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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 20 "Flow past a cylinder" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(plots):with(plottools):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Potential for uniform flow wi
th velocity (1,0)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "uf:=z->
z;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Zhukovsky map and its compo
sitional inverse" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "g:=z->z
+1/z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(w=g(z),z);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "gi:=w->(w+sqrt(w-2)*sqrt(
w+2))/2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "The unit circle and i
ts image under g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "circ:=e
xp(I*theta);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "cc:=z->(Re(
z),Im(z));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "pc:=plot([cc(
circ),theta=-Pi..Pi],color=blue,axes=none):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 59 "pim:=plot([cc(g(circ)),theta=-Pi..Pi],color=red,ax
es=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "display(pc,pim
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "The new potential and the f
low lines" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fcyl:=z->uf(g(
z));f(z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "a:=2: win:=-a.
.a: opts:=x=win,y=win,contours=40:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "equi:=contourplot(Re(fcyl(x+I*y)),opts):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "flow:=contourplot(Im(fcyl(x+I*y)),o
pts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "display(pc,equi,fl
ow);" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 41 "Flow past a plate with \+
an angle of attack" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "aa:=Pi
/6;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Rotation and its inverse" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rot:=z->exp(I*aa)*z;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "roti:=z->exp(-I*aa)*z;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ap:=t*exp(I*aa);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "app:=plot([cc(ap),t=-2..2],color=bl
ue,axes=none):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "The new potenti
al" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "faa:=z->uf(g(rot(gi(r
oti(z)))));faa(z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "a:=3:
 win:=-a..a: opts:=x=win,y=win,contours=40:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 40 "equia:=contourplot(Re(faa(x+I*y)),opts):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "flowa:=contourplot(Im(faa(x+
I*y)),opts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "ap:=t*exp(I
*aa): app:=plot([cc(ap),t=-2..2],color=blue,axes=none):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "display(app,equia,flowa);" }}}
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