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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 46 "Plane Curves, with prescribed p
lanar curvature" }}{PARA 257 "" 0 "" {TEXT -1 12 "Math 4530-1 " }}
{PARA 258 "" 0 "" {TEXT -1 17 "Friday January 18" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 361 "In your homework you sho
w how to reconstruct at plane curve from its planar curvature.  We wil
l use the procedure from page 48 of the text to illustrate this constr
uction.  This procedure didn't work until Gary pointed out an inapprop
riate \"local\" definition - I had defined b1 and b2 to be local, but \+
this apparently is not consistent with the way I used them." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 26 "with(plots):with(DEtools):" }}{PARA 7 "" 1 "" 
{TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 622 "recreate:=proc(kap,a,b,c,d,
f,g)\n   #kap is curvature, \n   #in plot, s ranges from a to b\n   #i
n plot, c<=x<=d,f<=y<=g\nlocal\n   sys,   #the DE system\n   ics,   #i
nitial conditions\n   p,     #dummy for solution to dsolve\n   p1,    \+
#dummy for plot of p\n   theta;\nsys:=\n   diff(theta(s),s)=kap(s),\n \+
  diff(b1(s),s)=cos(theta(s)),\n   diff(b2(s),s)=sin(theta(s));\nics:=
\n   theta(0)=0,  #start flat\n   b1(0)=0,     #start at origin\n   b2
(0)=0;\np:=dsolve(\{sys,ics\},\{theta(s),b1(s),b2(s)\},\n   type=numer
ic):\np1:=odeplot(p,[b1(s),b2(s)],a..b,numpoints=50,\n   thickness=1,a
xes=framed,color=black):\ndisplay(p1,view=[c..d,f..g]);\nend:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "kap1:=t->t;" }}{PARA 11 "" 
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