p$\"1ML$ ez6:B\"F07$Fep$\"1nmm;=C#o\"F07$F[q$\"1nmmm#pS1#F07$F`q$\"1++]i`A3DF07 $Feq$\"1mmmm(y8!HF07$Fjq$\"1,+]i.tKLF07$F_r$\"1,+](3zMu$F07$Fdr$\"1omm \"H_?<%F07$Fir$\"1nm;zihlXF07$F^s$\"1LLL3#G,*\\F07$Fds$\"1ML$ezw5V&F07 $Fis$\"1++]PQ#\\\"eF07$F^t$\"1NLLe\"*[HiF07$Fct$\"1++++dxdmF07$Fht$\"1 ,++D0xwqF07$F]u$\"1,+]i&p@[(F07$Fbu$\"1+++vgHKzF07$Fgu$\"1lmmmZvO$)F07 $F\\v$\"1,++]2go()F07$Fav$\"1KL$eR<*f\"*F07$Ffv$\"1-++])Hxe*F07$F[w$\" 1mm;H!o-***F07$F`w$\"1++DTO5T5F37$Few$\"1nmmT9C#3\"F37$Fjw$\"1++D1*3`7 \"F37$F_x$\"1MLL$*zym6F37$Fdx$\"1ML$3N1#47F37$Fix$\"1nm\"HYt7D\"F37$F^ y$\"1+++q(G**G\"F37$Fcy$\"1nm;9@BM8F37$Fhy$\"1MLL`v&QP\"F37$F]z$\"1++D Ol5;9F37$Fbz$\"1++v.Uac9F37$Fgz$\"#:F*-Fjz6&F\\[lF*F*F][l-Fa[l6#\"\"#- %+AXESLABELSG6$Q\"x6\"%!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" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 143 "If you had to draw several pieces of circles, you m ight define a function to simplify things. You can call the function w hatever you want, say " }{TEXT 0 4 "circ" }{TEXT -1 1 "." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "circ \+ := (h,k,r,f,l) -> [h+r*cos(t),k+r*sin(t),t=f..l];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%circGf*6'%\"hG%\"kG%\"rG%\"fG%\"lG6\"6$%)operatorG%& arrowGF,7%,&9$\"\"\"*&9&F3-%$cosG6#%\"tGF3F3,&9%F3*&F5F3-%$sinGF8F3F3/ F9;9'9(F,F,F," }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "So if we wanted circles of radius " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT -1 85 " centered at the corners of th e square \"pts\" we can construct the sequence of lists:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "circs := seq(circ(op(pts[i]),1/2,0,2*Pi),i=1..4);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&circsG6&7%,&\"\"\"F(*&#F(\"\"#F(-%$cosG6#%\"tGF(F(,& F(F(*&F*F(-%$sinGF.F(F(/F/;\"\"!,$*&F+F(%#PiGF(F(7%,&\"\"$F(*&F*F(F,F( F(F0F47%F;,&F " 0 "" {MPLTEXT 1 0 55 "plot([circs,pts],scaling=con strained,view=[0..4,0..4]);" }}{PARA 13 "" 1 "" {GLPLOT2D 284 288 288 {PLOTDATA 2 "6*-%'CURVESG6$7S7$$\"3++++++++:!#<$\"\"\"\"\"!7$$\"3ka!)p =\"=`\\\"F*$\"3;$)y74REo5F*7$$\"3sb6%\\5!p$[\"F*$\"3IY(zzWkm7\"F*7$$\" 3q^I%RKHCY\"F*$\"3y;GC;b:!>\"F*7$$\"31V)Rfa`EV\"F*$\"3uvE(p/@1D\"F*7$$ \"3q_Pk,E@&R\"F*$\"3kZ6]$GziI\"F*7$$\"3_n>V3(GTN\"F*$\"3C=Y/Nr(HN\"F*7 $$\"3YmfJ(yAeI\"F*$\"3iggZ_fc&R\"F*7$$\"3[r`\"ydQ0D\"F*$\"3wf%QpI,FV\" F*7$$\"3;TNB#)p+\">\"F*$\"3u,Ibv#y?Y\"F*7$$\"3Kt5\"QJpi7\"F*$\"3CpSs1M z$[\"F*7$$\"39c28ToDn5F*$\"3!*zr=oeX&\\\"F*7$$\"3')yH6lW,(***!#=$\"3U1 e'3\"*****\\\"F*7$$\"3_^#z.#)e(=$*Fbo$\"3at4QktL&\\\"F*7$$\"3iA9#[#*3p n)Fbo$\"3='4fuiw@[\"F*7$$\"3D5yYMbW8\")Fbo$\"3#*Q6zEL/j9F*7$$\"3G^()=j B%)yuFbo$\"3.KRl`UyJ9F*7$$\"3?o>#=Eb-)pFbo$\"393*>>]6&)R\"F*7$$\"3[xyh E=MbkFbo$\"3!zP=IgQEN\"F*7$$\"3_3PA(*y*y/'Fbo$\"3Q&e:#pBG18F*7$$\"3=g[ 4ImMqcFbo$\"3ykYZ??3]7F*7$$\"3-u\"F*7$$\"3aY! 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The Maple word " }{TEXT 0 3 "seq" }{TEXT -1 77 " is very handy for this. So to split off from \+ \"pts\" the odd and even terms --" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "xdat := [seq(pts[i,1],i=1..n ops(pts))];\nydat := [seq(pts[i,2],i=1..nops(pts))];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xdatG7'\"\"\"\"\"$F'F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ydatG7'\"\"\"F&\"\"$F'F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "The converse task of building \+ up a list of points to plot from two lists can also be performed using " }{TEXT 0 3 "seq" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "new_pts :=[seq([xdat[i],yda t[i]],i=1..nops(xdat))]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(new_pt sG7'7$\"\"\"F'7$\"\"$F'7$F)F)7$F'F)F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "is(new_pts=pts);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "If you have a very complicated dra wing to make, you can use " }{TEXT 0 14 "plots[display]" }{TEXT -1 124 " from the plots package. Just give names to the plots you want to display and then display the list of plots you have named." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "p 1 := plot([x^2-2,2*x+5],x=-5..5):\np2 := plot([[2,1],[3,20],[0,0],[2,1 ]],color=blue):\nplots[display]([p1,p2],ytickmarks=3);" }}{PARA 13 "" 1 "" {GLPLOT2D 258 294 294 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$!\"&\"\"!$ \"#BF*7$$!1LLLe%G?y%!#:$\"1))4j<'zn3#!#97$$!1mmT&esBf%F0$\"1c'Gjf))*3> F37$$!1LL$3s%3zVF0$\"1&fB#*HQwr\"F37$$!1ML$e/$QkTF0$\"16CC:'3U`\"F37$$ !1nmT5=q]RF0$\"1`H[zW!3O\"F37$$!1LL3_>f_PF0$\"1gS)ej%>37F37$$!1++vo1YZ NF0$\"1?Gj>xWe5F37$$!1LL3-OJNLF0$\"1*4UU#oJC\"*F07$$!1++v$*o%Q7$F0$\"1 A:f:%>%exF07$$!1mmm\"RFj!HF0$\"1o>b2*QnW'F07$$!1LL$e4OZr#F0$\"13/-q?zp `F07$$!1+++v'\\!*\\#F0$\"10w6y#\\_C%F07$$!1+++DwZ#G#F0$\"1Rci3Tq4KF07$ $!1+++D.xt?F0$\"101&3OB0I#F07$$!1LL3-TC%)=F0$\"1EeBOeP]:F07$$!1mmm\"4z )e;F0$\"1X#)o2%)z=v!#;7$$!1mmmm`'zY\"F0$\"1,!Gt1vHs%*)*)Fip7$$!1$***\\(=[jL) Fip$!1cw'*))H008F07$$!1'***\\iXg#G'Fip$!1UD6*z)G0;F07$$!1emmT&Q(RTFip$ !1'Rm![ciG=F07$$!1lm;/'=><#Fip$!1Z(odpFG&>F07$$!1EMLLe*e$\\!#=$!1AB$pj v***>F07$$\"1sm;zRQb@Fip$!1;N-*>VN&>F07$$\"1-+](=>Y2%Fip$!1o&oZyuR$=F0 7$$\"1vmm\"zXu9'Fip$!1(>&Q-\"*3A;F07$$\"1,+++&y))G)Fip$!1xB7K\\%HJ\"F0 7$$\"1++]i_QQ5F0$!1a!GiYgv@*Fip7$$\"1,+D\"y%3T7F0$!1$Q'\\dc3(f%Fip7$$ \"1++]P![hY\"F0$\"195ly1!f\\\"Fip7$$\"1LLL$Qx$o;F0$\"1!y\"=K4$[$yFip7$ $\"1+++v.I%)=F0$\"1U^A.ze]:F07$$\"1mm\"zpe*z?F0$\"1$>R]=GiK#F07$$\"1,+ +D\\'QH#F0$\"1h_9%H;=E$F07$$\"1LLe9S8&\\#F0$\"1S2t]PpDUF07$$\"1,+D1#=b q#F0$\"1A-Nk(G)>`F07$$\"1LLL3s?6HF0$\"1d>&)4u7vkF07$$\"1++DJXaEJF0$\"1 !G*)eq!GvxF07$$\"1ommm*RRL$F0$\"1StL,d::\"*F07$$\"1om;a<.YNF0$\"1Me:?T Vd5F37$$\"1NLe9tOcPF0$\"1,q?S&H5@\"F37$$\"1,++]Qk\\RF0$\"1$G%=a'o*f8F3 7$$\"1NL$3dg6<%F0$\"1nuw]!e)R:F37$$\"1ommmxGpVF0$\"1+Vzev14V.Uu3#F37$$\"\"&F*F+ -%'COLOURG6&%$RGBG$\"#5!\"\"F*F*-F$6$7S7$F(F(7$F.$!1nmm;p0kXF07$F5$!1L L$3s%H%Fip7$Fao$\"1.0+++l+>F`s7$Ffo$\" 1.+++vW]VFip7$F[p$\"1-+++NfC&)Fip7$F`p$\"1ML$ez6:B\"F07$Fep$\"1nmm;=C# o\"F07$F[q$\"1nmmm#pS1#F07$F`q$\"1++]i`A3DF07$Feq$\"1mmmm(y8!HF07$Fjq$ \"1,+]i.tKLF07$F_r$\"1,+](3zMu$F07$Fdr$\"1omm\"H_?<%F07$Fir$\"1nm;zihl XF07$F^s$\"1LLL3#G,*\\F07$Fds$\"1ML$ezw5V&F07$Fis$\"1++]PQ#\\\"eF07$F^ t$\"1NLLe\"*[HiF07$Fct$\"1++++dxdmF07$Fht$\"1,++D0xwqF07$F]u$\"1,+]i&p @[(F07$Fbu$\"1+++vgHKzF07$Fgu$\"1lmmmZvO$)F07$F\\v$\"1,++]2go()F07$Fav $\"1KL$eR<*f\"*F07$Ffv$\"1-++])Hxe*F07$F[w$\"1mm;H!o-***F07$F`w$\"1++D TO5T5F37$Few$\"1nmmT9C#3\"F37$Fjw$\"1++D1*3`7\"F37$F_x$\"1MLL$*zym6F37 $Fdx$\"1ML$3N1#47F37$Fix$\"1nm\"HYt7D\"F37$F^y$\"1+++q(G**G\"F37$Fcy$ \"1nm;9@BM8F37$Fhy$\"1MLL`v&QP\"F37$F]z$\"1++DOl5;9F37$Fbz$\"1++v.Uac9 F37$Fgz$\"#:F*-Fjz6&F\\[lF*F][lF*-F$6$7&7$$\"\"#F*$\"\"\"F*7$$\"\"$F*$ \"#?F*7$F*F*Fidl-Fjz6&F\\[lF*F*$\"*++++\"!\")-%+AXESLABELSG6$Q\"x6\"%! G-%*AXESTICKSG6$%(DEFAULTGF`el-%%VIEWG6$;F(FgzFbfl" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" } }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "Anothe r use of lists is with " }{TEXT 259 16 "parametric plots" }{TEXT -1 65 ". If you have a curve in the plane described parametrically with \+ " }{XPPEDIT 18 0 "x = f(t) " "6#/%\"xG-%\"fG6#%\"tG" }{TEXT -1 3 ", \+ " }{XPPEDIT 18 0 "y = g(t)" "6#/%\"yG-%\"gG6#%\"tG" }{TEXT -1 99 ", as the parameter t runs from a to b, then you can draw it by making up \+ a 3 term list to give to " }{TEXT 0 4 "plot" }{TEXT -1 58 ". Say you \+ wanted to draw a circle of radius 4 centered at" }{XPPEDIT 18 0 "``(1, 2)" "6#-%!G6$\"\"\"\"\"#" }{TEXT -1 130 ". Then the list consists of t he expressions for the x and y coordinates followed by an equation giv ing the range of the parameter." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot([1+4*cos(t),2+4*sin(t), t=0..2*Pi],\nscaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 270 242 242 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"&\"\"!$\"\"#F*7$$\"1PWe\\ \\ai\\!#:$\"1mI-t76YDF07$$\"1Y#H&R3_p[F0$\"1qz$Qe:L,$F07$$\"19Wa\"fM%* p%F0$\"1LD%*HTC@NF07$$\"1X(=vOG7Y%F0$\"119yv$o\\+%F07$$\"1A+:83qhTF0$ \"1\"=4!oUB]WF07$$\"1SdXn'HI$QF0$\"1XpN!3w_k^F07$$\"1rH_A'3V+$F0$\"1xw]b/hhaF07$$\"1H$oy&e0GDF0$\"18SU/ii'p& F07$$\"1(e)[5X:5?F0$\"1aDz`sMqeF07$$\"1\\g/HZ0Q:F0$\"1Ru\\XpkjfF07$$\" 1JQ!4s:h(**!#;$\"1^k#pG*****fF07$$\"13S.j02]XFbo$\"1)yZ]\"*)pifF07$$!1 NiG9gGZe!#<$\"1pFn>ITdeF07$$!1;vDCdV#4&Fbo$\"16\"HVhYVq&F07$$!1***[%4h #p,\"F0$\"1d9BHSFaaF07$$!1DCa!z&z:9F0$\"1l#f`,#4)=&F07$$!1)p0(QlsN=F0$ \"1Bq9C)36#[F07$$!1L5A#o\"oh@F0$\"1$oCP&*e-X%F07$$!17T#fpAPY#F0$\"1=tz jhl+SF07$$!1\"ea#4XP#p#F0$\"1n%zz;,$QNF07$$!1j:w.%\\a'GF0$\"1xekIvtGIF 07$$!1\"zmx+7G'HF0$\"1<3--+^3rUy@F0$! 1w*=h2x\\G%Fbo7$$!1Il$[PEU%=F0$!1#)GF[7RD\")Fbo7$$!1Qr/sXV>9F0$!1_I7N9 L&=\"F07$$!1')o,tOvi**Fbo$!1\"QXYO\\iY\"F07$$!1.C)o#f7\"4&Fbo$!1AT0w** R/ F07$$\"1&GDGm/x()*Fbo$!1V%pZI\")***>F07$$\"1#*GX,$*3::F0$!1**Q.Qnpm>F0 7$$\"1t:GQl,A?F0$!1$R(y^=Bn=F07$$\"1aJAa$>V`#F0$!1#Goo(3.%p\"F07$$\"1X !R/B?8+$F0$!17CAW!RLY\"F07$$\"1+`zf,uVMF0$!1#eRn\"Hsm6F07$$\"1Uqea,sRQ F0$!1%GaBC))3<)Fbo7$$\"1W()[d82gTF0$!1Ds\"p?aL_%Fbo7$$\"1cS[1]tpWF0$\" 1r@2o4@*y*Fft7$$\"1MjG\"Q++p%F0$\"1=7<$pD,c%Fbo7$$\"1Z\"*oZb(='[F0$\"1 h(*HTYEz&*Fbo7$$\"1KiQ9Ayi\\F0$\"157axIhb9F07$F($\"1b;G.+++?F0-%'COLOU RG6&%$RGBG$\"#5!\"\"F*F*-%+AXESLABELSG6$%!GFc[l-%(SCALINGG6#%,CONSTRAI NEDG-%%VIEWG6$%(DEFAULTGF[\\l" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 4 "Sets" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} {PARA 0 "" 0 "" {TEXT -1 2 "A " }{TEXT 259 3 "set" }{TEXT -1 366 " is \+ an expression sequence enclosed by curly brackets. A set is different from a list in two important ways. For one thing, the order of the m embers of a set is immaterial. In particular the order in which you sp ecify the members may not be the order in which they are stored. Also each member of the set is only stored once, no matter how many times \+ you list it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "A := \{y+x+1,1,2,1,4,4/2,`hello`,x+y+1,`hello`\}; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG<'\"\"\"\"\"#\"\"%%&helloG,( %\"yGF&%\"xGF&F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 21 "The set operation of " }{TEXT 0 5 "union" }{TEXT -1 2 " , " }{TEXT 0 9 "intersect" }{TEXT -1 6 ", and " }{TEXT 0 5 "minus" } {TEXT -1 31 " are built-in Maple operations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "B := \{x,`*`,sqrt (4),x+1+y\};\n'A union B'=A union B;\n'A intersect B'=A intersect B;\n 'A minus B'=A minus B;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG<&\"\" #%\"*G%\"xG,(%\"yG\"\"\"F(F+F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/- %&unionG6$%\"AG%\"BG<)\"\"\"\"\"#\"\"%%\"*G%\"xG%&helloG,(%\"yGF*F.F*F *F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%*intersectG6$%\"AG%\"BG<$\" \"#,(%\"yG\"\"\"%\"xGF-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&min usG6$%\"AG%\"BG<%\"\"\"\"\"%%&helloG" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 157 "Sets can be used as an alternative t o lists when plotting more than one function at time, if you do not wa nt to direct specific options to individual graphs." }}{PARA 0 "" 0 " " {TEXT -1 49 "We can plot the graphs of the quadratic function " } {XPPEDIT 18 0 "x^2-2" "6#,&*$%\"xG\"\"#\"\"\"F&!\"\"" }{TEXT -1 25 " a nd the linear function " }{XPPEDIT 18 0 "2*x+5" "6#,&*&\"\"#\"\"\"%\"x GF&F&\"\"&F&" }{TEXT -1 17 " over the domain " }{XPPEDIT 18 0 "x=-5..5 " "6#/%\"xG;,$\"\"&!\"\"F'" }{TEXT -1 24 " on the same axes by . ." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(\{x^2-2,2*x+5\},x=-5..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 222 244 244 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"&\"\"!F(7$$!1LLLe%G?y%! #:$!1nmm;p0kXF.7$$!1mmT&esBf%F.$!1LL$3f_PF.$!1nm;/R=0DF.7$$!1++vo1YZNF.$!1,+]P8#\\4#F.7$$!1LL3-OJNLF.$ !1mm;/siq;F.7$$!1++v$*o%Q7$F.$!1****\\(y$pZ7F.7$$!1mmm\"RFj!HF.$!1ELLL yaE\")!#;7$$!1LL$e4OZr#F.$!1imm;>s%H%Fhn7$$!1+++v'\\!*\\#F.$\"1.0+++l+ >!#=7$$!1+++DwZ#G#F.$\"1.+++vW]VFhn7$$!1+++D.xt?F.$\"1-+++NfC&)Fhn7$$! 1LL3-TC%)=F.$\"1ML$ez6:B\"F.7$$!1mmm\"4z)e;F.$\"1nmm;=C#o\"F.7$$!1mmmm `'zY\"F.$\"1nmmm#pS1#F.7$$!1++v=t)eC\"F.$\"1++]i`A3DF.7$$!1nmm;1J\\5F. $\"1mmmm(y8!HF.7$$!1$***\\(=[jL)Fhn$\"1,+]i.tKLF.7$$!1'***\\iXg#G'Fhn$ \"1,+](3zMu$F.7$$!1emmT&Q(RTFhn$\"1omm\"H_?<%F.7$$!1lm;/'=><#Fhn$\"1nm ;zihlXF.7$$!1EMLLe*e$\\Fco$\"1LLL3#G,*\\F.7$$\"1sm;zRQb@Fhn$\"1ML$ezw5 V&F.7$$\"1-+](=>Y2%Fhn$\"1++]PQ#\\\"eF.7$$\"1vmm\"zXu9'Fhn$\"1NLLe\"*[ HiF.7$$\"1,+++&y))G)Fhn$\"1++++dxdmF.7$$\"1++]i_QQ5F.$\"1,++D0xwqF.7$$ \"1,+D\"y%3T7F.$\"1,+]i&p@[(F.7$$\"1++]P![hY\"F.$\"1+++vgHKzF.7$$\"1LL L$Qx$o;F.$\"1lmmmZvO$)F.7$$\"1+++v.I%)=F.$\"1,++]2go()F.7$$\"1mm\"zpe* z?F.$\"1KL$eR<*f\"*F.7$$\"1,++D\\'QH#F.$\"1-++])Hxe*F.7$$\"1LLe9S8&\\# F.$\"1mm;H!o-***F.7$$\"1,+D1#=bq#F.$\"1++DTO5T5!#97$$\"1LLL3s?6HF.$\"1 nmmT9C#3\"Faw7$$\"1++DJXaEJF.$\"1++D1*3`7\"Faw7$$\"1ommm*RRL$F.$\"1MLL $*zym6Faw7$$\"1om;a<.YNF.$\"1ML$3N1#47Faw7$$\"1NLe9tOcPF.$\"1nm\"HYt7D \"Faw7$$\"1,++]Qk\\RF.$\"1+++q(G**G\"Faw7$$\"1NL$3dg6<%F.$\"1nm;9@BM8F aw7$$\"1ommmxGpVF.$\"1MLL`v&QP\"Faw7$$\"1++D\"oK0e%F.$\"1++DOl5;9Faw7$ $\"1,+v=5s#y%F.$\"1++v.Uac9Faw7$$\"\"&F*$\"#:F*-%'COLOURG6&%$RGBG$\"#5 !\"\"F*F*-F$6$7S7$F($\"#BF*7$F,$\"1))4j<'zn3#Faw7$F2$\"1c'Gjf))*3>Faw7 $F7$\"1&fB#*HQwr\"Faw7$F<$\"16CC:'3U`\"Faw7$FA$\"1`H[zW!3O\"Faw7$FF$\" 1gS)ej%>37Faw7$FK$\"1?Gj>xWe5Faw7$FP$\"1*4UU#oJC\"*F.7$FU$\"1A:f:%>%ex F.7$FZ$\"1o>b2*QnW'F.7$Fjn$\"13/-q?zp`F.7$F_o$\"10w6y#\\_C%F.7$Feo$\"1 Rci3Tq4KF.7$Fjo$\"101&3OB0I#F.7$F_p$\"1EeBOeP]:F.7$Fdp$\"1X#)o2%)z=vFh n7$Fip$\"1,!Gt1vHs%*)*)Fhn7$Fh q$!1cw'*))H008F.7$F]r$!1UD6*z)G0;F.7$Fbr$!1'Rm![ciG=F.7$Fgr$!1Z(odpFG& >F.7$F\\s$!1AB$pjv***>F.7$Fas$!1;N-*>VN&>F.7$Ffs$!1o&oZyuR$=F.7$F[t$!1 (>&Q-\"*3A;F.7$F`t$!1xB7K\\%HJ\"F.7$Fet$!1a!GiYgv@*Fhn7$Fjt$!1$Q'\\dc3 (f%Fhn7$F_u$\"195ly1!f\\\"Fhn7$Fdu$\"1!y\"=K4$[$yFhn7$Fiu$\"1U^A.ze]:F .7$F^v$\"1$>R]=GiK#F.7$Fcv$\"1h_9%H;=E$F.7$Fhv$\"1S2t]PpDUF.7$F]w$\"1A -Nk(G)>`F.7$Fcw$\"1d>&)4u7vkF.7$Fhw$\"1!G*)eq!GvxF.7$F]x$\"1StL,d::\"* F.7$Fbx$\"1Me:?TVd5Faw7$Fgx$\"1,q?S&H5@\"Faw7$F\\y$\"1$G%=a'o*f8Faw7$F ay$\"1nuw]!e)R:Faw7$Ffy$\"1+Vzev14V.Uu3#Faw7$FezFd[l-Fjz6&F\\[lF*F][lF*-%+AXESLABELSG6$Q\"x6\"%!G-%%VI EWG6$;F(Fez%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 122 "If you want to specify the colour, lines tyle or thickness of the individual graphs you should use a list inste ad of a set." }}{PARA 0 "" 0 "" {TEXT -1 16 "The command . . " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot(\{x^2-2,2*x+5\},x=-5..5,color=[red,blue]);" }}{PARA 13 "" 1 " " {GLPLOT2D 210 232 232 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"&\"\"!F(7$$ !3YLLLe%G?y%!#<$!3!pmmm\"p0kXF.7$$!3OmmT&esBf%F.$!3uKL$3f_PF.$!3fmm;/R=0DF.7$$!3K++vo1YZNF.$!3k ++]P8#\\4#F.7$$!3;LL3-OJNLF.$!3Kmm;/siq;F.7$$!3p***\\P*o%Q7$F.$!3Q**** \\(y$pZ7F.7$$!3Kmmm\"RFj!HF.$!3JELLLyaE\")!#=7$$!33LL$e4OZr#F.$!3qhmm; >s%H%Fhn7$$!3u*****\\n\\!*\\#F.$\"3L.0+++l+>!#?7$$!3%)*****\\ixCG#F.$ \"39.+++vW]VFhn7$$!3#******\\KqP2#F.$\"3r,+++NfC&)Fhn7$$!39LL3-TC%)=F. $\"3qLL$ez6:B\"F.7$$!3[mmm\"4z)e;F.$\"3/nmm;=C#o\"F.7$$!3Mmmmm`'zY\"F. $\"3Mnmmm#pS1#F.7$$!3#****\\(=t)eC\"F.$\"3<++]i`A3DF.7$$!3!ommmh5$\\5F .$\"3Rmmmm(y8!HF.7$$!3S$***\\(=[jL)Fhn$\"3K,+]i.tKLF.7$$!3)f***\\iXg#G 'Fhn$\"3!3++v3zMu$F.7$$!3ndmmT&Q(RTFhn$\"3Yomm\"H_?<%F.7$$!3%\\mmTg=>< #Fhn$\"3-nm;zihlXF.7$$!3vDMLLe*e$\\Fco$\"39LLL3#G,*\\F.7$$\"3!=nm\"zRQ b@Fhn$\"3OML$ezw5V&F.7$$\"3_,+](=>Y2%Fhn$\"3I++]PQ#\\\"eF.7$$\"3summ\" zXu9'Fhn$\"3%\\LL$e\"*[HiF.7$$\"3#4+++]y))G)Fhn$\"3=++++dxdmF.7$$\"3H+ +]i_QQ5F.$\"3e+++D0xwqF.7$$\"3b++D\"y%3T7F.$\"35,+]i&p@[(F.7$$\"3+++]P ![hY\"F.$\"3++++vgHKzF.7$$\"3iKLL$Qx$o;F.$\"3ElmmmZvO$)F.7$$\"3Y+++v.I %)=F.$\"3%4+++v+'o()F.7$$\"3?mm\"zpe*z?F.$\"3UKL$eR<*f\"*F.7$$\"3;,++D \\'QH#F.$\"3K-++])Hxe*F.7$$\"3%HL$e9S8&\\#F.$\"3!fmm\"H!o-***F.7$$\"3s ++D1#=bq#F.$\"3:++DTO5T5!#;7$$\"3\"HLL$3s?6HF.$\"3emmmT9C#3\"Faw7$$\"3 a***\\7`Wl7$F.$\"3\"****\\i!*3`7\"Faw7$$\"3enmmm*RRL$F.$\"3_LLL$*zym6F aw7$$\"3%zmmTvJga$F.$\"3fLL$3N1#47Faw7$$\"3]MLe9tOcPF.$\"3!pm;HYt7D\"F aw7$$\"31,++]Qk\\RF.$\"3A+++q(G**G\"Faw7$$\"3![LL3dg6<%F.$\"3'pmmT6KUL \"Faw7$$\"3%ymmmw(GpVF.$\"3eLLL`v&QP\"Faw7$$\"3C++D\"oK0e%F.$\"30++DOl 5;9Faw7$$\"35,+v=5s#y%F.$\"3A++v.Uac9Faw7$$\"\"&F*$\"#:F*-%'COLOURG6&% $RGBG$\"*++++\"!\")$F*F*F`[l-F$6$7S7$F($\"#BF*7$F,$\"3s()4j<'zn3#Faw7$ F2$\"3_b'Gjf))*3>Faw7$F7$\"31&fB#*HQwr\"Faw7$F<$\"3E6CC:'3U`\"Faw7$FA$ \"3!G&H[zW!3O\"Faw7$FF$\"3?gS)ej%>37Faw7$FK$\"3'*>Gj>xWe5Faw7$FP$\"3*) )4UU#oJC\"*F.7$FU$\"3/A:f:%>%exF.7$FZ$\"3mn>b2*QnW'F.7$Fjn$\"3g2/-q?zp `F.7$F_o$\"3y/w6y#\\_C%F.7$Feo$\"3[Rci3Tq4KF.7$Fjo$\"3\\01&3OB0I#F.7$F _p$\"3?EeBOeP]:F.7$Fdp$\"3EX#)o2%)z=vFhn7$Fip$\"3u+!Gt1vHs%*)*)Fhn7$Fhq$!3lbw'*))H008F.7$F]r$!3TUD 6*z)G0;F.7$Fbr$!30'Rm![ciG=F.7$Fgr$!3;Z(odpFG&>F.7$F\\s$!3]AB$pjv***>F .7$Fas$!3O;N-*>VN&>F.7$Ffs$!3Mo&oZyuR$=F.7$F[t$!3)o>&Q-\"*3A;F.7$F`t$! 3SxB7K\\%HJ\"F.7$Fet$!39a!GiYgv@*Fhn7$Fjt$!3_#Q'\\dc3(f%Fhn7$F_u$\"3G9 5ly1!f\\\"Fhn7$Fdu$\"3&*z<=K4$[$yFhn7$Fiu$\"3SU^A.ze]:F.7$F^v$\"3E$>R] =GiK#F.7$Fcv$\"3kg_9%H;=E$F.7$Fhv$\"3QS2t]PpDUF.7$F]w$\"3c@-Nk(G)>`F.7 $Fcw$\"3Md>&)4u7vkF.7$Fhw$\"3))z#*)eq!GvxF.7$F]x$\"3))RtL,d::\"*F.7$Fb x$\"3oLe:?TVd5Faw7$Fgx$\"3=,q?S&H5@\"Faw7$F\\y$\"3/$G%=a'o*f8Faw7$Fay$ \"3Hnuw]!e)R:Faw7$Ffy$\"3m*H%zev14V.Uu3#Faw7$FezFe[l-Fjz6&F\\[lF`[lF`[lF][l-%+AXESLABELSG6$Q\"x6\"Q! F[el-%%VIEWG6$;F(Fez%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 " . . may not produce the desire d result." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 39 "Tables and arrays: vectors and matrices" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 2 "A " }{TEXT 259 5 "table" } {TEXT -1 298 " is a special kind of data structure which is very flexi ble. The packages of special procedures are really tables whose indice s of the package are the names of the procedures and whose entries are the bodies of the procedures. We do not make much use of tables in th is worksheet, except for arrays." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "array" {TEXT -1 3 "An " }{TEXT 259 5 "Array" }{TEXT -1 58 " is a special kind of table whose indices are numerical. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 9 "Warnings: " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 91 "A 1 dimensional array looks the same as a list, but is, in fact a different data structure. " }}{PARA 0 "" 0 "" {TEXT -1 207 "Maple 7 has two different array stru ctures. The preferred newer array structure is denoted by \"Array\" us ing an upper case \"A\", and the older array data structure is denoted by \"array\" using a lower case \"a\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "a := Array([2,-3,7,4,9] );\nwhattype(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'RTABLEG6$ \"*CrTW\"-%'VECTORG6#7'\"\"#!\"$\"\"(\"\"%\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&ArrayG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 121 "In some ways, 1-dimensional arrays behave like li sts. We can access a member of such an array by the subscript operatio n " }{TEXT 0 3 "[ ]" }{TEXT -1 6 " . . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 " . . but " }{TEXT 0 2 "op" }{TEXT -1 16 " cannot b e used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(3,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'/6#\"\" \"\"\"#/6#F'!\"$/6#\"\"$\"\"(/6#\"\"%F1/6#\"\"&\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "An array can be conver ted to a list . . ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "alist := convert(a,list);\nop(3,alist);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alistG7'\"\"#!\"$\"\"(\"\"%\"\"*" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 177 "Why have arrays at all? Well, for \+ one thing, the terms in an array can be more easily modified. For exa mple, to change the third term in the array a to 0 just enter a[3] := \+ 0." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "a := Array([2,-3,7,4,9]);\na[3] := 0;\na;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'RTABLEG6$\"*/'))\\9-%'VECTORG6#7'\" \"#!\"$\"\"(\"\"%\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6#\" \"$\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"*/'))\\9-%'V ECTORG6#7'\"\"#!\"$\"\"!\"\"%\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 154 "To change the third term in the list \" alist\" to 0, you have to make an entirely new list whose terms are al l the same as before except for the third one.\n" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 40 "[alist[1],alist[2],0,alist[4],alist[5]];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"#!\"$\"\"!\"\"%\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "The entries of \+ a 2 dimensional array or Matrix are accessed by subscript operator " } {TEXT 0 3 "[ ]" }{TEXT -1 25 " using a pair of indices." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "M := M atrix(1..4,1..5);\nfor i from 1 to 4 do\n for j from 1 to 5 do\n \+ M[i,j] := i+j;\n end do;\nend do;\nM;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'RTABLEG6$\"*#4O[9-%'MATRIXG6#7&7'\"\"!F.F.F.F. F-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"*#4O[9-%'MATRI XG6#7&7'\"\"#\"\"$\"\"%\"\"&\"\"'7'F-F.F/F0\"\"(7'F.F/F0F2\"\")7'F/F0F 2F4\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "creates a 4 by 5 matrix M, with " }{XPPEDIT 18 0 "M[i,j] = i+j;" " 6#/&%\"MG6$%\"iG%\"jG,&F'\"\"\"F(F*" }{TEXT -1 18 ", for all indices \+ " }{TEXT 283 1 "i" }{TEXT -1 5 " and " }{TEXT 284 1 "j" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 46 "\nA vector can be multiplied by a ma trix using " }{TEXT 0 1 "." }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "v := Vector([1,1,1 ,1,1]);\nM.v;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'RTABLEG6$\"* #>Y]9-%'MATRIXG6#7'7#\"\"\"F-F-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'RTABLEG6$\"*![1^9-%'MATRIXG6#7&7#\"#?7#\"#D7#\"#I7#\"#N" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "As an example o f using vectors and matrices we rotate the square" }}{PARA 257 "" 0 " " {TEXT -1 3 " " }{XPPEDIT 18 0 "ab := [[1,1],[3,1],[3,3],[1,3],[1,1 ]];" "6#>%#abG7'7$\"\"\"F'7$\"\"$F'7$F)F)7$F'F)7$F'F'" }{TEXT -1 3 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 82 "through an angle of 31 degrees coun ter clockwise about the origin and display it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "The matrix for a rotation of an angle " }{XPPEDIT 18 0 "theta" "6#%&thetaG" }{TEXT -1 21 " abou t the origin is " }{XPPEDIT 18 0 "matrix([[cos(theta),-sin(theta)],[si n(theta),cos(theta)]])" "6#-%'matrixG6#7$7$-%$cosG6#%&thetaG,$-%$sinG6 #F+!\"\"7$-F.6#F+-F)6#F+" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "First construct the rotation matri x for a rotation of " }{XPPEDIT 18 0 "31^o" "6#)\"#J%\"oG" }{TEXT -1 19 " about the origin." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "theta := 'theta':\ntheta := evalf( Pi/180*31);\nR := Matrix([[cos(theta),-sin(theta)],[sin(theta),cos(the ta)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&thetaG$\"+\"o?0T&!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'RTABLEG6%\"*G_$[9-%'MATRIXG6# 7$7$$\"+2Inr&)!#5$!+\\2Q]^F07$$\"+\\2Q]^F0F.%'MatrixG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "A single point can b e rotated by multiplying with the rotation matrix R." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "R.Vector([ 3,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*S$p_9-%'MATRI XG6#7$7#$\"3)*****>FQYc?!#<7#$\"3%)****RD:G-CF.&%'VectorG6#%'columnG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "To rot ate the whole square we can procede as follows." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "pts := [[1, 1],[3,1],[3,3],[1,3],[1,1]];\nrot_pts := [seq(convert(R.Vector(pts[i]) ,list),i=1..nops(pts))];\nplot(\{pts,rot_pts\},view=[-1..3.1,0..4.1],s caling=constrained);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ptsG7'7$\" \"\"F'7$\"\"$F'7$F)F)7$F'F)F&" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(ro t_ptsG7'7$$\"3Z+++eAH@M!#=$\"35++gv`?s8!#<7$$\"3)*****>FQYc?F,$\"3%)** **RD:G-CF,7$$\"3D++SxwQE5F,$\"3L++!o7;m6%F,7$$!3#z*****R#p%zoF)$\"3;++ +x*Rl3$F,F&" }}{PARA 13 "" 1 "" {GLPLOT2D 360 270 270 {PLOTDATA 2 "6'- %'CURVESG6$7'7$$\"\"\"\"\"!F(7$$\"\"$F*F(7$F,F,7$F(F,F'-%'COLOURG6&%$R GBG$\"#5!\"\"$F*F*F7-F$6$7'7$$\"3Z+++eAH@M!#=$\"35++gv`?s8!#<7$$\"3)** ***>FQYc?FA$\"3%)****RD:G-CFA7$$\"3D++SxwQE5FA$\"3L++!o7;m6%FA7$$!3#z* ****R#p%zoF>$\"3;+++x*Rl3$FAF;-F16&F3F7F4F7-%+AXESLABELSG6$Q!6\"FV-%(S CALINGG6#%,CONSTRAINEDG-%%VIEWG6$;$F6F*$\"#JF6;F7$\"#TF6" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 263 25 "Maple control statements " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 66 "T here are two especially important control statements. One is the " } {TEXT 259 15 "repetition loop" }{TEXT -1 23 ", and the other is the " }{TEXT 259 31 "conditional execution statement" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " } {TEXT 259 15 "repetition loop" }{TEXT -1 5 " is " }}{PARA 257 "" 0 " " {TEXT 0 49 "for .. from .. by .. to .. while .. do .. end do;" } {TEXT 264 1 " " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 120 "This s tatement can be used interactively or in a procedure to perform repeti tive tasks or to do an iterative algorithm. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 270 7 "Example" }{TEXT 258 1 ":" } {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "Add up the first 100 numbers." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "s := 0:\nfor i fro m 1 to 100 do\n s := s+i\nend do:\ns;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%]]" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "Compute the factorials of the first 10 positive integers and st ore them in a list. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "factseq := NULL: # start with the empty exprseq\n for i from 1 to 10 do \n factseq := factseq ,i!;\nend \+ do: \nfactlist := [factseq]; # make a list" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)factlistG7,\"\"\"\"\"#\"\"'\"#C\"$?\"\"$?(\"%S]\"&?. %\"'!)GO\"(+)GO" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 219 "Note the way the list is built up from an empty exprseq \+ NULL. Each time through the loop, one more term is added onto the end \+ of the sequence. At the end, square brackets are put around the seque nce, making it a list. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Alternatively, an array can be used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "factar ray := array(1..10): # initialize the array.\nfor i from 1 to 10 do\n factarray[i]:= i!\nend do;\nfactlist := convert(factarray,list); \+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"\"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"\"$\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"\"%\"#C" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"\"&\"$?\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> &%*factarrayG6#\"\"'\"$?(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*facta rrayG6#\"\"(\"%S]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6# \"\")\"&?.%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"\"*\" '!)GO" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*factarrayG6#\"#5\"(+)GO" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)factlistG7,\"\"\"\"\"#\"\"'\"#C\" $?\"\"$?(\"%S]\"&?.%\"'!)GO\"(+)GO" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 272 21 "Conditional execution" }{TEXT 271 3 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 0 39 " if .. then .. elif .. else .. end if; " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 94 "There are lots of times when you need t o consider cases, and they can all be handled with the " }{TEXT 0 36 " if .. then .. elif .. else .. end if" }{TEXT -1 92 " statement. For e xample, many functions are defined piecewise. The absolute value funct ion " }{TEXT 0 3 "abs" }{TEXT -1 20 " is such a function." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 258 8 "Question" } {TEXT 273 2 ": " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 84 "Define a version of the absolute value function for real \+ numbers and plot its graph." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "myabs := proc(x) if x > 0 then x e lse -x end if end proc;\nplot(myabs,-2..2,scaling=constrained,title=`m y absolute value`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&myabsGf*6#% \"xG6\"F(F(@%2\"\"!9$F,,$F,!\"\"F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 360 270 270 {PLOTDATA 2 "6'-%'CURVESG6$7U7$$!\"#\"\"!$\"\"#F*7$$!3MLLL $Q6G\">!#<$\"3MLLL$Q6G\">F07$$!3bmm;M!\\p$=F0$\"3bmm;M!\\p$=F07$$!3MLL L))Qj^'***!#=$\"3w++++()>'***Fbo7$$!3E++ ++0\"*H\"*Fbo$\"3E++++0\"*H\"*Fbo7$$!35++++83&H)Fbo$\"35++++83&H)Fbo7$ $!3\\LLL3k(p`(Fbo$\"3\\LLL3k(p`(Fbo7$$!3Anmmmj^NmFbo$\"3Anmmmj^NmFbo7$ $!3)zmmmYh=(eFbo$\"3)zmmmYh=(eFbo7$$!3+,++v#\\N)\\Fbo$\"3+,++v#\\N)\\F bo7$$!3commmCC(>%Fbo$\"3commmCC(>%Fbo7$$!39*****\\FRXL$Fbo$\"39*****\\ FRXL$Fbo7$$!3t*****\\#=/8DFbo$\"3t*****\\#=/8DFbo7$$!3=mmm;a*el\"Fbo$ \"3=mmm;a*el\"Fbo7$$!3komm;Wn(o)!#>$\"3komm;Wn(o)Fjr7$$!3$G++]7bDW%Fjr $\"3$G++]7bDW%Fjr7$$!3IqLLL$eV(>!#?$\"3IqLLL$eV(>Fes7$$\"3V[mmT+07UFjr Fis7$$\"3)Qjmm\"f`@')FjrF\\t7$$\"3%z****\\nZ)H;FboF_t7$$\"3ckmm;$y*eCF boFbt7$$\"3f)******R^bJ$FboFet7$$\"3'e*****\\5a`TFboFht7$$\"3'o****\\7 RV'\\FboF[u7$$\"3Y'*****\\@fkeFboF^u7$$\"3_ILLL&4Nn'FboFau7$$\"3A***** **\\,s`(FboFdu7$$\"3%[mm;zM)>$)FboFgu7$$\"3M*******pfa<*FboFju7$$\"39H LLeg`!)**FboF]v7$$\"3w****\\#G2A3\"F0F`v7$$\"3;LLL$)G[k6F0Fcv7$$\"3#)* ***\\7yh]7F0Ffv7$$\"3xmmm')fdL8F0Fiv7$$\"3bmmm,FT=9F0F\\w7$$\"3FLL$e#p a-:F0F_w7$$\"3!*******Rv&)z:F0Fbw7$$\"3ILLLGUYo;F0Few7$$\"3_mmm1^rZF0F^x7$F+F+-%'COLOURG6&%$RGBG$ \"#5!\"\"$F*F*Fhx-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6$Q!6\"F`y-% &TITLEG6#%2my~absolute~valueG-%%VIEWG6$;F(F+%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 34 "A brief vocabulary of Maple words " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 198 "Her e are some Maple words useful in calculus problem solving, together wi th examples of their usage. For more information on these words and o thers, look at the helpsheets and use the help browser." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 40 "Use 'colon-equal' t o make an assignment." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "y := (x+3)/tan(x^2-1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG*&,&%\"xG\"\"\"\"\"$F(F(-%$tanG6#,&*$F'\"\"# F(!\"\"F(F0" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 33 "Collect the like powers of x in " }{XPPEDIT 18 0 "2*x+5*x^2+4 *x-x^2;" "6#,**&\"\"#\"\"\"%\"xGF&F&*&\"\"&F&*$F'F%F&F&*&\"\"%F&F'F&F& *$F'F%!\"\"" }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "collect(2*x+5*x^2+4*x-x^2,x) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"'*$)F$\"\"#\"\"\"\"\"% " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 31 "Fin d the derivative of cos(x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(cos(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"xG!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 38 "The derivative of cos (a s a function)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "D(cos);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%$si nG!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 51 "Extract the denominator of the rational expression " }{XPPEDIT 18 0 "(a+b)/(e+f)" "6#*&,&%\"aG\"\"\"%\"bGF&F&,&%\"eGF&%\"fGF&!\"\"" } {TEXT 257 20 " and assign it to y." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " y := denom((a+b)/(e+f)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&%\"eG\"\"\"%\"fGF'" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 35 "Make y a n \"unknown\" variable again." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "y := 'y'; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yGF$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 8 "Compute " }{XPPEDIT 18 0 "(2+3*I)^3" "6#*$,&\" \"#\"\"\"*&\"\"$F&%\"IGF&F&F(" }{TEXT 257 26 " using complex arithmeti c." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalc((2+3*I)^3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,&!#Y\"\"\"%\"IG\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 9 "Evaluate " }{XPPEDIT 18 0 "1/2^9" "6#*&\"\"\"F$*$\" \"#\"\"*!\"\"" }{TEXT -1 1 " " }{TEXT 257 20 "to a decimal number." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(1/2^9); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++]7`>!#7" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 19 "Expand \+ the product " }{XPPEDIT 18 0 "(x+b)^7" "6#*$,&%\"xG\"\"\"%\"bGF&\"\"( " }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((x+b)^7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,2*$%\"xG\"\"(\"\"\"*&F%\"\"'%\"bGF'F&*&F%\"\"&F*\"\"# \"#@*&F%\"\"%F*\"\"$\"#N*&F%F1F*F0F2*&F%F-F*F,F.*&F%F'F*F)F&*$F*F&F'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 21 "Assig n the quadratic " }{XPPEDIT 18 0 "x^2+5*x+6" "6#,(*$%\"xG\"\"#\"\"\"*& \"\"&F'F%F'F'\"\"'F'" }{TEXT 257 6 " to p." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "p := x^2+5*x+6; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,(*$%\"xG\"\"#\"\"\"F'\"\"&\" \"'F)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 24 "Factor the polynomial p." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(p);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"\"\"$F&F&,&F%F&\"\"#F&F &" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 16 "So lve equation " }{XPPEDIT 18 0 "x^5-3*x=1" "6#/,&*$%\"xG\"\"&\"\"\"*& \"\"$F(F&F(!\"\"F(" }{TEXT 257 26 " for x in between 0 and 2." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fsolve(x^5-3*x=1,x=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+% )>z)Q\"!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 5 "Find " }{XPPEDIT 18 0 "Int(x*exp(x),x);" "6#-%$IntG6$*&%\"xG\" \"\"-%$expG6#F'F(F'" }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(x*exp(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"-%$expG6#F%F&F&F'!\"\"" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 8 "Display \+ " }{XPPEDIT 18 0 "Int(x*exp(x),x=0..1)" "6#-%$IntG6$*&%\"xG\"\"\"-%$ex pG6#F'F(/F';\"\"!F(" }{TEXT 257 54 " unevaluated as a passive integral and assign it to y." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "y := Int(x*exp(x),x=0..1);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"yG-%$IntG6$*&%\"xG\"\"\"-%$expG6#F)F*/F);\" \"!F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 53 "Find the value of the passive integral assigned to y." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value( y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 43 "Square all the terms in \+ the list [1,3,2,5]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "map(x->x^2,[1,3,2,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"\"\"*\"\"%\"#D" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 257 47 "Find the number of terms in the list [3,4,x,1]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "nops([3,4,x,1]); " }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 49 "Extract the numerator of the rational expression " }{XPPEDIT 18 0 "(a+b)/c" "6#*&,&%\"aG\"\"\"%\"bGF&F&%\"cG!\"\"" }{TEXT 257 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "numer((a+b)/c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"aG\"\"\"% \"bGF%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 42 "Strip the brackets off the list [3,4,1,x]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "op([3,4,1,x] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"$\"\"%\"\"\"%\"xG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 5 "Plot " } {XPPEDIT 18 0 "x^2+x" "6#,&*$%\"xG\"\"#\"\"\"F%F'" }{TEXT 257 21 " for x from -3 to 3." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(x^2+x, x=-3..3); " }}{PARA 13 "" 1 "" {GLPLOT2D 270 263 263 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"$\"\"!$\"\"'F *7$$!1+++vq@pG!#:$\"1b:Z[&*=j`F07$$!1++D^NUbFF0$\"1gJ`&RNp$[F07$$!1++] K3XFEF0$\"1W\\qWq/wUF07$$!1++]F)H')\\#F0$\"1zEP(=@Xu$F07$$!1++D'3@/P#F 0$\"1I')))R]Z[KF07$$!1++Dr^b^AF0$\"1S#F07$$!1++Dh\")=,?F0$\"1crZ&*ec.?F07$$!1++DO\"3V(=F0$\"1\\HO`Gs Q;F07$$!1+++NkzViUC\"F0$\"1z@1\\@ERIFdo7$$!1++DhkaI6F0$\"1x*[zR))eZ\"Fdo7$$!1+++]XF `**Fdo$!10IABBr]Y!#=7$$!1++++Az2))Fdo$!1;>;c=2]5Fdo7$$!1++]7RKvuFdo$!1 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7400E38E38E38E391400EE38E38E38E3C400F8E38E38E38E640101C71C71C71C940107 1C71C71C71E4010C71C71C71C7340111C71C71C71C9401171C71C71C71E4011C71C71C 71C7340121C71C71C71C8401271C71C71C71E4012C71C71C71C7340131C71C71C71C84 01371C71C71C71E4013C71C71C71C7340141C71C71C71C8401471C71C71C71D4014C71 C71C71C7240151C71C71C71C8401571C71C71C71D40100000000000024010555555555 5574010AAAAAAAAAAAD401100000000000240115555555555574011AAAAAAAAAAAD401 200000000000240125555555555574012AAAAAAAAAAAD4013000000000002401355555 55555574013AAAAAAAAAAAD401400000000000240145555555555574014AAAAAAAAAAA C401500000000000240155555555555574015AAAAAAAAAAAC401600000000000240165 555555555574016AAAAAAAAAAAC401700000000000140175555555555564017AAAAAAA AAAAC4018000000000001-%+AXESLABELSG6%%\"xG%\"yG%!G-%*AXESSTYLEG6#%$BOX G" 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" } }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 20 "Defin e the function " }{XPPEDIT 18 0 "f(x) = x^2;" "6#/-%\"fG6#%\"xG*$F'\" \"#" }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f := x -> x^2; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$9$\"\"#F(F(6 \"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 15 "C alculate f(3)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 38 "Find \+ the quotient when the polynomial " }{XPPEDIT 18 0 "x^4-4" "6#,&*$%\"xG \"\"%\"\"\"F&!\"\"" }{TEXT 257 15 " is divided by " }{XPPEDIT 18 0 "x^ 2-2" "6#,&*$%\"xG\"\"#\"\"\"F&!\"\"" }{TEXT 257 1 "." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "quo(x^4-4, x^2-2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"F(F' F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 53 "F ind the integer quotient when 2351 is divided by 27." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "iquo(2351, 27) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#()" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 39 "Find the remainder when \+ the polynomial " }{XPPEDIT 18 0 "x^4-4*x+3" "6#,(*$%\"xG\"\"%\"\"\"*&F &F'F%F'!\"\"\"\"$F'" }{TEXT 257 15 " is divided by " }{XPPEDIT 18 0 "x ^2-2;" "6#,&*$%\"xG\"\"#\"\"\"F&!\"\"" }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "rem(x^4 -4*x+3,x^2-2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"(\"\"\"%\"xG !\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 54 "Find the integer remainder when 2351 is divided by 27." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "irem(23 51,27); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 62 "Clear all variables, tha t is, remove or reset all assignments." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 20 "Assign the equation " }{XPPEDIT 18 0 "x^2 + 3*x -1 = a" "6#/,(*$%\"xG\"\"#\"\"\"*&\"\"$F( F&F(F(F(!\"\"%\"aG" }{TEXT 257 21 " to the variable eq1." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "eq1 : = x^2 + 3*x - 1 = a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,(*$% \"xG\"\"#\"\"\"F(\"\"$!\"\"F*%\"aG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 257 53 "Extract the righthand side of eq1. The re is also an " }{TEXT 0 3 "lhs" }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "rhs(eq1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 31 "Try to simplify the expression " }{XPPEDIT 18 0 "x*(a/x+b/y);" "6#*&%\"xG\"\"\",&*&%\"aGF%F$!\"\"F%*&% \"bGF%%\"yGF)F%F%" }{TEXT 257 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "simplify(x*(a/x+b/y)); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*&%\"aG\"\"\"%\"yGF'F'*&%\"bGF'%\" xGF'F'F'F(!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 19 "Solve the equation " }{XPPEDIT 18 0 "a*x+4*y=0" "6#/,&*& %\"aG\"\"\"%\"xGF'F'*&\"\"%F'%\"yGF'F'\"\"!" }{TEXT 257 8 " for x." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(a*x+4*y=0,x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"y G\"\"\"%\"aG!\"\"!\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 42 "Substitute 5 for x whereever it occurs in " } {XPPEDIT 18 0 "x^2+x" "6#,&*$%\"xG\"\"#\"\"\"F%F'" }{TEXT 257 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(x=5,x^2+x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#I" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 40 "Add up t he 2nd to 9th squares inclusive." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "sum((i^2,i=2..9)); \+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$%G" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 "Trouble shooting notes" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 270 "Learning to use Maple can be an extremely frustrating experien ce, if you let it. There are some types of errors which occur from the beginning that can be spotted and corrected easily by a person fluent in Maple, so if you have access to such a person, use him or her. " }}{PARA 0 "" 0 "" {TEXT -1 115 "Here are a few suggestions that may be of use when you're stuck with a worksheet that's not working like it \+ should." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT 265 1 " " }{TEXT 256 8 "Use help" }{TEXT -1 235 ". There is a help sheet \+ with examples for every Maple word. A quick read through will often cl ear up syntax problems. One very common early mistake is to leave out \+ the parentheses around the inputs of a word. For example, typing . . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "plot x^2;" }}{PARA 8 "" 1 "" {TEXT -1 27 "`missing operator or \+ \\`;\\``" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 " . . will get you \+ a syntax error, because you left out the parentheses." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 1 " " }{TEXT 256 19 "The \+ Maple prompt is" }{TEXT 269 1 " " }{TEXT -1 120 " [ > . You can begin entering input after it. Make sure you are typing into an input cell, if you are expecting output." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 15 "" 0 "" {TEXT 256 38 "End maple statements with a semicolon \+ " }{TEXT 0 1 ";" }{TEXT -1 147 ". Maple does nothing until it finds a semicolon. If you are getting no output when you should be, try fee ding in a semicolon. This often works. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 15 "" 0 "" {TEXT 256 33 "When in doubt, put in parentheses " }{TEXT -1 16 ". For example, " }{TEXT 0 11 "(x+3)/(x-3)" }{TEXT -1 26 " is very different from " }{TEXT 0 7 "x+3/x-3" }{TEXT -1 1 "." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT 256 37 "Make s ure your variables are variable" }{TEXT -1 105 ". You may have assign ed a value, say 3, to x in a previous problem. To make x a variable a gain, type " }{TEXT 0 9 "x := 'x':" }{TEXT -1 187 ". Use the forwa rd quote ' key, just below the double quote \" here. If you forget this, strange things can happen. One way to handle this is to keep an input cell of variables used. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 15 "" 0 "" {TEXT -1 4 "Use " }{TEXT 0 8 "restart;" }{TEXT -1 12 " By typing " }{TEXT 0 8 "restart;" }{TEXT -1 174 " in an input cell \+ and pressing enter, you clear all assignments, and start with a clean \+ slate. This fixes a lot of problems fast, but you will need to re-exec ute input cells." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 14 "If you try to " }{TEXT 256 38 "plot a function defined as a procedure" }{TEXT -1 20 " which contains an \"" }{TEXT 0 2 "if" } {TEXT -1 43 "\" statement, you will get an error message." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f := proc(x) \nif x < 0 then 0 elif x < 1 then x elif x < 2 then 2-x else \+ 0 end if\nend;\nplot(f(x),x=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"fGf*6#%\"xG6\"F(F(@)29$\"\"!F,2F+\"\"\"F+2F+\"\"#,&F0F.F+!\"\"F,F( F(F(" }}{PARA 8 "" 1 "" {TEXT -1 45 "Error, (in f) cannot evaluate boo lean: x < 0\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 83 "The problem here is due to Maple's order of evaluation. W hen invoking the command: " }{TEXT 0 18 "plot(f(x),x=0..2);" }{TEXT -1 145 " Maple first tries to calculate the value of f(x), before subs tituting the numeric values in for x. In the procedure, Maple cannot e valuate the '" }{TEXT 0 2 "if" }{TEXT -1 188 "' statement, as it canno t compare the size of x to 0. Thus the error message. \nA simple solut ion is to use single quotes to delay evaluation until a numerical valu e has been passed to x: \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot('f(x)',x=0..2); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "forward quote" {TEXT 256 39 "Are you using the correct quote symbol?" }{TEXT -1 17 " \+ In Maple, the " }{TEXT 258 13 "forward quote" }{TEXT -1 1 " " } {TEXT 0 1 "'" }{TEXT -1 39 " is used to suppress evaluation. The " } {TEXT 258 10 "back quote" }{TEXT -1 2 " " }{TEXT 0 1 "`" }{TEXT -1 10 " and the " }{TEXT 258 12 "double quote" }{TEXT -1 2 " " }{TEXT 0 1 "\"" }{TEXT -1 30 " are used to define strings. " }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 15 "" 0 "" {TEXT 256 32 "Do not forget to e nd loops with " }{TEXT -1 1 "\"" }{TEXT 0 6 "end do" }{TEXT -1 9 "\", \+ and \"" }{TEXT 0 2 "if" }{TEXT -1 20 "\" statements with \"" }{TEXT 0 6 "end if" }{TEXT -1 24 "\", and procedures with \"" }{TEXT 0 8 "end proc" }{TEXT -1 30 "\". \nIf you start a loop with \"" }{TEXT 0 2 "do " }{TEXT -1 105 "\", Maple does not begin processing until it finds th e end of the loop, which is signaled by the words \"" }{TEXT 0 6 "en d do" }{TEXT -1 29 "\" The same applies to the \"" }{TEXT 0 21 "if . . then ... end if" }{TEXT -1 12 "\" and \"" }{TEXT 0 17 "proc ... end proc" }{TEXT -1 83 "\" contructions. If you are getting no outp ut when you should be, try feeding an \"" }{TEXT 0 6 "end do" }{TEXT -1 4 "\", \"" }{TEXT 0 6 "end if" }{TEXT -1 7 "\", or \"" }{TEXT 0 8 " end proc" }{TEXT -1 20 "\". This often works." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT 256 16 "Unwanted output?" } {TEXT 266 65 " Is there output you need but don't want to see? Use a colon `" }{TEXT 0 1 ":" }{TEXT 267 27 "` instead of a semicolon `" }{TEXT 0 1 ";" }{TEXT 268 56 "` to end the Maple statement which gener ates the output." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "pri ntlevel" {TEXT 256 3 "Use" }{TEXT -1 1 " " }{TEXT 0 17 "printlevel := \+ 10;" }{TEXT -1 117 " if you want to see what Maple is doing behind the scenes when you give it a command. If you want to see more, use " } {TEXT 0 17 "printlevel := 50;" }{TEXT -1 140 " or higher. Often by ins pecting the output when printlevel is greater than 1 (the default), y ou can discover what is ailing your worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "debug" {TEXT 256 9 "Use debug" }{TEXT -1 36 ". If you have defined a word, say \"" }{TEXT 0 9 "something" } {TEXT -1 79 "\" and it does not do what you want, you can often discov er the error by typing " }{TEXT 0 17 "debug(something);" }{TEXT -1 146 " in an input cell and pressing the enter key. When you use the w ord again, its behind the scene computations are printed out for your \+ inspection." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "verbosep roc" {TEXT 256 35 "Want to see a procedure definition?" }{TEXT -1 28 " Say you want to see how " }{TEXT 0 5 "plot " }{TEXT -1 19 "works. \+ \nType . . .\n" }{TEXT 0 64 "interface(verboseproc=2);\neval(plot);\ni nterface(verboseproc=1);\n" }{TEXT -1 42 " . . . in an input cell and \+ press enter. 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