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"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" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 294 18 "Welcome to Maple 8" }}{PARA 257 "" 0 "" {TEXT 295 54 "\"Command the Brilliance of a Thousand Mathematicians.\" " }}{PARA 258 "" 0 "" {TEXT -1 50 "[sic]\nCare of Adam Bowers, just on e mediocre mind." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "Basic Commands" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 144 "All Maple commands must end with either a semico lon ( ; ) or a colon ( : ). The difference between the two is that th e colon suppresses output." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b:=-6:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "When assigning values to a name, you must use a \n :=\nOt herwise, no assignment is made." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "c=13;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"cG\"#8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "You can view what is assigned to a name a t any time." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"'" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 2 "c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"cG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "The basic algebraic operators a re what you might expect: +, -, *, and /." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "a+b; a-b; a*b; a/b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#6" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#!#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"&\"\"'" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "You need not assign values to a n ame to work with it." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a*c+ z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"&\"\"\"%\"cGF&F&%\"zGF& " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "If you want to use a new valu e for a name, just go ahead and assign something new:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:=14570;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"&qX\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a;b;c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&qX\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"cG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "You can also unassign names, so th ey have no specified value:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('a');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=eval n(b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 54 "That command assigns the name of a name, not the v alue" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"bG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "You can also assign functiona l values." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f:=x^2-1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$)%\"xG\"\"#\"\"\"F*F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g:=x+1;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"gG,&%\"xG\"\"\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h:=1/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG*&\" \"\"F&%\"xG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "f+g;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"F(F&F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Try the " }{TEXT 256 6 "factor" } {TEXT -1 9 " command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "fa ctor(f+g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",&F$F%F%F%F %" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Maple is case sensitive." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "F:=(f+g)*h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG*&,&*$)%\"xG\"\"#\"\"\"F+F)F+F+F)!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "F;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$)%\"xG\"\"#\"\"\"F)F'F)F)F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "f;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,&*$)%\"xG\"\"#\"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "F/f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&*$)%\"xG\" \"#\"\"\"F)F'F)F)F'!\"\",&F%F)F)F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "If an expression can be simplified, use the command " }{TEXT 257 8 "simplify" }{TEXT -1 10 " to do so." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "simplify(F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&% \"xG\"\"\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "expand(F/ f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\",&*$)F%\"\"#F&F& F&!\"\"F+F&*&F&F&F'F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " simplify(F/f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$,&%\"xGF$F $!\"\"F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Now let's try somethi ng more complicated." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "h:=sin(x*y)/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG*&-%$sinG6#*&%\"xG\"\"\"%\"yGF+F+F*!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Mobius:=(a*z+b)/(c*z+d) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'MobiusG*&,&*&%\"aG\"\"\"%\"zGF )F)%\"bGF)F),&*&%\"cGF)F*F)F)%\"dGF)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "A name in Maple need not be only one letter." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 99 "So what if I want to know what a function is at a certain domai n value? How do we find, say, f(3)?" }}{PARA 0 "" 0 "" {TEXT -1 14 "W ell, we just " }{TEXT 273 4 "subs" }{TEXT -1 33 "titute the value 3 in place of x." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)-%\"xG6#\"\"$\"\"#\"\"\"F+F+!\"\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 81 "Well, that's not going to work, we have to tell Maple v ery explicitly what to do." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=3,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Here we substituted x=3 into the function f." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "subs(z=0,Mobius);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"bG\"\"\"%\"dG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(z=1-I,Mobius);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#*&,&*&^$\"\"\"!\"\"F'%\"aGF'F'%\"bGF'F',&*&F&F'%\"cGF'F'%\"dGF'F(" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Oh wait ... what was that \"I\" \+ thing? You probably can guess that " }{XPPEDIT 18 0 "I = sqrt(-1);" " 6#/%\"IG-%%sqrtG6#,$\"\"\"!\"\"" }{TEXT -1 58 ". That brings up a go od point, let's talk about some ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 31 "Special Commands and Characters" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Want some Pi?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 31 "The command for pi=3.1415... is" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#P iG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 "Wait a minute? What command was that? If you don't know a command, you open the help documentation by typing a question mark \+ and then the command. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "? evalf" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 265 21 "Complex numbers are n" }{TEXT 264 1 "I" }{TEXT 266 3 "ce ," }}{PARA 0 "" 0 "" {TEXT -1 17 "but remember that" }}{PARA 0 "" 0 " " {XPPEDIT 18 0 "sqrt(-1) = I" "6#/-%%sqrtG6#,$\"\"\"!\"\"%\"IG" } {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Use a capitol \"I\" for an imaginary numb er, not a lower case \"i\"." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "I^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x+I*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&% \"xG\"\"\"*&%\"yGF%^#F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "So how do you do square roots, anyway?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^#\"\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sqrt(-4*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#\"\"\",$%\"xG!\"\"#F&F%F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "Why didn't it pull out the I? May be x<0, Maple can't distinguish, unless we tell it in advance." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(x>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sqrt(-4*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&^#\"\"#\"\"\"%#x|irG#F&F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 136 "The ~ that appears after the x is Maple's way of letting us know it's assuming something about x. Let's make it forget that a ssumption." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('x') ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Good, the re is no ~ after the x, so Maple doesn't think it's positive anymore. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "Maple can also tell us the real and imaginary parts \+ of a complex number." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "w:=5 -I*3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG^$\"\"&!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Re(w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Im(w);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Re((3-4*1)/(2+3*I));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"#\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Im((3-4*1)/ (2+3*I));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"$\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Let's get back to our Mobius function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Mobius;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*& %\"aG\"\"\"%\"zGF'F'%\"bGF'F',&*&%\"cGF'F(F'F'%\"dGF'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Mo1:=simplify(subs(z=1-I,Mobius)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Mo1G*&,(%\"aG!\"\"*&F'\"\"\"^#F *F*F*%\"bGF(F*,(%\"cGF(*&F.F*F+F*F*%\"dGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Re(Mo1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#Re G6#*&,(%\"aG!\"\"*&F(\"\"\"^#F+F+F+%\"bGF)F+,(%\"cGF)*&F/F+F,F+F+%\"dG F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Maple cannot tell if a,b, c,d are real or imaginary, so it cannot give us the real part." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "assume(a,real);assume(b,real ),assume(c,real),assume(d,real);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Re(Mo1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,**(\"\" #\"\"\"%#a|irGF'%#c|irGF'F'*&F(F'%#d|irGF'F'*&%#b|irGF'F)F'F'*&F-F'F+F 'F'F',(*&F&F')F)F&F'F'*(F&F'F)F'F+F'F'*$)F+F&F'F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Im(Mo1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&*&%#b|irG\"\"\"%#c|irGF(!\"\"*&%#a|irGF(%#d|irGF( F(F(,(*&\"\"#F()F)F0F(F(*(F0F(F)F(F-F(F(*$)F-F0F(F(F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Actually we could have made those assumpt ions at the same time:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "a ssume(a,real,b,real,c,real,d,real);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "We can also check to see if those assumptions actually worked u sing the " }{TEXT 274 2 "is" }{TEXT -1 9 " command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "is(a,real);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "is(b,integ er);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 71 "Maple said b was not an integer, because we never \+ made that assumption." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ad ditionally(b,integer);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "i s(b,integer);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "For more assumption commands, type " } {TEXT 275 8 "? assume" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "? a ssume" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Just to be safe, I'll re move all of my assumptions by assigning names to a,b,c, and d." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "a:='a'; b:='b'; c:='c'; d:=' d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cGF$" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGF$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "is(a,real);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&fa lseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "is(b,integer);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT 263 12 "Trigonometry" }{TEXT -1 31 " is \+ a Pythagorean's best friend" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "The three main trig functi ons are:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%\"xG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 7 "cos(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$c osG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "tan(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$tanG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "To evaluate on numbers, just type them in:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "cos( Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$ *&\"\"#!\"\"F%#\"\"\"F%F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tan(Pi/2);" }}{PARA 8 "" 1 "" {TEXT -1 52 "Error, (in tan) numeric exception: division by zero\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 157 "Oops, I just tried to divide by zero. Whenever I try to do somet hing Maple can't do, it'll let me know. Although the error message mi ght be unintelligible." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "And all of our other favorites \+ are here, too." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "sin(x)*cs c(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$sinG6#%\"xG\"\"\"-%$cscG F&F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 145 "Oops, that didn't work. \+ Let's simplify, but I don't want to type the whole thing again, so I' ll use\n%\nwhich will input whatever was last output." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "si mplify(1/sec(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG6#%\"xG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "simplify((sin(x)/cos(x)*co t(x));" }}{PARA 8 "" 1 "" {TEXT -1 22 "Error, `;` unexpected\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Oops, I forgot to close up my pare ntheses, let me try that again." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify((sin(x)/cos(x))*cot(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "The inverse functions just have \+ \"arc\" written in front of them:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sin(arcsin(5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "arcsin(sin(5));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"&\"\"\"*&\"\"#F%%#PiGF%!\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "cos(arccos(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "arccos(cos(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'arccosG6 #-%$cosG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "arccos(c os(Pi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Mapl e is pretty good with trig identities, too." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "(sin(x))^2+(cos(x)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)-%$sinG6#%\"xG\"\"#\"\"\"F+*$)-%$cosGF(F*F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Not e that the ^2 was after the sin(x) and cos(x), not in the middle." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "tf:=sin(x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #tfG-%$sinG6#,&%\"xG\"\"\"%\"yGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand(tf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-% $sinG6#%\"xG\"\"\"-%$cosG6#%\"yGF)F)*&-F+F'F)-F&F,F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "combine(%,trig);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%$sinG6#,&%\"xG\"\"\"%\"yGF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "For more information on how to use trig commands, ju st type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "? trig" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 17 "It's very \+ natural" }}{PARA 0 "" 0 "" {TEXT -1 6 "Using " }{TEXT 259 3 "exp" } {TEXT -1 5 " and " }{TEXT 258 3 "log" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "If you want t o find an exponential, you have to use the " }{TEXT 260 3 "exp" } {TEXT -1 9 " command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp (x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "exp(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "exp(Pi*I)+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "exp(ln(2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "The \+ command" }{TEXT 262 3 " ln" }{TEXT -1 45 " is the natural log command, but you can use " }{TEXT 261 3 "log" }{TEXT -1 6 ", too." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "exp(log(2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 17 "Solving Equations" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "To solve equations for unknowns, simply use the " }{TEXT 286 5 "so lve" }{TEXT -1 9 " command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(x^2-1=3,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#!\"#" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "To put the solutions into a set, \+ put the equations or unknowns in a set." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve(\{x^2-1=3\},x);solve(x^2-1=3,\{x\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<#/%\"xG\"\"#<#/F%!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<#/%\"xG\"\"#<#/F%!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "If you want to solve for 0, you don't need the equals sig n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(x^2-4=0,x); sol ve(x^2-4,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "You can also solve a system of equations for several unknowns, bu t be sure to put all of the equations into a set, as well as the unkno wns." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(\{x^2-4,x-2\} ,\{x\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#/%\"xG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "solve(\{x+3*y-1, y-3\},\{x,y\});" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG!\")/%\"yG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(\{x+y+z,3*x-2*y\},\{x,y,z\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"xGF%/%\"zG,$*(\"\"&\"\"\"\" \"#!\"\"F%F+F-/%\"yG,$*(\"\"$F+F,F-F%F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "In this system, one of the unknowns is a free parameter, Maple chose it to be x. You can see that y and z are solved in terms of x." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 137 "In the above family of solutions, if you would rather have the unknowns in terms of z, you c an just leave it out of the list of unknowns." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve(\{x+y+z,3*x-2*y\},\{x,y\});" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#<$/%\"xG,$*(\"\"#\"\"\"\"\"&!\"\"%\"zGF)F+/%\"yG ,$*(\"\"$F)F*F+F,F)F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Of cours e, not all systems of equations have a solution." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(\{x-1,x-4\},\{x\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "In this case, I was given no output, to signal th at there was no solution." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Matr ix Manipulation" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "One of the thin gs I use Maple for most often is to solve linear algebra problems." }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "There are several ways to define \+ a matrix:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M:=matrix([[-2 ,0],[3,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7$7$ !\"#\"\"!7$\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "N :=matrix(2,3,[1,2,3,4,5,6]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG -%'matrixG6#7$7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 50 "I wonder what the product of those matrices are... " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm(M &* N);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%!\"#!\"%!\"'7%\"\"(\"# 6\"#:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Okay, so what happened t here? The command " }{TEXT 271 5 "evalm" }{TEXT -1 120 " tells Maple \+ I am about to evaluate something with matrices, and whenever that oper ation is matrix multiplication, I do " }{TEXT 272 3 "&* " }{TEXT -1 80 "so Maple knows a matrix is being multiplied by another matrix and \+ not a scalar. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A:=matrix(2,2,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7$\"\"\"F*F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "That's a 2x2 matrix with all entries 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "B:=matrix([[cos(x),sin(x) ],[-sin(x),cos(x)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matr ixG6#7$7$-%$cosG6#%\"xG-%$sinGF,7$,$F.!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "C:=evalm(3*A-B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7$7$,&\"\"$\"\"\"-%$cosG6#%\"xG!\"\",&F+F,-%$s inGF/F17$,&F+F,F3F,F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 215 "I have \+ just decided I am only interested in the case x=Pi/2, so why don't I s ubstitute in the value? I have to remember that Maple has a hard time knowing matrix commands from scalar commands, so I need to use the " }{TEXT 276 4 "map2" }{TEXT -1 45 " command. This command will map the command " }{TEXT 277 4 "subs" }{TEXT -1 25 " into each matrix entry. \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "BB:=map2(subs,x=Pi/2,B) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BBG-%'matrixG6#7$7$-%$cosG6#,$ *&\"\"#!\"\"%#PiG\"\"\"F2-%$sinGF,7$,$F3F0F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(BB);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'matrixG6#7$7$\"\"!\"\"\"7$!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "C:=simplify(evalm(3*A-BB));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7$7$\"\"$\"\"#7$\"\"%F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 151 "So now I have a matrix. Let's say I rea lly like looking at entries in the 2nd row 1st column. I can get it a ll by itself using the following command:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 7 "C[2,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "I put the name of the matrix, fo llowed by a list containing the row and column numbers:\nMatrixName[Ro wNumber,ColumnNumber]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "C[ 1,2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "C[1,1]-C[2,2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "1002*C[2,1]+ 999*C[1,2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%1g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "C[3,2];" }}{PARA 8 "" 1 "" {TEXT -1 53 "Er ror, 1st index, 3, larger than upper array bound 2\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "There is no third row in my matrix C, so I didn 't have a entry for C[3,2]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "If I want to do anything \+ more interesting, I'll have to use the PACKAGE made for linear algebra , called " }{TEXT 278 6 "linalg" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 7 "" 1 "" {TEXT -1 80 " Warning, the protected names norm and trace have been redefined and un protected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,Gr amSchmidtG%,JordanBlockG%)LUdecompG%)QRdecompG%*WronskianG%'addcolG%'a ddrowG%$adjG%(adjointG%&angleG%(augmentG%(backsubG%%bandG%&basisG%'bez outG%,blockmatrixG%(charmatG%)charpolyG%)choleskyG%$colG%'coldimG%)col spaceG%(colspanG%*companionG%'concatG%%condG%)copyintoG%*crossprodG%%c urlG%)definiteG%(delcolsG%(delrowsG%$detG%%diagG%(divergeG%(dotprodG%* eigenvalsG%,eigenvaluesG%-eigenvectorsG%+eigenvectsG%,entermatrixG%&eq ualG%,exponentialG%'extendG%,ffgausselimG%*fibonacciG%+forwardsubG%*fr obeniusG%*gausselimG%*gaussjordG%(geneqnsG%*genmatrixG%%gradG%)hadamar dG%(hermiteG%(hessianG%(hilbertG%+htransposeG%)ihermiteG%*indexfuncG%* innerprodG%)intbasisG%(inverseG%'ismithG%*issimilarG%'iszeroG%)jacobia nG%'jordanG%'kernelG%*laplacianG%*leastsqrsG%)linsolveG%'mataddG%'matr ixG%&minorG%(minpolyG%'mulcolG%'mulrowG%)multiplyG%%normG%*normalizeG% *nullspaceG%'orthogG%*permanentG%&pivotG%*potentialG%+randmatrixG%+ran dvectorG%%rankG%(ratformG%$rowG%'rowdimG%)rowspaceG%(rowspanG%%rrefG%* scalarmulG%-singularvalsG%&smithG%,stackmatrixG%*submatrixG%*subvector G%)sumbasisG%(swapcolG%(swaprowG%*sylvesterG%)toeplitzG%&traceG%*trans poseG%,vandermondeG%*vecpotentG%(vectdimG%'vectorG%*wronskianG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "The command " }{TEXT 279 4 "with" }{TEXT -1 259 " tells Maple to open up one of the predefined packages, in this case the linalg package. If you choose not to suppress the o utput with a colon, it lists all commands in the package. (For now, y ou can just ignore any warnings of \"redefined and unprotected\".)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Now we can take an " }{TEXT 280 7 "inverse" }{TEXT -1 12 ", or find a " }{TEXT 281 9 "transpose" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "C;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#%\"CG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"$\"\"#7$\"\"%F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 282 2 "op" }{TEXT -1 72 " command, among other things, shows the matrix instead of just the name." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Cinv:=inverse(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%%CinvG-%'matrixG6#7$7$\"\"$!\"#7$!\"%F*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "Ctrans:=transpose(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'CtransG-%'matrixG6#7$7$\"\"$\"\"%7$\"\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalm(C &* Cinv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"\"\"\"!7$F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A:=diag(a,b,c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%%\"aG\"\"!F+7%F+%\"bGF+7%F+F+%\"cG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "X:=diag(x,y,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG-%'matrixG6#7%7%%\"xG\"\"!F+7%F+%\"yGF+7% F+F+%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm(A &* X); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%*&%\"aG\"\"\"%\"xG F*\"\"!F,7%F,*&%\"bGF*%\"yGF*F,7%F,F,*&%\"cGF*%\"zGF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "You can do some nifty things with linalg. For example, using the " }{TEXT 283 8 "linsolve" }{TEXT -1 69 " comm and, you can find which matrix will get you from one to another." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "phil:=randmatrix(3,3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%philG-%'matrixG6#7%7%!#&)!#b!#P7%!# N\"#(*\"#]7%\"#z\"#c\"#\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "george:=randmatrix(3,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'geo rgeG-%'matrixG6#7%7%\"#j\"#d!#f7%\"#X!\")!#$*7%\"##*\"#V!#i" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "(" }{TEXT 284 10 "randmatrix" } {TEXT -1 48 " gives a random matrix of specified dimensions.)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "martha:=linsolve(phil,george );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'marthaG-%'matrixG6#7%7%#!'i#G #\"'H:7#!'9C9F,#\"'%=D#F,7%#!'X6\")F,#!'w7dF,#\"'>DcF,7%#\"(9K_\"F,#\" 'T\"*)*F,#!(-(f6F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "So martha s hould take us from phil to george." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalm(phil &* martha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"#j\"#d!#f7%\"#X!\")!#$*7%\"##*\"#V!#i" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "If you didn't trust your matrix re ading ability, then you could check by subtraction." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "evalm(phil &* martha - george);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"!F(F(F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Now let's try something involving unknown quantities." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "M:=matrix([ [2,8],[-1,-4]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6# 7$7$\"\"#\"\")7$!\"\"!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "N:=matrix([[a,b],[c,d]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"N G-%'matrixG6#7$7$%\"aG%\"bG7$%\"cG%\"dG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "I want M &* N to be the zero matrix." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "MN:=evalm(M &* N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#MNG-%'matrixG6#7$7$,&*&\"\"#\"\"\"%\"aGF-F-*&\"\")F- %\"cGF-F-,&*&F,F-%\"bGF-F-*&F0F-%\"dGF-F-7$,&F.!\"\"*&\"\"%F-F1F-F9,&F 4F9*&F;F-F6F-F9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Let's list the entries in a set:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "eqs:= \{MN[1,1],MN[1,2],MN[2,1],MN[2,2]\};" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$eqsG<&,&*&\"\"#\"\"\"%\"aGF)F)*&\"\")F)%\"cGF)F),&*&F(F)%\"bGF)F) *&F,F)%\"dGF)F),&F*!\"\"*&\"\"%F)F-F)F4,&F0F4*&F6F)F2F)F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Now we " }{TEXT 285 5 "solve" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sols:=solve(eqs,\{a,b ,c,d\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solsG<&/%\"cGF'/%\"dGF) /%\"bG,$*&\"\"%\"\"\"F)F/!\"\"/%\"aG,$*&F.F/F'F/F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 129 "So any matrix of the form a=-4c and b=-4d will s uffice. We can substitute these values into out matrix, but remember \+ to use the " }{TEXT 287 5 "map2 " }{TEXT -1 44 "command, otherwise Map le might get confused." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "n ewN:=map2(subs,sols,N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%newNG-%' matrixG6#7$7$,$*&\"\"%\"\"\"%\"cGF-!\"\",$*&F,F-%\"dGF-F/7$F.F2" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "This is just the tip of the linalg iceberg. For more information, just type " }{TEXT 288 7 "?linalg" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 27 "Plots in 2 and 3 Dimensions" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "If you want t o graph a function (for example, the function y=1/x), use the " } {TEXT 267 4 "plot" }{TEXT -1 11 " command..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "plot(1/x);" }}{PARA 8 "" 1 "" {TEXT -1 26 "Plott ing error, empty plot" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 "... but you'll have to enter a domain. Be sure to separate the endpoints of \+ the domain with two periods (as in \"..\")." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(1/x,x=-5..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6%-%'CURVESG6$7ao7$$!\"&\"\"!$!35+++++++?!#=7 $$!3YLLLe%G?y%!#<$!3?G0p&zi64#F-7$$!3OmmT&esBf%F1$!3q)3\\'oO_x@F-7$$!3 ALL$3s%3zVF1$!3-Z*)3=Ae$G#F-7$$!3_LL$e/$QkTF1$!3bMk!p3;8S#F-7$$!3ommT5 =q]RF1$!3'p(o8Ve>JDF-7$$!3ILL3_>f_PF1$!3yJN$QxC[m#F-7$$!3K++vo1YZNF1$! 3*Rr^Kz<*=GF-7$$!3;LL3-OJNLF1$!3eI_xM@#[F-7$$!39LL3-TC%)=F1$!35c B`)*z;2`F-7$$!3[mmm\"4z)e;F1$!3]s!>5)o;GgF-7$$!3Mmmmm`'zY\"F1$!341GM9) \\@\"oF-7$$!3#****\\(=t)eC\"F1$!3t*\\,j/3k-)F-7$$!3!ommmh5$\\5F1$!32\\ C%>am+`*F-7$$!3S$***\\(=[jL)F-$!3G\"42!=gc*>\"F17$$!3)f***\\iXg#G'F-$! 3m_E')[lp\"f\"F17$$!3ndmmT&Q(RTF-$!3aQv<$\\6cT#F17$$!3Ihm\"HdGe:$F-$!3 KA'Rk#*R(oJF17$$!3%\\mmTg=><#F-$!3>g'e*3TA/YF17$$!3FK$3Fpy7k\"F-$!3=)G )4o/\"G4'F17$$!3g***\\7yQ16\"F-$!3HRG$*)\\FQ+*F17$$!3iK$3_D)=`%)!#>$!3 G-fO-c)H=\"!#;7$$!3Epm\"zp))**z&F^t$!3EXmv!HTTs\"Fat7$$!3gP3F>*)QtWF^t $!3PIt$3nTaB#Fat7$$!3#f+D19*yYJF^t$!3#p3?VTUy<$Fat7$$!35!4-8D*[$[#F^t$ !3/oi*[#GfESFat7$$!3Du\"z>O*=?=F^t$!3/oh\"z(Q$R\\&Fat7$$!3Ueils%*)o:\" F^t$!3<,Z:$4oQk)Fat7$$!3vDMLLe*e$\\!#?$!3Kwzv$ouf-#!#:7$$\"3=$4aj%e#R& >Fcv$\"3@hEz*[,z6&Ffv7$$\"337;/EvuV))Fcv$\"3pE[ylBuI6Ffv7$$\"358Hd?pNt :F^t$\"3/#o%QF*>Fat7$$\"37!o \"HKk>uxF^t$\"3!zJvnd1jG\"Fat7$$\"3womT5D,`5F-$\"39Of;PLc'\\*F17$$\"3G q;zW#)>/;F-$\"3il')3CNkLiF17$$\"3!=nm\"zRQb@F-$\"3D#*G#HbW&RYF17$$\"3m OLL$e,]6$F-$\"3'*f^VT7F5KF17$$\"3_,+](=>Y2%F-$\"3gae!*yq@aCF17$$\"3sum m\"zXu9'F-$\"3GpqEb=pE;F17$$\"3#4+++]y))G)F-$\"3H)oT%GeV17F17$$\"3H++] i_QQ5F1$\"3w&G)z')pLI'*F-7$$\"3b++D\"y%3T7F1$\"3;v@gmsYd!)F-7$$\"3+++] P![hY\"F1$\"3e&=HPl$f?oF-7$$\"3iKLL$Qx$o;F1$\"3s+&p[tZQ*fF-7$$\"3Y+++v .I%)=F1$\"3=%o(y/&4qI&F-7$$\"3?mm\"zpe*z?F1$\"3&)oB$[x(y2[F-7$$\"3;,++ D\\'QH#F1$\"3]oaS+YXfVF-7$$\"3%HL$e9S8&\\#F1$\"3\"oY?+w+y+%F-7$$\"3s++ D1#=bq#F1$\"3[S!fne\\hp$F-7$$\"3\"HLL$3s?6HF1$\"3atcs76+NMF-7$$\"3a*** \\7`Wl7$F1$\"3KL'>8=>%)>$F-7$$\"3enmmm*RRL$F1$\"3#***HMHTX**HF-7$$\"3% zmmTvJga$F1$\"3@,%R)3P0?GF-7$$\"3]MLe9tOcPF1$\"3QvGetk9iEF-7$$\"31,++] Qk\\RF1$\"3xjY!\\&Q(=`#F-7$$\"3![LL3dg6<%F1$\"3-\\J(**H9uR#F-7$$\"3%ym mmw(GpVF1$\"3c(y6y`-()G#F-7$$\"3C++D\"oK0e%F1$\"3'\\)p%**>_J=#F-7$$\"3 5,+v=5s#y%F1$\"3?Xz^&)*f34#F-7$$\"\"&F*$\"35+++++++?F--%'COLOURG6&%$RG BG$\"#5!\"\"$F*F*Fhal-%+AXESLABELSG6$Q\"x6\"Q!F]bl-%%VIEWG6$;F(F]al%(D EFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curv e 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Ouch! That's not very us eful. Try specifying a range ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(1/x,x=-5..5,y=-5..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6%-%'CURVESG6$7ao7$$!\"&\"\"!$!35++ +++++?!#=7$$!3YLLLe%G?y%!#<$!3?G0p&zi64#F-7$$!3OmmT&esBf%F1$!3q)3\\'oO _x@F-7$$!3ALL$3s%3zVF1$!3-Z*)3=Ae$G#F-7$$!3_LL$e/$QkTF1$!3bMk!p3;8S#F- 7$$!3ommT5=q]RF1$!3'p(o8Ve>JDF-7$$!3ILL3_>f_PF1$!3yJN$QxC[m#F-7$$!3K++ vo1YZNF1$!3*Rr^Kz<*=GF-7$$!3;LL3-OJNLF1$!3eI_xM@#[F-7$$!39LL3-TC %)=F1$!35cB`)*z;2`F-7$$!3[mmm\"4z)e;F1$!3]s!>5)o;GgF-7$$!3Mmmmm`'zY\"F 1$!341GM9)\\@\"oF-7$$!3#****\\(=t)eC\"F1$!3t*\\,j/3k-)F-7$$!3!ommmh5$ \\5F1$!32\\C%>am+`*F-7$$!3S$***\\(=[jL)F-$!3G\"42!=gc*>\"F17$$!3)f*** \\iXg#G'F-$!3m_E')[lp\"f\"F17$$!3ndmmT&Q(RTF-$!3aQv<$\\6cT#F17$$!3Ihm \"HdGe:$F-$!3KA'Rk#*R(oJF17$$!3%\\mmTg=><#F-$!3>g'e*3TA/YF17$$!3FK$3Fp y7k\"F-$!3=)G)4o/\"G4'F17$$!3g***\\7yQ16\"F-$!3HRG$*)\\FQ+*F17$$!3iK$3 _D)=`%)!#>$!3G-fO-c)H=\"!#;7$$!3Epm\"zp))**z&F^t$!3EXmv!HTTs\"Fat7$$!3 gP3F>*)QtWF^t$!3PIt$3nTaB#Fat7$$!3#f+D19*yYJF^t$!3#p3?VTUy<$Fat7$$!35! 4-8D*[$[#F^t$!3/oi*[#GfESFat7$$!3Du\"z>O*=?=F^t$!3/oh\"z(Q$R\\&Fat7$$! 3Ueils%*)o:\"F^t$!3<,Z:$4oQk)Fat7$$!3vDMLLe*e$\\!#?$!3Kwzv$ouf-#!#:7$$ \"3=$4aj%e#R&>Fcv$\"3@hEz*[,z6&Ffv7$$\"337;/EvuV))Fcv$\"3pE[ylBuI6Ffv7 $$\"358Hd?pNt:F^t$\"3/#o%QF*> Fat7$$\"37!o\"HKk>uxF^t$\"3!zJvnd1jG\"Fat7$$\"3womT5D,`5F-$\"39Of;PLc' \\*F17$$\"3Gq;zW#)>/;F-$\"3il')3CNkLiF17$$\"3!=nm\"zRQb@F-$\"3D#*G#HbW &RYF17$$\"3mOLL$e,]6$F-$\"3'*f^VT7F5KF17$$\"3_,+](=>Y2%F-$\"3gae!*yq@a CF17$$\"3summ\"zXu9'F-$\"3GpqEb=pE;F17$$\"3#4+++]y))G)F-$\"3H)oT%GeV17 F17$$\"3H++]i_QQ5F1$\"3w&G)z')pLI'*F-7$$\"3b++D\"y%3T7F1$\"3;v@gmsYd!) 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xG%\"yGQ!F/ " 1 2 0 1 10 0 2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }} }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 177 "If you want, you can move it ar ound by clicking on it and dragging your pointer around. If you right click, you can change colors, export as an eps file, and many other t hings." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "For more advanced plott ing, you should try the " }{TEXT 269 5 "plots" }{TEXT -1 29 " package. The plots command " }{TEXT 270 7 "inequal" }{TEXT -1 69 " will allow you graph sets of inequalities. For more info, just type " }{TEXT 289 6 "?plots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "? plots" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 48 "Segregatio n is Bad, but Differentiation is Good." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Differentiation is quite straightforward. Just use the \+ " }{TEXT 290 4 "diff" }{TEXT -1 96 " command on your function, remembe ring to tell Maple which variable with which to differentiate." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Let's differentiate the function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=x^3+2*x^2-4*x+1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,**$)%\"xG\"\"$\"\"\"F**&\"\"#F* )F(F,F*F**&\"\"%F*F(F*!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"$\"\"\") %\"xG\"\"#F&F&*&\"\"%F&F(F&F&F+!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "If we want a second derivative, just nest the " }{TEXT 291 4 "d iff" }{TEXT -1 10 " commands." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(diff(f,x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"' \"\"\"%\"xGF&F&\"\"%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "d iff(%,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "And that was a third derivative." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Let's do something a bit more interesting ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "g:=(sin(x))^2+tan(x)+e xp(y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,(*$)-%$sinG6#%\"xG\" \"#\"\"\"F--%$tanGF*F--%$expG6#%\"yGF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(g,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*(\" \"#\"\"\"-%$sinG6#%\"xGF&-%$cosGF)F&F&F&F&*$)-%$tanGF)F%F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(g,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(diff(g,x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,(*&\"\"#\"\"\")-%$cosG6#%\"xGF%F&F&*&F%F&)-%$sinGF*F%F&!\"\"*(F%F&-% $tanGF*F&,&F&F&*$)F2F%F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(diff(g,y),y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6 #%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(diff(g,x),y) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Two more examples." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "diff(sin(x*y)/x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG 6#*&%\"xG\"\"\"%\"yGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d iff(log(x)/x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%*$)%\" xG\"\"#F%!\"\"F%*&-%#lnG6#F(F%F(!\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 "Integratio n" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Integration is done much like differentiation, but the command is " }{TEXT 292 4 "int." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x^3+x^2+x+1;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"fG,**$)%\"xG\"\"$\"\"\"F**$)F(\"\"#F*F*F(F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&#\"\"\"\"\"%F&*$)%\"xGF'F&F&F&*&#F&\"\"$F&*$)F *F-F&F&F&*&#F&\"\"#F&*$)F*F2F&F&F&F*F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "the diff and int commands can work together." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff(int(f,x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"$\"\"\"F(*$)F&\"\"#F(F(F&F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(diff(f,x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"$\"\"\"F(*$)F&\"\"#F(F(F&F(" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Notice that there is no constant of integration." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "You can also \+ do definite integrals (don't forget the \"..\")." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(f,x=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#K\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(sin (x),x=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "A function might be discontinuous, but yo u can tell Maple to overlook that problem." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "int(1/x,x=-10..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*undefinedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "int(1 /x,x=-10..10,'continuous');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&^#!\" \"\"\"\"%#PiGF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Some function s might be hard to integrate, so Maple might give you something like t his:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "h:=exp(-x^2)*log(x) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG*&-%$expG6#,$*$)%\"xG\"\"# \"\"\"!\"\"F.-%#lnG6#F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(h,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&-%$expG6#,$*$ )%\"xG\"\"#\"\"\"!\"\"F/-%#lnG6#F-F/F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "But don't give up, some things can still be done." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(h,x=0..infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"%!\"\"%#PiG#\"\"\"\"\"#%&gamma GF)F&*&#F)F*F)*&-%#lnG6#F*F)F'F(F)F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "One more example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "P:=r*cos(theta)*sin(phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG*( %\"rG\"\"\"-%$cosG6#%&thetaGF'-%$sinG6#%$phiGF'" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "P1:=int(P,phi=0..Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P1G*&%\"rG\"\"\"-%$cosG6#%&thetaGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "P2:=int(P1,theta=0..Pi/4);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P2G,$*(\"\"#!\"\"F'#\"\"\"F'%\"rGF* F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "P3:=int(P2,r=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P3G*$\"\"##\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Of course, you could do it all in one go: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "int(int(int(r*cos(theta )*sin(phi),phi=0..Pi/2),theta=0..Pi/4),r=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$\"\"##\"\"\"F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "For more, just type " }{TEXT 293 5 "?int " }{TEXT -1 14 "at the pr ompt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 48 " If-Then, For-Do, and other ways to get confused." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " lantern:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lanternG\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "if lantern=1 then print(`By \+ land`) fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(By~landG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "When writing an " }{TEXT 305 2 "if" } {TEXT -1 1 "-" }{TEXT 306 4 "then" }{TEXT -1 23 " command, the syntax \+ is" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 " \+ if [condition] then [result] fi;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 10 "For every " }{TEXT 307 2 "if" }{TEXT -1 28 ", you must have an opposing " }{TEXT 308 2 "fi" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 15 "(Note that any " }{TEXT 313 5 "text " } {TEXT -1 7 "in the " }{TEXT 309 5 "print" }{TEXT -1 62 " command must \+ be inside `single quotes`, not 'single quotes'.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "a:=3;b:=4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "if a " 0 " " {MPLTEXT 1 0 50 "if a>=b then print(`greater than or equal to`) fi; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "In cases where this might hap pen, you can use the " }{TEXT 310 4 "else" }{TEXT -1 9 " command." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 77 "if a>=b then print(`greater than or equal to`) else \n print(`less than`);\nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*less ~thanG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "In this example, I use d more than one line, but that's okay, as long as I remember to put se mi-colons (or colons) in all but the first line." }}{PARA 0 "" 0 "" {TEXT -1 82 "In the previous example, I used shift-enter to make a bla nk line below the prompt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "if lantern=1 then prin t(`By land`) else\n print(`By sea`);\nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(By~landG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "lantern:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lanternG\"\"#" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "if lantern=1 then print(`B y land`) else\n print(`By sea`);\nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'By~seaG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 176 "This might no t be exactly what you want, because any value for lantern other than 1 will give `By sea`. How do we solve this problem? By making our pro gram longer, of course." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " lantern:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lanternG\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 171 "if lantern=1 then print(`By land`) else\n if lantern=2 then print(`By sea`) else\n print(`I s aid ONE if by land, TWO if by sea. There are no other choices!`);\n \+ fi;\nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%]oI~said~ONE~if~by~land,~ TWO~if~by~sea.~~There~are~no~other~choices!G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "Usually , if-than commands are not used on there own. Usually, they are used \+ inside of other structures, like a " }{TEXT 311 3 "for" }{TEXT -1 1 "- " }{TEXT 312 2 "do" }{TEXT -1 9 " command." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 33 "for i from 1 to 3 do print(i) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "When writing a " }{TEXT 315 3 "for" }{TEXT -1 1 "-" } {TEXT 316 2 "do" }{TEXT -1 23 " command, the syntax is" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 319 1 " " }{TEXT -1 74 "for [index] from [starting value] to [finishing value] d o [expression] od;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "For every " }{TEXT 317 2 "do" }{TEXT -1 27 ", you must ha ve a opposing " }{TEXT 318 2 "od" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "The for-do commands make it much easier t o do repeated calculations." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for i from 1 to 3 do i^5 od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$V#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "for k from 9997 to 9999 do 1/k+k/3-k^2 od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!.2*p3?(*H\"&\"**H" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!.p**R+ \")*H\"&%**H" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!-JLqm'***\"%****" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "We can put if-then commands insid e of for-do loops." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lante rn:='lantern';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lanternGF$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Now I have made sure that the name \"lantern\" has no value assigned to it." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 203 "for lantern from 1 to 3 do\n if lantern=1 then pr int(lantern,`By land`) fi;\n if lantern=2 then print(lantern,`By sea` ) fi;\n if lantern>2 then print(lantern,`Are you smoking on the job, \+ Henry?`) fi;\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"%(By~landG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#%'By~seaG" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$\"\"$%CAre~you~smoking~on~the~job,~Henry?G" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "A few simple examples:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for j to 6 do x||j:=j od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x2G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x3G\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x4G\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x5G\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x6G\" \"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "for m to 6 do\n if \+ is(x||m,even) then print(`even`) else print(`odd`) fi;\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$oddG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%% evenG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$oddG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%evenG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$oddG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%%evenG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "for number from 4 to 6 do\n y||(number-3):=x||number ;\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# y3G\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Now something a bit t rickier." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "M1:=matrix([[0, 1,3],[-1,-1,3],[0,1,0]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M1G-%' matrixG6#7%7%\"\"!\"\"\"\"\"$7%!\"\"F.F,7%F*F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "M2:=matrix([[2,2,-2],[0,-4,4],[2,1,4]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M2G-%'matrixG6#7%7%\"\"#F*!\"#7%\" \"!!\"%\"\"%7%F*\"\"\"F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "M3:=matrix([[1,1,1],[2,2,2],[3,3,Pi]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M3G-%'matrixG6#7%7%\"\"\"F*F*7%\"\"#F,F,7%\"\"$F.%#PiG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "for i to 3 do\n linalg[det] (M||i);\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#S" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "for i to 3 do\n for j to 3 \+ do\n if M3[i,j]=Pi then print(M3[i,j],`huh?`) fi\n od;\nod;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%#PiG%%huh?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "For loo ps can get really complicated. Usually they are planted in programs, \+ but that is a topic for another time. For more information just type \+ " }{TEXT 320 4 "?for" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?for " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Go on ... do it ... you know \+ you want to ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 1 0 0" 109 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }