{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 "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 1 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 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "with(plottools):with (plots):with(linalg):with(process):" }}{PARA 7 "" 1 "" {TEXT -1 62 "Wa rning, the names arrow and changecoords have been redefined\n" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "#plotsetup(tek, kermit);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 58 "#plotsetup(gif,plotoutput=`obr1.gif`,plotoptions=`c olor`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "az:=61;el:=79;r:=4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#azG\"#h" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e lG\"#z" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "az:=63:el:=53:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "xgu:=4*cos(u)*cos(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xguG,$*&-%$cosG6#%\"uG\"\"\"-F(6#%\"vGF+\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ygu:=4*cos(u)*sin(v);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yguG,$*&-%$cosG6#%\"uG\"\"\"-%$sinG 6#%\"vGF+\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "zgu:=4*si n(u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$zguG,$-%$sinG6#%\"uG\"\"% " }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "s1:=0;s 2:=Pi*r*sqrt(2);t1:=0;t2:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s2G,$*&%#PiG\"\"\"-%%sqrtG 6#\"\"#F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t1G\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t2G\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "r1:=r/sqrt(2);pars:=s*sqrt(2)/r;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r1G,$*$-%%sqrtG6#\"\"#\"\"\"F*" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%parsG,$*&%\"sG\"\"\"-%%sqrtG6#\"\"#F(#F(\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "omega:=2*s/(r*sqrt(2));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&omegaG,$*&%\"sG\"\"\"-%%sqrtG6#\"\" #F(#F(\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "epsilon:=1; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(epsilonG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sigma:=1/4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "xu:=r1*cos(pars);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#xuG,$*&-%%sqrtG6#\"\"#\"\"\"-%$cosG6#,$*&%\"sGF+F'F+#F+\"\"%F+F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "yu:=r1*sin(pars);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yuG,$*&-%%sqrtG6#\"\"#\"\"\"-%$sinG 6#,$*&%\"sGF+F'F+#F+\"\"%F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "zu:=r1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zuG,$*$-%%sqrtG6#\" \"#\"\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "t3:=vector(3,[diff(xu,s),diff(yu,s) ,diff(zu,s)]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "nort:=sim plify(1/sqrt(t3[1]^2+t3[2]^2+t3[3]^2)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "tj:=evalm(nort*t3);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#tjG-%'vectorG6#7%,$-%$sinG6#,$*&%\"sG\"\"\"-%%sqrtG6#\"\"#F0#F0\" \"%!\"\"-%$cosGF,\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "# n2:=vector(3,[diff(xu,s,s),diff(yu,s,s),diff(zu,s,s)]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "#ro:=1/norm(n2,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "#nj:=evalm(ro*n2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "nj:=vector(3,[cos(pars)/sqrt(2),sin (pars)/sqrt(2),1/sqrt(2)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#njG- %'vectorG6#7%,$*&-%%sqrtG6#\"\"#\"\"\"-%$cosG6#,$*&%\"sGF/F+F/#F/\"\"% F/#F/F.,$*&F+F/-%$sinGF2F/F8,$*$F+F/F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ej:=crossprod(nj,tj);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ejG-%'vectorG6#7%,$*&-%%sqrtG6#\"\"#\"\"\"-%$cosG6#,$*&%\"sGF /F+F/#F/\"\"%F/#!\"\"F.,$*&F+F/-%$sinGF2F/F8,&*&F+F/)F0F.F/#F/F.*(FAF/ F+F/)F " 0 "" {MPLTEXT 1 0 21 "ej:=map(si mplify,ej);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ejG-%'vectorG6#7%,$* &-%%sqrtG6#\"\"#\"\"\"-%$cosG6#,$*&%\"sGF/F+F/#F/\"\"%F/#!\"\"F.,$*&F+ F/-%$sinGF2F/F8,$*$F+F/#F/F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "ux:=sin(omega)*tj[1]+cos(omega)*ej[1]+epsilon*sigma*nj[1];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#uxG,(*$)-%$sinG6#,$*&%\"sG\"\"\"-%% sqrtG6#\"\"#F.#F.\"\"%F2F.!\"\"*&#F.F2F.*&F/F.)-%$cosGF*F2F.F.F5*(#F. \"\")F.F/F.F:F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "uy:=si n(omega)*tj[2]+cos(omega)*ej[2]+epsilon*sigma*nj[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#uyG,(*&-%$sinG6#,$*&%\"sG\"\"\"-%%sqrtG6#\"\"#F-# F-\"\"%F--%$cosGF)F-F-*&#F-F1F-*(F4F-F.F-F'F-F-!\"\"*(#F-\"\")F-F.F-F' F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "uz:=sin(omega)*tj[3 ]+cos(omega)*ej[3]+epsilon*sigma*nj[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#uzG,&*&-%%sqrtG6#\"\"#\"\"\"-%$cosG6#,$*&%\"sGF+F'F+#F+\"\"%F +#F+F**&#F+\"\")F+F'F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x:=xu+t*ux;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG,&*&-%%sqrtG6#\" \"#\"\"\"-%$cosG6#,$*&%\"sGF+F'F+#F+\"\"%F+F**&%\"tGF+,(*$)-%$sinGF.F* F+!\"\"*&#F+F*F+*&F'F+)F,F*F+F+F;*(#F+\"\")F+F'F+F,F+F+F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "y:=yu+t*uy;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&*&-%%sqrtG6#\"\"#\"\"\"-%$sinG6#,$*&%\"sGF +F'F+#F+\"\"%F+F**&%\"tGF+,(*&F,F+-%$cosGF.F+F+*&#F+F*F+*(F8F+F'F+F,F+ F+!\"\"*(#F+\"\")F+F'F+F,F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "z:=zu+t*uz;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG ,&*$-%%sqrtG6#\"\"#\"\"\"F**&%\"tGF+,&*&F'F+-%$cosG6#,$*&%\"sGF+F'F+#F +\"\"%F+#F+F**&#F+\"\")F+F'F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "xk:=4*cos(Pi/4)*cos(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xkG,$*&-%%sqrtG6#\"\"#\"\"\"-%$cosG6#%\"vGF+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "yk:=4*cos(Pi/4)*sin(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ykG,$*&-%%sqrtG6#\"\"#\"\"\"-%$sinG6#%\"v GF+F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "zk:=4*sin(Pi/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#zkG,$*$-%%sqrtG6#\"\"#\"\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "surf1: =plot3d([x,y,z],s=s1..s2,t=t1..t2,axes=none,color=yellow, orientation= [az,el], grid=[50,10],style=HIDDEN):" 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