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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "An example: a low-pass fil
ter [on the whiteboard].  Now find the impluse response." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "sys:=i1(t)=i2(t)+i3(t), diff(v2(t)
,t)=i2(t)/C2, v1(t)=R*i1(t)+L*diff(i2(t),t)+v2(t), diff(v1(t),t)=R*dif
f(i1(t),t)+i3(t)/C2; init:=i1(0)=0, i2(0)=0, i3(0)=0, v2(0)=0;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "C1:=1/1000; C2:=C1; R:=1; L:
=1; v1:=t->Dirac(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "wit
h(inttrans):dsolve(\{sys,init\}, \{i1(t),i2(t),i3(t),v2(t)\},laplace);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(I=0,\");" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 132 "plot(-1.002000992*exp(-.4999994990*t)*cos(31
.63464873*t)+31.62665090*exp(-.4999994990*t)*sin(31.63464873*t), t=0..
5, numpoints=100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lapla
ce(v1(t),t,s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "laplace(
-1.002000992*exp(-.4999994990*t)*cos(31.63464873*t)+31.62665090*exp(-.
4999994990*t)*sin(31.63464873*t),t,s);" }}}}{MARK "0 0 0" 82 }
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