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It is no surpris e that Maple can draw graphs handily. The two questions that remain ar e: What is the syntax to control drawings? and, What are visualization s that are " }{TEXT 259 6 "worthy" }{TEXT 260 16 " of this tool? " }} {PARA 264 "" 0 "" {TEXT -1 1 " " }}{PARA 265 "" 0 "" {TEXT 262 83 " \+ To illustrate this last point, I suggest that having Maple to draw a graph of " }{XPPEDIT 266 0 "f(x)=x^2-1" "6#/-%\"fG6#%\"xG,&*$F'\"\"# \"\"\"F+!\"\"" }{TEXT 261 69 " is a waste of the power of Maple. Havi ng said that, draw the graph!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(x^2-1,x=-2..2);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 266 "" 0 "" {TEXT -1 5 " " }{TEXT 263 131 "The purpose for drawing that graph is to illustrate that one might wish for other arrangement s of\n scaling. Consider the following." }}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 40 "plot([x,x^2-1,x=-2..2],x=-3..3,y=-5..5);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 267 "" 0 "" {TEXT -1 64 "Or, one might m ake the scaling on the x and the y axes the same." }}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 60 "plot([x,x^2-1,x=-2..2],x=-3..3,y=-5..5,scal ing=CONSTRAINED);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 267 111 " Also, to make the point that this gr aph is \"near-linear\" when examined \"up-close,\" draw the following \+ graph." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(x^2,x=0.48..0 .52);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 268 "" 0 "" {TEXT -1 6 " O" }{TEXT 264 133 "ften superimposing two graphs on top of eac h other is needed. For example, we draw the graph of the sine and cosi ne on the same axes." }}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 33 "pl ot([cos(x),sin(x)], x=0..2*Pi);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 268 114 " Sometimes, one want s to have two functions on the same graphs, but to have them defined o n different intervals" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 81 "plot(\{[x,x,x=-1..1],[ x,sum(-2*cos(n*Pi)*sin(n*Pi*x)/(n*Pi),n=1..5),\n\011\011x=-2..2]\});" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT 269 217 "Th e syntax for drawing the cosine and the sine on the same axis is simil ar to that for doing a parameteric curve. It is so similar, that care \+ must be taken to know how the syntax differs for drawing the two graph s are" }{TEXT 271 1 " " }{TEXT 270 10 "different." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot([cos(x),sin(x),x=0..5*Pi/4]);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 270 "" 0 "" {TEXT 272 41 "This suggest s interesting possibilities. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot([x^2,x,x=-1..1]);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 273 84 "Sometimes, for various reasons, it is of value to have a function defined piecewise." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "h:=x->piecewise( x<-2, 4, -2<=x and x <=2, x^2, 4) ;\nplot(h(x),x=-3..3);" }}}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 274 37 "Of course, polar graphs ca n be drawn." }{TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot([cos(3*theta),theta,theta=0..Pi],coords=polar);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot([1+2*sin(t),t,t=0..2*Pi],coord s=polar);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 275 68 "It is fun to imagine what happens if this graph were given ani mation" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "wi th(plots);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "animate([a+2* sin(t),t,t=0..2*Pi],a=-2..2,coords=polar);" }}}{PARA 0 "" 0 "" {TEXT -1 62 " Here is an animation that draws graphs as a calculator would. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "for n from 0 by 1 to 10 do\n P||n :=plot(sin(x),x=0..n/10*2*Pi,y=-2..2):\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display([seq(P||n,n=0..10)],insequence=true);" }}} {PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 276 105 "One of the best use s of Maple in beginning mathematics is the ability to draw three dimen sional graphics." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "plot3d(s in(x)*cos(y),x=-Pi..Pi,y=0..Pi,style=PATCHNOGRID,light=[50,25,0,1,0], \naxes=NORMAL);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 153 "All the se are illustration for how to draw graphs with Maple. Return to this \+ worksheet from time-to-time to recall the correct syntax for drawing g raphs." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 271 "" 0 "" {TEXT -1 9 "Exercise." }}{PARA 272 "" 0 "" {TEXT -1 49 "Draw two graphs. The fi rst is to be the graph of " }{XPPEDIT 18 0 "x^2" "6#*$%\"xG\"\"#" } {TEXT -1 5 " and " }{XPPEDIT 18 0 "x^3" "6#*$%\"xG\"\"$" }{TEXT -1 66 " on the same axis and the second is to be the parametric curve [ " } {XPPEDIT 18 0 "t^2" "6#*$%\"tG\"\"#" }{TEXT -1 2 ", " }{XPPEDIT 18 0 " t^3" "6#*$%\"tG\"\"$" }{TEXT -1 33 " ] for t in the interval [-2, 2]. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }