{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 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 "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 "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 "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 0 "" 0 "" {TEXT -1 238 "Note: This handout is actually a \+ \"Maple Session\"; everything in here was created in Maple. The actua l Maple commands that I entered are shown in the lines preceded by the \">\"; these lines are immediately followed by the resulting 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 89 "Note the semicolon at the end of the line. Each Maple command must end with a semicolon." }}}{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 no t convert the rational number to its decimal representation. You can \+ find the decimal representation with the \"evalf\" command." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(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#-%$cosG6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Note that Maple didn't display the numerical value of cos(1). To see the numerical value, use \"evalf\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(cos(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" +fI-.a!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "To take a square roo t, 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 -1 193 "Maple has several predefined cons tants. The one that we will need most is pi. The Maple name of pi th at can be used in an input line is \"Pi\". 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 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+a EfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sin(Pi);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 142 "Another predefined constant that you will see occasional ly is \"I\". In Maple, \"I\" is the square root of -1 (a complex numb er). For example: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt (-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^#\"\"\"" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "sqrt(-16);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#^#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "I*I;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "The function name \"exp\" is used for the exponential function:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(0);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "e xp(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 143 "Note that the number \"e\" is displayed \+ in the output as a boldface e. However, you should not use e^x for th e exponential function; use exp(x)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" +G=G=F!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 254 "Typically we want \+ to do a lot more than calculate a few numbers. We want to define func tion, plot graphs, solve equations, etc. We need to be able to define and store expressions in Maple. This is done with the assignment sta tement \":=\". For example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "m := 355/113;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG#\"$b$\"$ 8\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "Now the variable \"m\" ha s been created, and it has the value 355/113. We can now use \"m\" in subsequent commands." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eva lf(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##\"$b$\"$8\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 222 "A variable can be an expression more complicated than just a n umber. For example, suppose we want to work with the expression 4x^2-1 . We can create a variable that will hold this expression. I will ca ll the variable \"q\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q := 4*x^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,&*$)%\"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\" command." }}}{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;p0 k&*!#=$\"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+++]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'pkBmBk^(F07$$!3EMLLL7i)4#F0$!3/!*4gn bJQ#)F07$$!3c****\\P'psm\"F0$!3%yC[By%3))))F07$$!3')****\\74_c7F0$!3_m +ey?Yo$*F07$$!3)3LLL3x%z#)!#>$!35Li!p.,es*F07$$!3KMLL3s$QM%Ffr$!3S&**H KJCX#**F07$$!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$$\"3B)*** *\\2'HKHF0$!3%>%eT\"*elglF07$$\"3ElmmmZvOLF0$!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$$ \"3y)***\\7k.6aF0$\"3gU.'H-E " 0 "" {MPLTEXT 1 0 16 "dq := diff(q,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#dqG,$%\"xG\"\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 "We could ha ve done the same things without defining q. We can give the expressio n itself as an argument to the functions:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "plot(4*x^2-1,x=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 357 243 243 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"\"\"\"!$\"\"$ 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$$!31+++]1aZTF0$!3@J!REii\">JF07$$! 3umm;/#)[oPF0$!3`wE-i')R>VF07$$!3hLLL$=exJ$F0$!3;z)pZD#*pf&F07$$!3*RLL LtIf$HF0$!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$$!3)3LLL3x%z#)!#>$!35Li!p.,es*F07$$!3KMLL3s$ QM%Ffr$!3S&**HKJCX#**F07$$!3]^omm;zr)*Feo$!3U:<4>5'*****F07$$\"3%pJL$e zw5VFfr$!3yFwV=\"pc#**F07$$\"3s*)***\\PQ#\\\")Ffr$!3i4(HclfVt*F07$$\"3 GKLLe\"*[H7F0$!3#zJ;QcU`R*F07$$\"3I*******pvxl\"F0$!3*\\!eR\"*=r+*)F07 $$\"3#z****\\_qn2#F0$!3w#\\'fu'4[F)F07$$\"3U)***\\i&p@[#F0$!3XE%*>0P`N vF07$$\"3B)****\\2'HKHF0$!3%>%eT\"*elglF07$$\"3ElmmmZvOLF0$!3/:4&30Fka &F07$$\"3i******\\2goPF0$!3*fxR[Nf!>VF07$$\"3UKL$eR<*fTF0$!31!HPR!\\.y IF07$$\"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 attempt to solve the e quation 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 find 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 severa l arguments, and has many options. The basic command takes two argume nts. The first is the expression (i.e. function) to be plotted, and th e second is the range of the independent variable of the expression. \+ For example, the following command plots x^2 on the interval -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=0v F0$\"3(4CONayFj&F07$$!3u****\\P8#\\4(F0$\"30z7`y3zL]F07$$!3+nm;/siqmF0 $\"3qSopHns\\WF07$$!3[++](y$pZiF0$\"335mBmxO.RF07$$!33LLL$yaE\"eF0$\"3 m(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$$\"3%pJL$ezw5VF]q$\"3Q>$f!R?Fe=Fgr7$$\"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$$\"3[++]i`1h\"*F0$\"31F(*fd=^#R)F07$$\"3W++]P?Wl& *F0$\"3]:sFP\"o(\\\"*F07$F+F+-%'COLOURG6&%$RGBG$\"#5F)$F*F*F^[l-%+AXES LABELSG6$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 th at specifies the vertical range of the plot. For example:" }}}{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%-%'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$$!3\"ommT!R=0vF 0$\"3(4CONayFj&F07$$!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$$!3hLLL$=exJ$F0$\"3@Iv IO>v+6F07$$!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$\"3;&R g9Fg$)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$$\"3W++]P?Wl&*F 0$\"3]:sFP\"o(\\\"*F07$F+F+-%'COLOURG6&%$RGBG$\"#5F)$F*F*F^[l-%+AXESLA BELSG6$Q\"x6\"Q!Fc[l-%%VIEWG6$;F(F+;F($\"#:F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 "You can specify more optional arguments. In the next ex ample, I've changed the color to black, used a dashed line, and I've g iven the plot a title:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "p lot(x^2,x=-1..1,-1..1.5,title=`y=x^2`,color=black,linestyle=DASH);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6#7S7$ $!\"\"\"\"!$\"\"\"F*7$$!3ommm;p0k&*!#=$\"3c]R_q%=r9*F07$$!3wKL$3`0n(F07$$!3:mmm\"4m(G$) F0$\"32V'p4YMo$pF07$$!3\"QLL3i.9!zF0$\"3Z6=$z\"z@ViF07$$!3\"ommT!R=0vF 0$\"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@Iv IO>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$$\"3B)****\\2'HKHF0$\"3;&R g9Fg$)f)F]q7$$\"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&*F 0$\"3]:sFP\"o(\\\"*F07$F+F+-%'COLOURG6&%$RGBGF*F*F*-%&TITLEG6#%&y=x^2G -%*LINESTYLEG6#\"\"$-%+AXESLABELSG6$Q\"x6\"Q!Fh[l-%%VIEWG6$;F(F+;F($\" #:F)" 1 2 0 3 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1 " }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "To see more examples, look u p \"plot\" in the Maple Help. Or enter the command \"?plot\"." }}} {EXCHG {PARA 18 "" 0 "" {TEXT 257 16 "The Diff Command" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 334 "You can take derivatives in Maple with t he \"diff\" command (\"diff\" stands for \"differentiate\"). The basi c command takes two arguments. The first is the expression to be diffe rentiated, and the second is the variable with respect to which the de rivative is to be taken. Maple knows the derivatives of most of the e lementary functions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 124 "Here are some examples. The first finds the derivativ e of sin(t)+4t, and the second finds the derivative of 1/x + exp(x^2). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "diff(sin(t)+4*t,t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$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#*$F'F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 109 "To \+ take a second or higher order derivative, just list the variable again . Here are some second derivatives:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "diff(sin(t)+4*t,t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"tG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "diff(1/x + exp(x^2),x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*& \"\"\"F%*$)%\"xG\"\"$F%!\"\"\"\"#*&F+F%-%$expG6#*$)F(F+F%F%F%*(\"\"%F% F1F%F-F%F%" }}}{EXCHG {PARA 18 "" 0 "" {TEXT 258 17 "The Solve Command " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 291 "The \"solve\" command can so lve many algebraic equations. We saw an example earlier where we solv ed a quadratic. In the simplest form of the command, the first argume nt is the equation to be solved, and the second is the variable to be \+ solved for. Here we find the solutions to x^2+5x+6=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x^2+5*x+6=0,x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$!\"#!\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 115 "If there expression does not contain an equals sign, Maple assume s that the expression should be set equal to zero." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+5*x+6,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"#!\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Next w e solve a cubic:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x ^3-2*x+1=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\",&#!\"\"\"\"#F #*&#F#F'F#-%%sqrtG6#\"\"&F#F#,&F%F#*&#F#F'F#*$F*F#F#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Let's make one small change to the cubic: " }}}{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#F0F(,&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 the above output, you will see that Maple has fo und three solutions, two of which are complex numbers. (Recall that t he 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 e quation has no solution, or if Maple can not find it? Here are some e xamples. First, a trivial 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)\"\" \"-%$sinG6#F(F+F+F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 282 "The \"R ootOf\" function means the root of the expression; in the expression, \+ _Z is the variable. In this example, Maple found one solution to be 0 , but the other \"solution\" is just the solution to 4*_Z + 4*sin(*_Z) +1=0. Maple could not find an analytical solution to this equation. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 94 "Let's create a function, plot it, and then use \"diff\" and \"solv e\" to find the critical points." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "w := (x^4+3*x^2)/(1+x^4);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG*&,&*$)%\"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%-%'CURVESG6$7ep7$$!\"$\"\"!$\"3Q20(RdW8F-7$$!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]z o:K:F-7$$!3$****\\7Sw%G@F-$\"3kL^B)po\\e\"F-7$$!3*****\\7;)=,?F-$\"3qB Myt1XY;F-7$$!3/++DO\"3V(=F-$\"3xct)*3,+:F-7$$!3/+++vl[p8F-$\"3V&e3waHT-#F-7$$!3(******\\Qu oI\"F-$\"35l'*>(o(y_?F-7$$!3\"******\\>iUC\"F-$\"3]c*\\`=8H2#F-7$$!3/+ 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gl-%%VIEWG6$;F(F[fl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(dw=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\" \"!,$*$-%%sqrtG6#,&\"\"$\"\"\"*&F*F+-F'6#\"#5F+F+F+#!\"\"F*,$F%#F+F*,$ *$-F'6#,&F*F+*&F*F+F-F+F1F+F0,$F5F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Note that two of the five solutions found by \"solve\" are actually complex numbers ." }}}}{MARK "30 0 0" 67 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 1 1 2 33 1 1 }