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{SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 52 "Construction of Flowlines \+
around a Circular Obstacle" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 59 "This routine plots the flowlines of fluid flowing
 around a " }}{PARA 0 "" 0 "" {TEXT -1 42 "circular object (like a log
 in the water)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 67 "f:=z->z+1/z;  # map that takes the outside of \+
the log to the plane." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"z
G6\"6$%)operatorG%&arrowGF(,&9$\"\"\"*&\"\"\"F0F-!\"\"F.F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 74 "logg:=plot([cos(t), sin(t),t=0..2*Pi]): #plot of th
e log (circular object)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "# Do loop for some flowlines
 in the upper half plane" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 
"for j from 1 to 5 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a:=j*.1:" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "w:=t+I*a:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "s:=w->(w+sqrt(w-2)*sqrt(w+2))/2: # the inverse of f" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "p[j]:=plot([Re(s(w)),Im(s(w)),t=-
3..3]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 51 "# Do loop for the flowlines in the lower half
 plane" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for j from 1 to 5
 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:=-j*.1:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "w:=t+I*a:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "s:=w
->(w+sqrt(w-2)*sqrt(w+2))/2:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "q[j
]:=plot([Re(s(w)),Im(s(w)),t=-3..3]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "display([logg,p[1],p[2],p[
3],p[4],p[5],q[1],q[2],q[3],q[4],q[5]],scaling=constrained);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "plotsetup(x11);" }}}{EXCHG 
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1 0 1 1 1803 }