{VERSION 5 0 "IBM INTEL LINUX" "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 14 0 0 0 0 2 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R 3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 0 2 1 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "?cylinderplot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "cylinderplot([r,theta,r^4*sin(2*the ta)],theta=0..2*Pi,r=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "phi:=(r,theta)->(1-r^2)*sin(theta);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "psi:=(r,theta)->0; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "MAX:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "k:=array(0..MAX,1..MAX);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for n from 0 by 1 to MAX" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " k[n,1]:=fsolve(B esselJ(n,x),x=0.1..(5+n));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " \+ for m from 2 by 1 to MAX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 " \+ k[n,m]:=fsolve(BesselJ(n,x),x=k[n,m-1]..k[n,m-1]+4);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "unassign('n'):unassign('m');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(BesselJ(4,x),x=0..30);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 7 "k[4,4];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "normfac:=array(0..MAX,1..MAX);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "for m from 1 by 1 to MAX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " no rmfac[0,m]:=2*Pi*int(r*(BesselJ(0,k[0,m]*r))^2 ,r=0..1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('m');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for n from 1 by 1 to MAX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " for m from 1 by 1 to MAX" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 72 " normfac[n,m]:=Pi*int(r*(BesselJ(n,k [n,m]*r))^2 ,r=0..1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " \+ od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('n');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('m');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "b:=array(0..MAX,1..MAX); c:=array(0..MAX,1..MAX); B:=arra y(0..MAX,1..MAX); C:=array(0..MAX,1..MAX);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fo r m from 1 by 1 to MAX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 " b[0,m]:=evalf(int(r*int(Bes selJ(0,k[0,m]*r)*phi(r,theta) ,theta=0..2*Pi),r=0..1));" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 " od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('m');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for m from 1 by 1 to MAX" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 90 " B[0,m]:=evalf(int(r*int(BesselJ(0,k[0,m]*r)*p si(r,theta) ,theta=0..2*Pi),r=0..1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('m') ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for n from 1 by 1 to M AX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " for m from 1 by 1 to MAX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 114 " b[n,m]:=evalf(int(r*int(BesselJ(n,k[n,m]*r)*cos(n*th eta)*phi(r,theta) ,theta=0..2*Pi),r=0..1)); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 112 " c[n,m]:=evalf(int(r*int(BesselJ(n,k [n,m]*r)*sin(n*theta)*phi(r,theta) ,theta=0..2*Pi),r=0..1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "un assign('n');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('m ');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 24 "for n from 1 by 1 to MAX" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 5 " do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " f or m from 1 by 1 to MAX" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " \+ do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 114 " B[n,m]: =evalf(int(r*int(BesselJ(n,k[n,m]*r)*cos(n*theta)*psi(r,theta) ,theta= 0..2*Pi),r=0..1)); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 112 " \+ C[n,m]:=evalf(int(r*int(BesselJ(n,k[n,m]*r)*sin(n*theta)*psi(r, theta) ,theta=0..2*Pi),r=0..1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('n');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('m');" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 87 "u:=(t,r,theta)->sum((b[0,m]/normfac[0,m])*Be sselJ(0,k[0,m]*r)*cos(k[0,m]*t) ,m=1..MAX)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 110 " +sum((B[0,m]/(normfac[0, m]*k[0,m]))*BesselJ(0,k[0,m]*r)*sin(k[0,m]*t) ,m=1..MAX)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 110 " \+ +sum(sum((c[n,m]/normfac[n,m])*BesselJ(n,k[n,m]*r)*sin(n*theta )*cos(k[n,m]*t) ,m=1..MAX),n=1..MAX)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 120 " +sum(sum((C[n,m]/(normfac[n,m]*k[n,m]))*BesselJ(n,k[ n,m]*r)*sin(n*theta)*sin(k[n,m]*t) ,m=1..MAX),n=1..MAX)" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 110 " +sum(sum((b[n,m]/normfac[n,m])*B esselJ(n,k[n,m]*r)*cos(n*theta)*cos(k[n,m]*t) ,m=1..MAX),n=1..MAX)" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 121 " +sum(sum((B[n,m]/(norm fac[n,m]*k[n,m]))*BesselJ(n,k[n,m]*r)*cos(n*theta)*sin(k[n,m]*t) ,m= 1..MAX),n=1..MAX);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "cylin derplot([r,theta,u(0,r,theta)],theta=0..2*Pi,r=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "cylinderplot([r,theta,u(0.5,r,theta )],theta=0..2*Pi,r=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "cylinderplot([r,theta,u(1,r,theta)],theta=0..2*Pi,r=0..1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "cylinderplot([r,theta,u(1.5, r,theta)],theta=0..2*Pi,r=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "u(1,0.5,3);" }}}}{MARK "12 0 0" 24 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }