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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 22 "Section 10.7 Problem 4" }}
{PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 144 "Solvin
g the wave equation with initial value f(x), initial velocity 0, where
 f(x)=1 if L/2-1<x<L/2+1 and 0\notherwise.  Here, we take L=10, a=1.\n
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "assume(m,integer);" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "b := proc(m)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "  int(sin(m*x*P
i/10),x=4..6)/5;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}}{PARA 
0 "" 0 "" {TEXT -1 26 "Let's check that it works." }{TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "b(m);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "u := proc(n,x,t)" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "  sum(b(m)*sin(m*Pi*x/10)*cos(m*Pi*t/10),m=1..n);    \+
      " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}}{PARA 0 "" 0 "" 
{TEXT -1 26 "Let's check that it works." }{TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "u(5,x,t);" }}}{PARA 0 "" 0 "" {TEXT 
-1 106 "Here are some plots of u(x,t) versus x for some fixed values o
f t (taking 100 terms in the series for u).\n" }{TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(u(100,x,0),x=0..10,nump
oints=500);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(u(100
,x,5),x=0..10,numpoints=500);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 41 "plot(u(100,x,10),x=0..10,numpoints=500);\n" }}}{PARA 0 "" 0 "
" {TEXT -1 66 "Here are some plots of u(x,t) versus t for some fixed v
alues of x." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 40 "plot(u(100,5,t),t=0..20,numpoints=500);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(u(100,10,t),t=0..20,num
points=500);" }}}{PARA 0 "" 0 "" {TEXT -1 44 "Here is a movie of the m
otion of the string." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 60 "animate(u(100,x,t),x=0..10,t=0..20,numpoints=500,fr
ames=20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "24
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