{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 "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "Cour ier" 0 1 0 0 0 0 0 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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple 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 "T imes" 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" -1 19 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 8 8 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 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 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 17 "Plotting Surfaces" }} {PARA 19 "" 0 "" {TEXT -1 16 "Warren Weckesser" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 50 "Plotting the graph \+ of a function of two variables." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 84 "Let's plot the graph of f(x,y) = x^2-y^2. To do this, we'll use the plot3d command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 199 "In its most basic form, the pl ot3d command takes three arguments. The first is the expression that \+ defines the function to be plotted, and the next two are the ranges of the independent variables. 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To chang e some of the plot options, right-click on the plot, and select an opt ion. For example, try using the mouse to add axes to the plot." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 164 "Just lik e the plot command, the plot3d command can be given many optional argu ments. Look for plot3d in the Maple Help, or enter the command ?plot3 d to learn more." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "Here is the same command as above, with some options adde d directly to the command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "plot3d(x^2-y^2,x=-1..1,y=-1..1,axes =boxed,grid=[64,64],style=patchcontour);" }}{PARA 13 "" 1 "" {GLPLOT3D 292 273 273 {PLOTDATA 3 "6&-%%GRIDG6%;$!\"\"\"\"!$\"\"\"F)F& X,%)anythingG6\"6\"[gl'!%\"!!#[[[l\"[o\"[o00000000000000003FAFFDEF9DF5 CF203FBF79D71B6996183FC7384EF2A605CC3FCE71A61651240C3FD2B4787C5B12E63F D60F17CCEA85843FD948B0FCD6E9E03FDC61440C203FFC3FDF58D0FAC687D63FE117AB E464E0B83FE2726C3B14F6643FE3BCA9817384EF3FE4F663B7808C5A3FE61F9ADD3C0C A43FE7384EF2A605CE3FE8407FF7BE77D73FE9382DEC8562C03FEA1F58D0FAC6883FEA F600A51EA32F3FEBBC2568F0F8B63FEC71C71C71C71C3FED16E5BFA10E623FEDAB8152 7ECE873FEE2F99D50B078C3FEEA32F4745B9703FEF0641A92EE4333FEF58D0FAC687D6 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For exam ple, here is a \"monkey saddle\": f(x,y) = x*(y-sqrt(3)*x)*(y+sqrt(3)* x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 18 " " 0 "" {TEXT -1 27 "Surfaces Defined Implicitly" }{TEXT 257 0 "" }} {PARA 19 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 233 "A surfa ce can be defined implicitly, rather than as the graph of a function o f two variables. That is, instead of defining the surface as z=f(x,y) , it may be defined as a level set g(x,y,z) = C. There is a command i n Maple, called " }{TEXT 258 15 "implicitplot3d " }{TEXT -1 103 "that \+ can be used to plot such surfaces. To use it, we must first load a li brary of functions with the " }{TEXT 259 13 "with(plots): " }{TEXT -1 85 "command. (Don't worry about the warning that appears after this c ommand is entered.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with (plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoord s has been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Let's f irst plot something simple: the sphere x^2+y^2+z^2=1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "implicitplot3d(x^2+y^2+z^2=1,x=-2. .2,y=-2..2,z=-2..2,grid=[20,20,20],style=patchcontour,scaling=constrai ned,axes=boxed);" }}{PARA 13 "" 1 "" {GLPLOT3D 326 237 237 {PLOTDATA 3 "6'-%+ISOSURFACEG6#X0%)anythingG6\"6\"[gl'!%\"!!%[[hr\"5\"5\"5\"%C00 0000000000000C000000000000000C0000000000000004026000000000000C00000000 0000000C000000000000000BFFCA1AF286BCA1B40246788DD408828C00000000000000 0C000000000000000BFF9435E50D794364022FC744C965684C000000000000000C0000 00000000000BFF5E50D79435E514021BEC24E016B15C000000000000000C0000000000 00000BFF286BCA1AF286C4020AE72E181C5DAC000000000000000C000000000000000B 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