{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "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 50 "grad:=proc(f);[diff( f,x),diff(f,y),diff(f,z)] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "div:=proc(g);diff(g[1],x)+diff(g[2],y)+diff(g[3],z) end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "curl:=proc(g);[diff(g[3],y)- diff(g[2],z),diff(g[1],z)-diff(g[3],x),diff(g[2],x)-diff(g[1],y)]end: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q);simplify (add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "cross:=proc(r,q);[r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]*q[3],r[1]*q [2]-r[2]*q[1]] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "mag: =proc(q);sqrt(add(q[i]^2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plugin:=proc(g,r);eval(g,\{x=r[1],y=r[2],z=r[3]\})end :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "r:=[sin(v)*cos(u),sin( v)*sin(u),cos(v)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG7%*&-%$sin G6#%\"vG\"\"\"-%$cosG6#%\"uGF+*&F'F+-F(F.F+-F-F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot3d(r,v=0..Pi,u=0..2*Pi,numpoints=1000);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "int(int(mag(cross(diff(r,u),diff(r,v))),u=0..2*Pi),v=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%\"\"\"%#PiGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "r:=[v*cos(u),v*sin(u),v];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG7%*&%\"vG\"\"\"-%$cosG6#%\"uGF(*&F'F(- %$sinGF+F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot3d(r,v= 0..3,u=0..2*Pi,numpoints=1000);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(int(mag(cross(diff(r,u), diff(r,v))),u=0..2*Pi),v=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* (\"\"*\"\"\"%#PiGF&\"\"##F&F(F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "r:=[cos(u),sin(u),v];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"r G7%-%$cosG6#%\"uG-%$sinGF(%\"vG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot3d(r,v=0..3,u=0..2*Pi,numpoints=1000);" }}{PARA 13 "" 1 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(int(m ag(cross(diff(r,u),diff(r,v))),u=0..2*Pi),v=0..3);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&\"\"'\"\"\"%#PiGF&F&" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "r:=[v*cos(u),v*sin(u),v^2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG7%*&%\"vG\"\"\"-%$cosG6#%\"uGF(*&F'F(-%$sinGF+F(* $)F'\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot3d(r,v=0 ..3,u=0..2*Pi,numpoints=1000);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(int(mag(cross(diff(r,u), diff(r,v))),u=0..2*Pi),v=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* (\"\")!\"\"%#PiG#\"\"\"\"\"#,&**\"$[\"F)\"\"$F&F'F(\"#PF(F&*(\"\"%F)F. 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