{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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 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 1 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 "" -1 301 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 302 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 303 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 304 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 305 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 306 "Couri er" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 307 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 308 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 309 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 310 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 311 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 312 "" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 313 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 314 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 326 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 327 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 371 "Courier " 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 372 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 373 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 374 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 375 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 376 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 377 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 378 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 379 "Courier" 0 1 255 0 0 1 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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 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 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 "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -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" -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 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 30 "Plotting Parametric Surf aces " }}{PARA 19 "" 0 "" {TEXT -1 14 "Brian E. Blank" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 " Load (Open first) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "with(plots); # The set of commands in the plots \+ package is displayed\n # If a warning is issued then just ignore it!" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changeco ords has been redefined\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7Z%(anima teG%*animate3dG%-animatecurveG%&arrowG%-changecoordsG%,complexplotG%.c omplexplot3dG%*conformalG%,conformal3dG%,contourplotG%.contourplot3dG% *coordplotG%,coordplot3dG%-cylinderplotG%,densityplotG%(displayG%*disp lay3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradplot3dG%,graphplot3dG %-implicitplotG%/implicitplot3dG%(inequalG%,interactiveG%-listcontplot G%/listcontplot3dG%0listdensityplotG%)listplotG%+listplot3dG%+loglogpl otG%(logplotG%+matrixplotG%(odeplotG%'paretoG%,plotcompareG%*pointplot G%,pointplot3dG%*polarplotG%,polygonplotG%.polygonplot3dG%4polyhedra_s upportedG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+setoptio nsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)surfd ataG%)textplotG%+textplot3dG%)tubeplotG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 30 " Plotting A Parametric Surface " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 92 "Plott ing a parametric surface is like plotting a space curve. However, we u se the function " }{HYPERLNK 17 "plot3d" 2 "plot3d" "" }{TEXT -1 15 " instead of " }{HYPERLNK 17 "spacecurve" 2 "spacecurve" "" }{TEXT -1 107 ". Also, the argument list includes two parameter ranges rather than one. Thus the typical call has the form" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 371 2 "[>" }{TEXT 372 2 " " } {TEXT 373 56 "plot3d([x(u,v), y(u,v), z(u,v)], u = a ..b, v = c .. d); " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 374 7 "Example" }{TEXT 377 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 53 "Plot the cone whose parametric equations are given by" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 376 101 " \+ x = v*cos(u)\n y = v*sin(u)\n z = \+ v, u = 0 .. 2*Pi, v = 0.. " }{TEXT -1 2 "1\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 375 8 "Solution" }{TEXT 378 1 ":" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "plot3d([v*cos(u),v*sin(u),v], u = 0 .. 2*Pi, v = 0 .. 1, orientati on=[45,75]);" }}{PARA 13 "" 1 "" {GLPLOT3D 374 374 374 {PLOTDATA 3 "6$ -%%MESHG6#X.%)anythingG6\"6\"[gl'!%\"!!$^`r\":\":\"$000000000000000000 0000000000000000000000000000003FA555555555555500000000000000003FA55555 555555553FB555555555555500000000000000003FB55555555555553FC00000000000 0000000000000000003FC00000000000003FC555555555555500000000000000003FC5 5555555555553FCAAAAAAAAAAAAA00000000000000003FCAAAAAAAAAAAAA3FCFFFFFFF FFFFFF00000000000000003FCFFFFFFFFFFFFF3FD2AAAAAAAAAAAA0000000000000000 3FD2AAAAAAAAAAAA3FD555555555555500000000000000003FD55555555555553FD800 000000000000000000000000003FD80000000000003FDAAAAAAAAAAAAB000000000000 00003FDAAAAAAAAAAAAB3FDD55555555555600000000000000003FDD5555555555563F 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3145BC3FEFFFFFFFFFFFFC-%+PROJECTIONG6%$\"#X\"\"!$\"#vF/\"\"\"" 1 2 0 1 10 0 2 1 1 1 2 1.000000 75.000000 45.000000 1 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 301 7 "Example" }{TEXT 304 1 ":" }} {PARA 0 "" 0 "" {TEXT -1 54 "Plot the torus whose parametric equations are given by" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 303 134 " x = (3+2*sin(v))*cos(u)\n \+ y = (3+2*sin(v))*sin(u)\n z = 2*cos(v), u = 0 .. 2*Pi, v = 0.. 2*Pi" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 302 8 "Solution" }{TEXT 305 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "b := 3: a : = 2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "r := (u,v) -> [(b+a *sin(v))*cos(u),(b+a*sin(v))*sin(u),a*cos(v)];" }}{PARA 11 "" 1 "" 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}}{PARA 0 "" 0 "" {TEXT -1 138 "If the ranges of the parameters are \+ the same for each surface, then we simply specify