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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "MAPLE Worksheet:  " }
{TEXT 256 12 "PDE_Lab1.mws" }}{PARA 18 "" 0 "" {TEXT -1 8 "PCMI-UFP" }
}{PARA 18 "" 0 "" {TEXT -1 52 "LAB 1:  Verifying and Visualizing Solut
ions to PDE's" }}{PARA 19 "" 0 "" {TEXT -1 33 "Andrew J. Bernoff & Jon
 Jacobsen " }}{PARA 19 "" 0 "" {TEXT -1 19 "Harvey Mudd College" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 37 "
A Solution to the Convection Equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "F:=x->exp(-x^2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "plot(F(x),x=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "u:=F(x-c*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "ut:=diff(u,t);ux:=diff(u,x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "PDE:=ut+c*ux;simplify(PDE);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "c:=1;u;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 48 "u1:=subs(t=0,u);u2:=subs(t=1,u);u3:=subs(t=2,u);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot(\{u1,u2,u3\},x=-5..5,color=[re
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,x=-6..6,t=0..2,axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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-1 32 "A Solution to Laplace's Equation" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "F:=exp(-x)*cos(y);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 34 "Fxx:=diff(F,x$2);Fyy:=diff(F,y$2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "PDE:=Fxx+Fyy;" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 38 "plot3d(F,x=0..1,y=0..2*Pi,axes=frame);" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "A Fourier Series" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "F:=N->2*sum((-1)^(m+1)*sin(m*x)/m,m
=1..N);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "F2:=F(2);F4:=F(4
);F8:=F(8);F16:=F(16);F32:=F(32);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "plot(\{x,F2,F4,F8,F16,F32\},x=0..Pi);" }}}{EXCHG 
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