{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 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 "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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Map le 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 "Title" -1 18 1 {CSTYLE " " -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 256 26 "Getting Started with Map le" }}{PARA 19 "" 0 "" {TEXT -1 16 "Warren Weckesser" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 238 "Note: This handout is \+ actually a \"Maple Session\"; everything in here was created in Maple. The actual Maple commands that I entered are shown in the lines prec eded by the \">\"; these lines are immediately followed by the resulti ng output." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Simple calculations:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "Note the semicolon at the end of \+ the line. Each Maple command must end with a semicolon (or a colon). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "(12+3*5)/4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#F\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 150 "Note that Maple does not convert the rational number to its de cimal representation. You can find the decimal representation with th e \"evalf\" command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "eva lf(27/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++]n!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Maple has many predefined functions. For example, sine and cosine:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(1.23);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+>!))[U*!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "cos(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "cos (1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Note that Maple didn't display the numer ical value of cos(1). To see the numerical value, use \"evalf\":" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(cos(1));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+fI-.a!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "To take a square root, you can use the \"sqrt\" function:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 154 "Maple ha s several predefined constants. The one that we will need most is pi. The Maple name of pi that can be used in an input line is \"Pi\". M aple is " }{TEXT 259 14 "case sensitive" }{TEXT -1 86 ", so the P must be a capital letter. In the output, Maple will show the Greek letter ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%#PiG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "e valf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sin(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 142 "Another \+ predefined constant that you will see occasionally is \"I\". In Maple , \"I\" is the square root of -1 (a complex number). For example: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(-16);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^#\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "I*I;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "The funct ion name \"exp\" is used for the exponential function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp (1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Note that the number \"e\" is displayed i n the output as a boldface e. However, " }{TEXT 260 55 "do not use e^ x for the exponential function; use exp(x)" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+G=G=F!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 255 " Typically we want to do a lot more than calculate a few numbers. We w ant to define functions, plot graphs, solve equations, etc. We need t o be able to define and store expressions in Maple. This is done with the assignment statement \":=\". For example:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "m := 355/113;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG#\"$b$\"$8\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "Now the variable \"m\" has been created, and it has the value 355/113. We ca n now use \"m\" in subsequent commands." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+?HfTJ !\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6##\"$b$\"$8\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 243 "The value of a variable can be an expression that is m ore complicated than just a number. For example, suppose we want to wo rk with the expression 4x^2-1. We can create a variable that will hol d this expression. I will call the variable \"q\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q := 4*x^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,&*$)%\"xG\"\"#\"\"\"\"\"%F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "Now there are many things we can do with this expressions. For example, we can plot it, using the \"plot\" co mmand." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(q,x=-1..1); " }}{PARA 13 "" 1 "" {GLPLOT2D 308 233 233 {PLOTDATA 2 "6%-%'CURVESG6$ 7S7$$!\"\"\"\"!$\"\"$F*7$$!3ommm;p0k&*!#=$\"3A!e4#)QZ)eE!#<7$$!3wKL$3< XZ=*F0$\"3'*[e7as%HaF0$\"3GaE.7tm\"z\"F07$$!3Q+++]$*4) *\\F0$!3RT$H=,b6g(!#@7$$!39+++]_&\\c%F0$!3ku*)>EMZk;F07$$!31+++]1aZTF0 $!3@J!REii\">JF07$$!3umm;/#)[oPF0$!3`wE-i')R>VF07$$!3hLLL$=exJ$F0$!3;z )pZD#*pf&F07$$!3*RLLLtIf$HF0$!3'o^F;HC@b'F07$$!3]++]PYx\"\\#F0$!3G'pkB mBk^(F07$$!3EMLLL7i)4#F0$!3/!*4gnbJQ#)F07$$!3c****\\P'psm\"F0$!3%yC[By %3))))F07$$!3')****\\74_c7F0$!3_m+ey?Yo$*F07$$!3)3LLL3x%z#)!#>$!35Li!p .,es*F07$$!3KMLL3s$QM%Ffr$!3S&**HKJCX#**F07$$!3]^omm;zr)*Feo$!3U:<4>5' *****F07$$\"3%pJL$ezw5VFfr$!3yFwV=\"pc#**F07$$\"3s*)***\\PQ#\\\")Ffr$! 3i4(HclfVt*F07$$\"3GKLLe\"*[H7F0$!3#zJ;QcU`R*F07$$\"3I*******pvxl\"F0$ !3*\\!eR\"*=r+*)F07$$\"3#z****\\_qn2#F0$!3w#\\'fu'4[F)F07$$\"3U)***\\i &p@[#F0$!3XE%*>0P`NvF07$$\"3B)****\\2'HKHF0$!3%>%eT\"*elglF07$$\"3Elmm mZvOLF0$!3/:4&30Fka&F07$$\"3i******\\2goPF0$!3*fxR[Nf!>VF07$$\"3UKL$eR <*fTF0$!31!HPR!\\.yIF07$$\"3m******\\)Hxe%F0$!3'=fn$HR4\"e\"F07$$\"3ck m;H!o-*\\F0$!3a6@3$))***))Q!#?7$$\"3y)***\\7k.6aF0$\"3gU.'H-E " 0 "" {MPLTEXT 1 0 16 "dq := diff(q,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dqG,$%\"xG\"\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 "We could have done the same things without defin ing q. We can give the expression itself as an argument to the functi ons:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(4*x^2-1,x=-1.. 1);" }}{PARA 13 "" 1 "" {GLPLOT2D 357 243 243 {PLOTDATA 2 "6%-%'CURVES G6$7S7$$!\"\"\"\"!$\"\"$F*7$$!3ommm;p0k&*!#=$\"3A!e4#)QZ)eE!#<7$$!3wKL $3s%HaF0$\"3GaE.7tm\"z\"F07$$!3Q+++]$ *4)*\\F0$!3RT$H=,b6g(!#@7$$!39+++]_&\\c%F0$!3ku*)>EMZk;F07$$!31+++]1aZ TF0$!3@J!REii\">JF07$$!3umm;/#)[oPF0$!3`wE-i')R>VF07$$!3hLLL$=exJ$F0$! 3;z)pZD#*pf&F07$$!3*RLLLtIf$HF0$!3'o^F;HC@b'F07$$!3]++]PYx\"\\#F0$!3G' pkBmBk^(F07$$!3EMLLL7i)4#F0$!3/!*4gnbJQ#)F07$$!3c****\\P'psm\"F0$!3%yC [By%3))))F07$$!3')****\\74_c7F0$!3_m+ey?Yo$*F07$$!3)3LLL3x%z#)!#>$!35L i!p.,es*F07$$!3KMLL3s$QM%Ffr$!3S&**HKJCX#**F07$$!3]^omm;zr)*Feo$!3U:<4 >5'*****F07$$\"3%pJL$ezw5VFfr$!3yFwV=\"pc#**F07$$\"3s*)***\\PQ#\\\")Ff r$!3i4(HclfVt*F07$$\"3GKLLe\"*[H7F0$!3#zJ;QcU`R*F07$$\"3I*******pvxl\" F0$!3*\\!eR\"*=r+*)F07$$\"3#z****\\_qn2#F0$!3w#\\'fu'4[F)F07$$\"3U)*** \\i&p@[#F0$!3XE%*>0P`NvF07$$\"3B)****\\2'HKHF0$!3%>%eT\"*elglF07$$\"3E lmmmZvOLF0$!3/:4&30Fka&F07$$\"3i******\\2goPF0$!3*fxR[Nf!>VF07$$\"3UKL $eR<*fTF0$!31!HPR!\\.yIF07$$\"3m******\\)Hxe%F0$!3'=fn$HR4\"e\"F07$$\" 3ckm;H!o-*\\F0$!3a6@3$))***))Q!#?7$$\"3y)***\\7k.6aF0$\"3gU.'H-E " 0 " " {MPLTEXT 1 0 16 "diff(4*x^2-1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,$%\"xG\"\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "We can also atte mpt to solve the equation 4x^2-1=0 with the \"solve\" command:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(4*x^2-1=0,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$#\"\"\"\"\"##!\"\"F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "In this case, the solve command was able to fin d the solutions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Let's take a closer look at the commands \"plot\", \"diff \", and \"solve\"." }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 16 "The Plot \+ Command" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 313 "The \"plot\" command \+ takes several arguments, and has many options. The basic command take s two arguments. The first is the expression (i.e. function) to be plo tted, and the second is the range of the independent variable of the e xpression. For example, the following command plots x^2 on the interv al -1 < x < 1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(x^2, x=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 453 273 273 {PLOTDATA 2 "6%-%' CURVESG6$7S7$$!\"\"\"\"!$\"\"\"F*7$$!3ommm;p0k&*!#=$\"3c]R_q%=r9*F07$$ !3wKL$3`0n(F07$$! 3:mmm\"4m(G$)F0$\"32V'p4YMo$pF07$$!3\"QLL3i.9!zF0$\"3Z6=$z\"z@ViF07$$! 3\"ommT!R=0vF0$\"3(4CONayFj&F07$$!3u****\\P8#\\4(F0$\"30z7`y3zL]F07$$! 3+nm;/siqmF0$\"3qSopHns\\WF07$$!3[++](y$pZiF0$\"335mBmxO.RF07$$!33LLL$ yaE\"eF0$\"3m(y?Ic&pyLF07$$!3hmmm\">s%HaF0$\"3ej\"3!Go\"z%HF07$$!3Q+++ ]$*4)*\\F0$\"3mUqC6(*4)\\#F07$$!39+++]_&\\c%F0$\"3Mc-XV;)Q3#F07$$!31++ +]1aZTF0$\"3?U-MW$4-s\"F07$$!3umm;/#)[oPF0$\"3(3L%\\M.:?9F07$$!3hLLL$= exJ$F0$\"3@IvIO>v+6F07$$!3*RLLLtIf$HF0$\"3&y?J4F*o>')!#>7$$!3]++]PYx\" \\#F0$\"3he#)3W3%*3iF]q7$$!3EMLLL7i)4#F0$\"3!\\_(*436US%F]q7$$!3c**** \\P'psm\"F0$\"31!QHT/)yzFF]q7$$!3')****\\74_c7F0$\"3KK)\\N![%)y:F]q7$$ !3)3LLL3x%z#)F]q$\"3M!=Wt2u\\&o!#?7$$!3KMLL3s$QM%F]q$\"3a8,Dp@*o)=Fgr7 $$!3]^omm;zr)*!#@$\"3+4t+rqAX(*!#C7$$\"3%pJL$ezw5VF]q$\"3Q>$f!R?Fe=Fgr 7$$\"3s*)***\\PQ#\\\")F]q$\"3UZsD4'35k'Fgr7$$\"3GKLLe\"*[H7F0$\"3&e?f/ fV;^\"F]q7$$\"3I*******pvxl\"F0$\"3a([5:F?#[FF]q7$$\"3#z****\\_qn2#F0$ \"3um(3N\"e(HJ%F]q7$$\"3U)***\\i&p@[#F0$\"3!RV,qtl6;'F]q7$$\"3B)****\\ 2'HKHF0$\"3;&Rg9Fg$)f)F]q7$$\"3ElmmmZvOLF0$\"3CrsGPKR86F07$$\"3i****** \\2goPF0$\"3+c+Hh^B?9F07$$\"3UKL$eR<*fTF0$\"3[xc,u7\\Ix^Bqij(F07$$\"3[++]i`1h\"*F0$\"31F(*fd=^#R)F07$$ \"3W++]P?Wl&*F0$\"3]:sFP\"o(\\\"*F07$F+F+-%'COLOURG6&%$RGBG$\"#5F)$F*F *F^[l-%+AXESLABELSG6$Q\"x6\"Q!Fc[l-%%VIEWG6$;F(F+%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Note that a..b is the standard method for describing a range in Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 114 "We can also give a third argument to the plot command that specifies the vertical range of the plot. For exam ple:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(x^2,x=-1..1,-1 ..1.5);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CU RVESG6$7S7$$!\"\"\"\"!$\"\"\"F*7$$!3ommm;p0k&*!#=$\"3c]R_q%=r9*F07$$!3 wKL$3`0n(F07$$!3: mmm\"4m(G$)F0$\"32V'p4YMo$pF07$$!3\"QLL3i.9!zF0$\"3Z6=$z\"z@ViF07$$!3 \"ommT!R=0vF0$\"3(4CONayFj&F07$$!3u****\\P8#\\4(F0$\"30z7`y3zL]F07$$!3 +nm;/siqmF0$\"3qSopHns\\WF07$$!3[++](y$pZiF0$\"335mBmxO.RF07$$!33LLL$y aE\"eF0$\"3m(y?Ic&pyLF07$$!3hmmm\">s%HaF0$\"3ej\"3!Go\"z%HF07$$!3Q+++] $*4)*\\F0$\"3mUqC6(*4)\\#F07$$!39+++]_&\\c%F0$\"3Mc-XV;)Q3#F07$$!31+++ ]1aZTF0$\"3?U-MW$4-s\"F07$$!3umm;/#)[oPF0$\"3(3L%\\M.:?9F07$$!3hLLL$=e xJ$F0$\"3@IvIO>v+6F07$$!3*RLLLtIf$HF0$\"3&y?J4F*o>')!#>7$$!3]++]PYx\" \\#F0$\"3he#)3W3%*3iF]q7$$!3EMLLL7i)4#F0$\"3!\\_(*436US%F]q7$$!3c**** \\P'psm\"F0$\"31!QHT/)yzFF]q7$$!3')****\\74_c7F0$\"3KK)\\N![%)y:F]q7$$ !3)3LLL3x%z#)F]q$\"3M!=Wt2u\\&o!#?7$$!3KMLL3s$QM%F]q$\"3a8,Dp@*o)=Fgr7 $$!3]^omm;zr)*!#@$\"3+4t+rqAX(*!#C7$$\"3%pJL$ezw5VF]q$\"3Q>$f!R?Fe=Fgr 7$$\"3s*)***\\PQ#\\\")F]q$\"3UZsD4'35k'Fgr7$$\"3GKLLe\"*[H7F0$\"3&e?f/ fV;^\"F]q7$$\"3I*******pvxl\"F0$\"3a([5:F?#[FF]q7$$\"3#z****\\_qn2#F0$ \"3um(3N\"e(HJ%F]q7$$\"3U)***\\i&p@[#F0$\"3!RV,qtl6;'F]q7$$\"3B)****\\ 2'HKHF0$\"3;&Rg9Fg$)f)F]q7$$\"3ElmmmZvOLF0$\"3CrsGPKR86F07$$\"3i****** \\2goPF0$\"3+c+Hh^B?9F07$$\"3UKL$eR<*fTF0$\"3[xc,u7\\Ix^Bqij(F07$$\"3[++]i`1h\"*F0$\"31F(*fd=^#R)F07$$ \"3W++]P?Wl&*F0$\"3]:sFP\"o(\\\"*F07$F+F+-%'COLOURG6&%$RGBG$\"#5F)$F*F *F^[l-%+AXESLABELSG6$Q\"x6\"Q!Fc[l-%%VIEWG6$;F(F+;F($\"#:F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 "You can specify more optional arguments. In the next example, I've changed the color to black, used a dashed \+ line, and I've given the plot a title:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot(x^2,x=-1..1,-1..1.5,title=`y=x^2`,color=black,li nestyle=DASH);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 " 6(-%'CURVESG6#7S7$$!\"\"\"\"!$\"\"\"F*7$$!3ommm;p0k&*!#=$\"3c]R_q%=r9* F07$$!3wKL$3`0n(F 07$$!3:mmm\"4m(G$)F0$\"32V'p4YMo$pF07$$!3\"QLL3i.9!zF0$\"3Z6=$z\"z@ViF 07$$!3\"ommT!R=0vF0$\"3(4CONayFj&F07$$!3u****\\P8#\\4(F0$\"30z7`y3zL]F 07$$!3+nm;/siqmF0$\"3qSopHns\\WF07$$!3[++](y$pZiF0$\"335mBmxO.RF07$$!3 3LLL$yaE\"eF0$\"3m(y?Ic&pyLF07$$!3hmmm\">s%HaF0$\"3ej\"3!Go\"z%HF07$$! 3Q+++]$*4)*\\F0$\"3mUqC6(*4)\\#F07$$!39+++]_&\\c%F0$\"3Mc-XV;)Q3#F07$$ !31+++]1aZTF0$\"3?U-MW$4-s\"F07$$!3umm;/#)[oPF0$\"3(3L%\\M.:?9F07$$!3h LLL$=exJ$F0$\"3@IvIO>v+6F07$$!3*RLLLtIf$HF0$\"3&y?J4F*o>')!#>7$$!3]++] PYx\"\\#F0$\"3he#)3W3%*3iF]q7$$!3EMLLL7i)4#F0$\"3!\\_(*436US%F]q7$$!3c ****\\P'psm\"F0$\"31!QHT/)yzFF]q7$$!3')****\\74_c7F0$\"3KK)\\N![%)y:F] q7$$!3)3LLL3x%z#)F]q$\"3M!=Wt2u\\&o!#?7$$!3KMLL3s$QM%F]q$\"3a8,Dp@*o)= Fgr7$$!3]^omm;zr)*!#@$\"3+4t+rqAX(*!#C7$$\"3%pJL$ezw5VF]q$\"3Q>$f!R?Fe =Fgr7$$\"3s*)***\\PQ#\\\")F]q$\"3UZsD4'35k'Fgr7$$\"3GKLLe\"*[H7F0$\"3& e?f/fV;^\"F]q7$$\"3I*******pvxl\"F0$\"3a([5:F?#[FF]q7$$\"3#z****\\_qn2 #F0$\"3um(3N\"e(HJ%F]q7$$\"3U)***\\i&p@[#F0$\"3!RV,qtl6;'F]q7$$\"3B)** **\\2'HKHF0$\"3;&Rg9Fg$)f)F]q7$$\"3ElmmmZvOLF0$\"3CrsGPKR86F07$$\"3i** ****\\2goPF0$\"3+c+Hh^B?9F07$$\"3UKL$eR<*fTF0$\"3[xc,u7\\Ix^Bqij(F07$$\"3[++]i`1h\"*F0$\"31F(*fd=^#R)F 07$$\"3W++]P?Wl&*F0$\"3]:sFP\"o(\\\"*F07$F+F+-%'COLOURG6&%$RGBGF*F*F*- %&TITLEG6#%&y=x^2G-%*LINESTYLEG6#\"\"$-%+AXESLABELSG6$Q\"x6\"Q!Fh[l-%% VIEWG6$;F(F+;F($\"#:F)" 1 2 0 3 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "To see more examples, look up \"plot\" in the Maple Help, or enter the comm and \"?plot\"." }}}{EXCHG {PARA 18 "" 0 "" {TEXT 257 16 "The Diff Comm and" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 334 "You can take derivatives \+ in Maple with the \"diff\" command (\"diff\" stands for \"differentiat e\"). The basic command takes two arguments. The first is the express ion to be differentiated, and the second is the variable with respect \+ to which the derivative is to be taken. Maple knows the derivatives o f most of the elementary functions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 124 "Here are some examples. The first find s the derivative of sin(t)+4t, and the second finds the derivative of \+ 1/x + exp(x^2)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "diff(sin (t)+4*t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cosG6#%\"tG\"\"\" \"\"%F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "diff(1/x + exp(x ^2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%*$)%\"xG\"\"#F% !\"\"F**(F)F%F(F%-%$expG6#*$F'F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 109 "To take a second or higher order derivative, just list the var iable again. Here are some second derivatives:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "diff(sin(t)+4*t,t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"tG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "diff(1/x + exp(x^2),x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"\"F%*$)%\"xG\"\"$F%!\"\"\"\"#*&F+F%-%$expG6#*$) F(F+F%F%F%*(\"\"%F%F1F%F-F%F%" }}}{EXCHG {PARA 18 "" 0 "" {TEXT 258 17 "The Solve Command" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 291 "The \"s olve\" command can solve many algebraic equations. We saw an example \+ earlier where we solved a quadratic. In the simplest form of the comm and, the first argument is the equation to be solved, and the second i s the variable to be solved for. Here we find the solutions to x^2+5 x+6=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x^2+5*x+6=0 ,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"#!\"$" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 115 "If there expression does not contain an equals si gn, Maple assumes that the expression should be set equal to zero." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+5*x+6,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$!\"#!\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Next we solve a cubic polynomial:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "solve(x^3-2*x+1=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\",&#!\"\"\"\"#F#*&#F#F'F#-%%sqrtG6#\"\"&F#F#,&F%F# *&#F#F'F#*$F*F#F#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Let's make one small change to the cubic polynomial:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "solve(x^3-x+1=0,x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%,&*$),&\"$3\"\"\"\"*&\"#7F(-%%sqrtG6#\"#pF(F(#F(\"\"$F(#!\"\"\" \"'*&\"\"#F(F&#F2F0F2,(F$#F(F**&F(F(*$)F&#F(F0F(F2F(*(^##F(F5F(-F,6#F0 F(,&F$F1*&F5F(F&F6F(F(F(,(F$F8F9F(*(^##F2F5F(F@F(FBF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 210 "What a mess! If you look carefully at t he above output, you will see that Maple has found three solutions, tw o of which are complex numbers. (Recall that the symbol I in Maple is the complex number sqrt(-1).)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 142 "What happens if the equation has no solu tion, or if Maple can not find it? Here are some examples. First, a t rivial example with no solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(1=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Maple gave no output; this means that either there is no solution , or Maple can not find any solutions." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 88 "Note that Maple can solve an equation like x^2=-1, because Maple allows complex numbers:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(x^2=-1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$^#\"\"\"^#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Sometimes Maple gives a partial solution:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "solve(x*(sin(x)+x+1/4)=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!-%'RootOfG6#,(%#_ZG\"\"%*&F)\"\"\"-%$sinG6#F(F+F+F +F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 282 "The \"RootOf\" function m eans the root of the expression; in the expression, _Z is the variable . In this example, Maple found one solution to be 0, but the other \" solution\" is just the solution to 4*_Z + 4*sin(*_Z) +1=0. Maple coul d not find an analytical solution to this equation." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 94 "Let's create a \+ function, plot it, and then use \"diff\" and \"solve\" to find the cri tical points." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "w := (x^4+3*x^2)/(1+x^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG*&,&*$)%\"xG\"\"%\"\"\"F+*&\"\"$F+)F)\"\"#F+F+F+, &F+F+F'F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(w,x= -3..3);" }}{PARA 13 "" 1 "" {GLPLOT2D 366 195 195 {PLOTDATA 2 "6%-%'CU RVESG6$7ep7$$!\"$\"\"!$\"3Q20(R dW8F-7$$!3#)***\\7bBav#F-$\"3E^\"y#*=W8P\"F-7$$!36++]K3XFEF-$\"3[%\\jb #*z]S\"F-7$$!3%)****\\F)H')\\#F-$\"3iN*>#f?\\V9F-7$$!3#****\\i3@/P#F-$ \"39)=(y0(>o[\"F-7$$!3;++Dr^b^AF-$\"33<1]zo:K:F-7$$!3$****\\7Sw%G@F-$ \"3kL^B)po\\e\"F-7$$!3*****\\7;)=,?F-$\"3qBMyt1XY;F-7$$!3/++DO\"3V(=F- $\"3xct)*3,+:F-7$$!3/ +++vl[p8F-$\"3V&e3waHT-#F-7$$!3(******\\QuoI\"F-$\"35l'*>(o(y_?F-7$$!3 \"******\\>iUC\"F-$\"3]c*\\`=8H2#F-7$$!3/+DchK$e@\"F-$\"3g@==!*)Q$y?F- 7$$!3'***\\7GVS(=\"F-$\"3u:wu(fb43#F-7$$!3#*\\iSh)*=t6F-$\"3%o`e'4K4\" 3#F-7$$!3))*\\(o%Rv*e6F-$\"33UtcmbQ!3#F-7$$!31](oz#4wW6F-$\"3_KSObIyy? 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