{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 }{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 "Headi ng 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 24 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;\nwith(plots ):" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 38 "Horizontal and Vertical c ross-sections" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "About this work sheet" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 15 "Author and Date" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Matthias Kawski" }}{PARA 0 "" 0 " " {TEXT -1 14 "kawski@asu.edu" }}{PARA 0 "" 0 "" {TEXT -1 26 "http://m ath.asu.edu/~kawki" }}{PARA 0 "" 0 "" {TEXT -1 43 "Febuary 2003 (MAPLE 8)\nAll rights reserved." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "Content, Purpose and Use" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 332 "Sample commands to plot functions of 2 variables w/ focus on level-curves \nand vertical cross-sections parallel to coordinate axes, along any vertical half-\nplanes w/ z-ax cis as boundar, and along vertical cylinders centered along z-axis.\nI ncludes animations.\n\nAll is done twice -- once using pure functions, once using expressions." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 150 "Use as a template to COPY THE PRE FERRED CODE and then quickly \ngenerate lots of plots, and spend time \+ on prediction, discussion, and further trials. " }}{PARA 0 "" 0 "" {TEXT -1 276 "\nLittle intervention needed in general beyond enetring \+ a new formula, EXCEPT, \nsome ranges need to be readjusted.... HOWEVER , itis strongly preferred if user\ncopies (and adapts) suitabel code t o her/his own worksheet -- else there are too\nmany repitions inside t his worksheet." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 33 "Updates and log of modifications." }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Under construction.." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "Wo rking with \"pure functions\"" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 44 " Define a function of 2 variables and plot it" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 7 "example" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f:=(x,y)-> 12*x/(1+x^2+y^2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Define globa l plotranges" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "xrange:=-10..10;\ny range:=-5..5;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "A basic plot" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot3d(f,xrange,yrange);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Lots of plot-options" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "plot3d(f,xrange,yrange,\n style=patchnog rid,\n grid=[80,50],\n shading=ZHUE,\n axes=FRAME,\n t ickmarks=[3,3,3],\n labels=[`x`,`y`,`f(x,y)`],\n labelfont=[TI MES,BOLD,16],\n title=`This is my favorite function`,\n titlef ont=[TIMES,BOLD,24],\n scaling=unconstrained,\n orientation=[- 107,68]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 25 "Contours and level curves" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "plot3d(f,xrange,yrange,\n style =patchcontour);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 221 "plot3d( f,xrange,yrange,\n style=patchcontour,\n contours=[seq(-7+k/4, k=0..60)],\n grid=[80,50],\n shading=ZHUE,\n axes=FRAME,\n tickmarks=[3,3,3],\n scaling=unconstrained,\n orientation =[-107,68]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Rotate the above \+ into top-view, or plot again:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "p lot3d(f,xrange,yrange,\n style=patchcontour,\n contours=[seq(- 7+k/4,k=0..60)],\n grid=[80,50],\n shading=ZHUE,\n axes=FR AME,\n tickmarks=[3,3,3],\n scaling=unconstrained,\n orien tation=[-90,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "Cross-sections parallel to xz pla ne" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cross-sect ion" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(f(x,2),x=xrange);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sec tions - static" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "display([ \n seq(\n plot(f(x,y),\n x=xrange),\n y=yrange) \n ]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animat e a sequence of vertical cross-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "display([\n seq(\n plot(f(x,y),x=xrange),\n y=yra nge)],\n insequence=true, \n title=`Animation -- run me w/ contin uous looping`,\n titlefont=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Fancier -- finetuning the locatio n of the cross-section, and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 295 "display([\n seq(\n display([\n p lot(f(x,k/5),x=xrange),\n textplot([6,5,cat(`y=`,convert(evalf (k/5,2),string))],font=[TIMES,BOLD,16])\n ]),\n k=-25..25 )],\n insequence=true, \n title=`Animation -- run me w/ continuou s looping`,\n titlefont=[TIMES,BOLD,24]\n );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "Cro ss-sections parallel to yz plane" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cross-section" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(f(2,y),y=yrange);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Ove rlay several vertical cross-sections - static" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sections - static" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "display([\n seq(\n pl ot(f(x,y),\n y=yrange),\n x=xrange)\n ]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a sequence of vert ical cross-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "display([\n seq(\n plot(f(x,y),y=xrange),\n x=yrange)],\n insequenc e=true, \n title=`Animation -- run me w/ continuous looping`,\n t itlefont=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Fancier -- finetuning the location of the cross-sect ion, and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 295 "display([\n seq(\n display([\n plot(f(k/5,y),y=yra nge),\n textplot([6,5,cat(`x=`,convert(evalf(k/5,2),string))], font=[TIMES,BOLD,16])\n ]),\n k=-50..50)],\n insequence =true, \n title=`Animation -- run me w/ continuous looping`,\n ti tlefont=[TIMES,BOLD,24]\n );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 21 "Radial cross-section s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "rrange:=0..5;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cross-section" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(f(r*cos(Pi/6),r*sin(Pi/6)),r= rrange);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several verti cal cross-sections - static" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Ov erlay several vertical cross-sections - static" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "N:=12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "display([\n seq(\n plot(f(r*cos(k*Pi/N),r*sin(k*Pi/N)),r= rrange),\n k=0..2*N-1)\n ]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a sequence of vertical cross-sections" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 201 "display([\n seq(\n plot(f(r *cos(k*Pi/N),r*sin(k*Pi/N)),r=rrange),\n k=0..2*N-1)],\n insequ ence=true, \n title=`Animation -- run me w/ continuous looping`,\n \+ titlefont=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 85 "Fancier -- finetuning the location of the cross-se ction, and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 325 "display([\n seq(\n display([\n plot(f(r*cos(k*Pi/N ),r*sin(k*Pi/N)),r=rrange),\n textplot([4,5,cat(`theta=`,conve rt(evalf(Pi/N*k,4),string))],font=[TIMES,BOLD,16])\n ]),\n \+ k=0..2*N-1)],\n insequence=true, \n title=`Animation -- run me \+ w/ continuous looping`,\n titlefont=[TIMES,BOLD,24]\n );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 " " {TEXT -1 23 "Circular cross-sections" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cross-section" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "plot(f(2*cos(theta),2*sin(theta)),theta=0..2*Pi);" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-se ctions - static" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay severa l vertical cross-sections - static" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "display([\n seq(\n plot(f(r*cos(theta),r*sin(t heta)),theta=0..2*Pi),\n r=1..10)\n ]);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a sequence of vertical cro ss-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 201 "display([\n seq( \n plot(f(r*cos(theta),r*sin(theta)),theta=0..2*Pi),\n r=1.. 10)],\n insequence=true, \n title=`Animation -- run me w/ continu ous looping`,\n titlefont=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Fancier -- finetuning the location of the cross-section, and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 331 "display([\n seq(\n display([\n plo t(f((k/10)*cos(theta),(k/10)*sin(theta)),theta=0..2*Pi),\n tex tplot([4,5,cat(`r = `,convert(evalf(k/10,2),string))],font=[TIMES,BOLD ,16])\n ]),\n k=1..50)],\n insequence=true, \n title =`Animation -- run me w/ continuous looping`,\n titlefont=[TIMES,BOL D,24]\n );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 26 "Working with \"expressions\"" }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 56 "Define a expression depending on \+ 2 variables and plot it" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "r estart;\nwith(plots);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "example" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "z:=12*x/(1+x^2+y^2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Define global plotranges" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "xrange:=-10..10;\nyrange:=-5..5;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "A basic plot" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot3d(z,x=xrange,y=yrange);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Lots of plot-options" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 326 "plot3d(z,x=xrange,y=yrange,\n style=patchnogrid,\n grid =[80,50],\n shading=ZHUE,\n axes=FRAME,\n tickmarks=[3,3,3 ],\n labels=[`x`,`y`,`f(x,y)`],\n labelfont=[TIMES,BOLD,16],\n title=`This is my favorite function`,\n titlefont=[TIMES,BOLD ,24],\n scaling=unconstrained,\n orientation=[-107,68]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 25 "Contours and level curves" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot3d(z,x=xrange,y=yrange,\n style=patchcontour) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 225 "plot3d(z,x=xrange,y=y range,\n style=patchcontour,\n contours=[seq(-7+k/4,k=0..60)], \n grid=[80,50],\n shading=ZHUE,\n axes=FRAME,\n tickm arks=[3,3,3],\n scaling=unconstrained,\n orientation=[-107,68] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Rotate the above into top-v iew, or plot again:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "plot3d(z,x= xrange,y=yrange,\n style=patchcontour,\n contours=[seq(-7+k/4, k=0..60)],\n grid=[80,50],\n shading=ZHUE,\n axes=FRAME,\n tickmarks=[3,3,3],\n scaling=unconstrained,\n orientation =[-90,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "Cross-sections parallel to xz plane" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cross-section" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(subs(y=2,z),x=xrange);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sec tions - static" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "display([ \n seq(\n plot(z,\n x=xrange),\n y=yrange)\n ] );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a se quence of vertical cross-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "display([\n seq(\n plot(z,x=xrange),\n y=yrange)],\n \+ insequence=true, \n title=`Animation -- run me w/ continuous loop ing`,\n titlefont=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Fancier -- finetuning the location of the cross-section, and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 300 "display([\n seq(\n display([\n plot(s ubs(y=k/5,z),x=xrange),\n textplot([6,5,cat(`y=`,convert(evalf (k/5,2),string))],font=[TIMES,BOLD,16])\n ]),\n k=-25..25 )],\n insequence=true, \n title=`Animation -- run me w/ continuou s looping`,\n titlefont=[TIMES,BOLD,24]\n );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "Cro ss-sections parallel to yz plane" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cross-section" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(subs(x=2,z),y=yrange);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sections - static" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sections - stati c" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "display([\n seq(\n \+ plot(z,\n y=yrange),\n x=xrange)\n ]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a sequence of v ertical cross-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "display( [\n seq(\n plot(z,y=xrange),\n x=yrange)],\n insequence= true, \n title=`Animation -- run me w/ continuous looping`,\n tit lefont=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 85 "Fancier -- finetuning the location of the cross-section , and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 300 " display([\n seq(\n display([\n plot(subs(x=k/5,z),y=yra nge),\n textplot([6,5,cat(`x=`,convert(evalf(k/5,2),string))], font=[TIMES,BOLD,16])\n ]),\n k=-50..50)],\n insequence =true, \n title=`Animation -- run me w/ continuous looping`,\n ti tlefont=[TIMES,BOLD,24]\n );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 21 "Radial cross-section s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "zz:=subs(x=r*cos(theta) ,y=r*sin(theta),z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "rran ge:=0..5;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vertical cr oss-section" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot(subs(theta=(Pi/ 6),zz),r=rrange);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay seve ral vertical cross-sections - static" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sections - static" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "N:=12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "display([\n seq(\n plot(subs(theta=k*Pi/N,zz), r=rrange),\n k=0..2*N-1)\n ]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a sequence of vertical cross-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 192 "display([\n seq(\n plot(s ubs(theta=k*Pi/N,zz),r=rrange),\n k=0..2*N-1)],\n insequence=tr ue, \n title=`Animation -- run me w/ continuous looping`,\n title font=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Fancier -- finetuning the location of the cross-section, \+ and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 316 "di splay([\n seq(\n display([\n plot(subs(theta=k*Pi/N,zz) ,r=rrange),\n textplot([4,5,cat(`theta=`,convert(evalf(Pi/N*k, 4),string))],font=[TIMES,BOLD,16])\n ]),\n k=0..2*N-1)], \n insequence=true, \n title=`Animation -- run me w/ continuous l ooping`,\n titlefont=[TIMES,BOLD,24]\n );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 23 "Circul ar cross-sections" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Plot one vert ical cross-section" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(subs(r=1 ,zz),theta=0..2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay s everal vertical cross-sections - static" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Overlay several vertical cross-sections - static" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "display([\n seq(\n pl ot(zz,theta=0..2*Pi),\n r=1..10)\n ]);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Animate a sequence of vertical cro ss-sections" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "display([\n seq( \n plot(zz,theta=0..2*Pi),\n r=1..10)],\n insequence=true, \n title=`Animation -- run me w/ continuous looping`,\n titlefon t=[TIMES,BOLD,24]\n );" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Fancier -- finetuning the location of the cross-section, \+ and displaying this location" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 308 "di splay([\n seq(\n display([\n plot(subs(r=k/10,zz),theta =0..2*Pi),\n textplot([4,5,cat(`r = `,convert(evalf(k/10,2),st ring))],font=[TIMES,BOLD,16])\n ]),\n k=1..50)],\n inse quence=true, \n title=`Animation -- run me w/ continuous looping`, \n titlefont=[TIMES,BOLD,24]\n );" }}}{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 "" }}}}{MARK "8" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }