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200 9 "Maple Lab" }}{PARA 209 "" 0 "" {TEXT 200 7 "Week 13" }}{PARA 210 "" 0 "" {TEXT 200 19 "Parametric surfaces" }}{PARA 211 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 217 11 "We'll need:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with (plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 218 19 "Parametric surfaces" }}{EXCHG {PARA 0 "" 0 "" {TEXT 200 92 "Produce the 3D graphs of parametric surfaces is quite ea sy in Maple. You need to specify the" }}{PARA 0 "" 0 "" {TEXT 200 77 " functions x(u,v), y(u,v), z(u,v) and a range for the variables. For ex ample: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot3d([sin(u),cos(u),v],v=0..1,u=0 ..2*Pi,labels=[x,y,z],\n" }{MPLTEXT 1 0 50 " axes=boxed,view=[-1.5..1 .5,-1.5..1.5,-.1..1.5]);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 39 "Let us try a more interesting function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "plot3d([(1-abs(u))*sin(v),(1-abs(u) )*cos(v),u],u=-3..3,v=0..2*Pi,labels=[x,y,z],\n" }{MPLTEXT 1 0 14 " a xes=boxed);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 96 "An animated plot can be used to show the role of the variables in \+ a parametric surface. Compare:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "animate(plot3d, [" }{MPLTEXT 1 0 61 "[u*cos(v),u*sin(v),v],v=0 ..4*Pi*t,u=0..2],t=0..1,axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "animate(plot3d, [[u*cos(v),u*sin(v),v],v=0..4*Pi,u=0. .2*t],t=0..1,axes=boxed);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }