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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 67 "ENGI 3424 - Demonstration
 of Inverse Laplace Transforms using Maple" }}{PARA 0 "" 0 "" {TEXT 
-1 42 "using some examples from the lecture notes" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 15 "with(inttrans):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 35 "Example 3.05.1 [part:  inverse of  " }{TEXT 257 1 "Y" }
{TEXT -1 1 "(" }{TEXT 258 1 "s" }{TEXT -1 34 ")  to find the complete \+
solution  " }{TEXT 259 1 "y" }{TEXT -1 1 "(" }{TEXT 260 1 "t" }{TEXT 
-1 31 ")  of an initial value problem]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "F(s,w) := (s-5)/((s-2)*(s-3));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"FG6$%\"sG%\"wG*(,&F'\"\"\"\"\"&!\"\"F+,&F'F+\"\"#F
-F-,&F'F+\"\"$F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "invla
place(F(s,w), s, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"#\"\"
\"-%$expG6#,$*&\"\"$F&%\"tGF&F&F&!\"\"*&F,F&-F(6#,$*&F%F&F-F&F&F&F&" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Example 3.05.2 [part:  inverse o
f  " }{TEXT 261 1 "Y" }{TEXT -1 1 "(" }{TEXT 262 1 "s" }{TEXT -1 34 ")
  to find the complete solution  " }{TEXT 263 1 "y" }{TEXT -1 1 "(" }
{TEXT 264 1 "t" }{TEXT -1 31 ")  of an initial value problem]" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "F(s,w) := (5*s^2+11*s-10)/((
s+4)*(s^2+4*s+13));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"FG6$%\"sG%
\"wG*(,(*&\"\"&\"\"\")F'\"\"#F-F-*&\"#6F-F'F-F-\"#5!\"\"F-,&F'F-\"\"%F
-F3,(*$F.F-F-*&F5F-F'F-F-\"#8F-F3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "invlaplace(F(s,w), s, t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&,&*&\"\"$\"\"\"-%$cosG6#,$*&F'F(%\"tGF(F(F(F(*&\"\"
&F(-%$sinGF+F(!\"\"F(-%$expG6#,$*&\"\"#F(F.F(F3F(F(*&F9F(-F56#,$*&\"\"
%F(F.F(F3F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Example 3.06.1 -
 a standard inverse" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "F(s,
w) := 1/(s*(s^2 + w^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"FG6$%
\"sG%\"wG*&\"\"\"F**&F'F*,&*$)F'\"\"#F*F**$)F(F/F*F*F*!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "invlaplace(F(s,w), s, t);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&-%$cosG6#*&%\"wG\"\"\"%\"tGF*!\"
\"F*F*F*F)!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Example 3.06.2 \+
- a standard inverse" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "F(s
,w) := 1/(s^2*(s^2 + w^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"FG
6$%\"sG%\"wG*&\"\"\"F**&)F'\"\"#F*,&*$F,F*F**$)F(F-F*F*F*!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "invlaplace(F(s,w), s, t);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"wG!\"$-%$sinG6#*&F%\"\"\"%\"tG
F+F+!\"\"*&F%!\"#F,F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Exampl
e 3.07.2 - Laplace transform involving the Heaviside unit step functio
n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f(t) := Heaviside(t-4)
*(t-4)^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"fG6#%\"tG*&-%*Heavis
ideG6#,&F'\"\"\"\"\"%!\"\"F-)F,\"\"$F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "laplace(f(t), t, s);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,$*(\"\"'\"\"\"-%$expG6#,$*&\"\"%F&%\"sGF&!\"\"F&F-!\"%F&" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Example 3.07.3 - inverse Laplace t
ransform involving the Heaviside unit step function" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "F(s,w) := exp(-5*s)/(s^2 + 4);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"FG6$%\"sG%\"wG*&-%$expG6#,$*&\"\"&\"\"
\"F'F0!\"\"F0,&*$)F'\"\"#F0F0\"\"%F0F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "invlaplace(F(s,w), s, t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&*&-%*HeavisideG6#,&%\"tGF&\"\"&!\"\"F
&-%$sinG6#,&*&F'F&F-F&F&\"#5F/F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 85 "Example 3.07.5 - inverse Laplace transform involving the Heavis
ide unit step function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "F
(s,w) := exp(-3*s)*(3*s+1)/(s^2*(s^2 + 4));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"FG6$%\"sG%\"wG**-%$expG6#,$*&\"\"$\"\"\"F'F0!\"\"F
0,&*&F/F0F'F0F0F0F0F0F'!\"#,&*$)F'\"\"#F0F0\"\"%F0F1" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 25 "invlaplace(F(s,w), s, t);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\")F&*&-%*HeavisideG6#,&%\"tGF&\"\"$!
\"\"F&,**&\"#7F&)-%$sinGF+\"\"#F&F&*&F6F&F-F&F&\"\"'F/-F56#,&*&F6F&F-F
&F&F8F/F/F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "[which is equi
valent to (3/4 + (" }{TEXT 265 1 "t" }{TEXT 274 1 "-" }{TEXT -1 5 "3)/
4 " }{TEXT 273 1 "-" }{TEXT -1 10 " 3/4 cos2(" }{TEXT 266 1 "t" }
{TEXT 272 1 "-" }{TEXT -1 3 "3) " }{TEXT 275 1 "-" }{TEXT -1 10 " 1/8 \+
sin2(" }{TEXT 267 1 "t" }{TEXT 271 1 "-" }{TEXT -1 4 "3)) " }{TEXT 
269 1 "H" }{TEXT -1 1 "(" }{TEXT 268 1 "t" }{TEXT 270 1 "-" }{TEXT -1 
4 "3) ]" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Example 3.10.2 - a sta
ndard Laplace transform" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "
f(t,w) := t*sin(w*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"fG6$%\"t
G%\"wG*&F'\"\"\"-%$sinG6#*&F(F*F'F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "laplace(f(t,w), t, s);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,$**\"\"#\"\"\"%\"sGF&%\"wGF&,&*$)F'F%F&F&*$)F(F%F&F&!\"#F&" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Example 3.11.2 - a standard invers
e Laplace transform" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "F(s,
w) := 1/(s^2 + w^2)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"FG6$%\"
sG%\"wG*&\"\"\"F**$),&*$)F'\"\"#F*F**$)F(F0F*F*F0F*!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "invlaplace(F(s,w), s, t);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&*&%\"wG!\"$-%$sinG6#*&F)F&
%\"tGF&F&F&F&*&#F&F'F&*(F/F&F)!\"#-%$cosGF-F&F&!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 42 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }