<html><head><title></title><style type="text/css"> p { margin: 0 0 0 0; font-family: Arial, sans-serif; font-size:10pt; font-weight: normal; font-style: normal; vertical-align: baseline; color: black; text-decoration: none; } div { border-width:0px; border-style: solid; border-color: red; } body { background-color: #fff; } p img { vertical-align: middle; } p b, li b { font-weight : bold; } p i, li i { font-style : italic; } p u, li u { text-decoration : underline; } p so, li so { text-decoration : line-through; } p sub, p sub { font-size : 70%; vertical-align: sub; } p sup, p sup { font-size : 70%; vertical-align: super; } ul { padding-left : 2em; /* for mozilla list marker box */ margin-left : 0; /* for IE list marker box */ } ol { padding-left : 2em; /* for mozilla list marker box */ margin-right : -0.5em; margin-left : 0; /* for IE list marker box */ } p.Style1, li.Style1 /*Normal*/ { margin-left: 0pt; margin-right: 0pt; text-indent: 0pt; text-align: left; list-style-type: none; font-family: 'Arial', sans-serif;; font-size: 10pt;font-weight: bold; font-style: normal; vertical-align: baseline; color: #00f; } </style></head><body><div id="mc-region-333" style="position: absolute; top: 14.25pt; left: 48pt; width: 351.5pt; "><a name="" /><p class="Style1">Here's an old problem from my notes from years ago. I'm embarrassed to</p><p class="Style1">say I cannot see how I got equation (2) from equation (1) below. Why</p><p class="Style1">did I think I needed to do that extra step?</p></div><div id="mc-region-301" style="position: absolute; top: 68.25pt; left: 48pt; width: 192pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0002_7553593.PNG" id="generatedImage301" path=".\HMWK1_images/IMG0002_7553593.PNG" style="width: 192pt;height: 33.75pt;"></img></div><div id="mc-region-302" style="position: absolute; top: 117pt; left: 48pt; width: 151.5pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0003_7553609.PNG" id="generatedImage302" path=".\HMWK1_images/IMG0003_7553609.PNG" style="width: 151.5pt;height: 18.75pt;"></img></div><div id="mc-region-303" style="position: absolute; top: 141pt; left: 48pt; width: 162pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0004_7553625.PNG" id="generatedImage303" path=".\HMWK1_images/IMG0004_7553625.PNG" style="width: 162pt;height: 18.75pt;"></img></div><div id="mc-region-304" style="position: absolute; top: 170.25pt; left: 48pt; width: 104pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">Equating coefficients</span></b></p></div><div id="mc-region-305" style="position: absolute; top: 200.25pt; left: 48pt; width: 20.75pt; "><a name="" /><p class="Style1">s^0</p></div><div id="mc-region-306" style="position: absolute; top: 201pt; left: 90pt; width: 40.5pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0005_7553640.PNG" id="generatedImage306" path=".\HMWK1_images/IMG0005_7553640.PNG" style="width: 40.5pt;height: 12.75pt;"></img></div><div id="mc-region-307" style="position: absolute; top: 201pt; left: 156pt; width: 24pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0006_7553640.PNG" id="generatedImage307" path=".\HMWK1_images/IMG0006_7553640.PNG" style="width: 24pt;height: 12.75pt;"></img></div><div id="mc-region-308" style="position: absolute; top: 219pt; left: 90pt; width: 49.5pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0007_7553640.PNG" id="generatedImage308" path=".\HMWK1_images/IMG0007_7553640.PNG" style="width: 49.5pt;height: 12.75pt;"></img></div><div id="mc-region-309" style="position: absolute; top: 219pt; left: 156pt; width: 27.75pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0008_7553640.PNG" id="generatedImage309" path=".\HMWK1_images/IMG0008_7553640.PNG" style="width: 27.75pt;height: 12.75pt;"></img></div><div id="mc-region-310" style="position: absolute; top: 224.25pt; left: 48pt; width: 20.75pt; "><a name="" /><p class="Style1">s^1</p></div><div id="mc-region-311" style="position: absolute; top: 242.25pt; left: 48pt; width: 20.75pt; "><a name="" /><p class="Style1">s^2</p></div><div id="mc-region-312" style="position: absolute; top: 243pt; left: 90pt; width: 42pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0009_7553656.PNG" id="generatedImage312" path=".\HMWK1_images/IMG0009_7553656.PNG" style="width: 42pt;height: 12.75pt;"></img></div><div id="mc-region-313" style="position: absolute; top: 243pt; left: 156pt; width: 27.75pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0010_7553656.PNG" id="generatedImage313" path=".\HMWK1_images/IMG0010_7553656.PNG" style="width: 27.75pt;height: 12.75pt;"></img></div><div id="mc-region-314" style="position: absolute; top: 290.25pt; left: 48pt; width: 347.25pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0011_7553656.PNG" id="generatedImage314" path=".\HMWK1_images/IMG0011_7553656.PNG" style="width: 347.25pt;height: 33.75pt;"></img></div><div id="mc-region-315" style="position: absolute; top: 344.25pt; left: 48pt; width: 37.25pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">Finally</span></b></p></div><div id="mc-region-316" style="position: absolute; top: 372.75pt; left: 54pt; width: 228pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0012_7553656.PNG" id="generatedImage316" path=".\HMWK1_images/IMG0012_7553656.PNG" style="width: 228pt;height: 36.75pt;"></img></div><div id="mc-region-317" style="position: absolute; top: 428.25pt; left: 54pt; width: 108.5pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">Inverse Laplace gives</span></b></p></div><div id="mc-region-318" style="position: absolute; top: 458.25pt; left: 54pt; width: 205.5pt; background-color: #ffff80; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0013_7553656.PNG" id="generatedImage318" path=".\HMWK1_images/IMG0013_7553656.PNG" style="width: 205.5pt;height: 29.25pt;"></img></div><div id="mc-region-319" style="position: absolute; top: 464.25pt; left: 282pt; width: 49.25pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">...........(1)</span></b></p></div><div id="mc-region-320" style="position: absolute; top: 500.25pt; left: 48pt; width: 203.75pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">Years ago I wrote this transformation... </span></b></p></div><div id="mc-region-321" style="position: absolute; top: 525pt; left: 54pt; width: 154.5pt; background-color: inherit; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0014_7553671.PNG" id="generatedImage321" path=".\HMWK1_images/IMG0014_7553671.PNG" style="width: 154.5pt;height: 18.75pt;"></img></div><div id="mc-region-322" style="position: absolute; top: 530.25pt; left: 228pt; width: 76.25pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">....................(2)</span></b></p></div><div id="mc-region-323" style="position: absolute; top: 560.25pt; left: 90pt; width: 61.5pt; background-color: inherit; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0015_7553671.PNG" id="generatedImage323" path=".\HMWK1_images/IMG0015_7553671.PNG" style="width: 61.5pt;height: 29.25pt;"></img></div><div id="mc-region-324" style="position: absolute; top: 572.25pt; left: 48pt; width: 35pt; "><a name="" /><p class="Style1"><b><span style="color: #00f; ">where</span></b></p></div><div id="mc-region-325" style="position: absolute; top: 572.25pt; left: 174pt; width: 42pt; background-color: inherit; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0016_7553671.PNG" id="generatedImage325" path=".\HMWK1_images/IMG0016_7553671.PNG" style="width: 42pt;height: 13.5pt;"></img></div><div id="mc-region-326" style="position: absolute; top: 572.25pt; left: 246pt; width: 62pt; "><a name="" /><p class="Style1"><span style="color: #00f; ">reminder </span></p></div><div id="mc-region-327" style="position: absolute; top: 571.5pt; left: 306pt; width: 46.5pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0017_7553671.PNG" id="generatedImage327" path=".\HMWK1_images/IMG0017_7553671.PNG" style="width: 46.5pt;height: 14.25pt;"></img></div><div id="mc-region-328" style="position: absolute; top: 618.75pt; left: 48pt; width: 396.5pt; background-color: #ffff80; "><a name="" /><p class="Style1"><span style="font-size: 12pt; "><b><span style="color: #00f; ">QUESTION: HOW DID I GET (2) from (1) AND WHY??? MY MATH/TRIG IS SO RUSTY</span></b></span></p></div><div id="mc-region-329" style="position: absolute; top: 675pt; left: 42pt; width: 156pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0018_7553671.PNG" id="generatedImage329" path=".\HMWK1_images/IMG0018_7553671.PNG" style="width: 156pt;height: 18.75pt;"></img></div><div id="mc-region-330" style="position: absolute; top: 717pt; left: 48pt; width: 48.75pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0019_7553687.PNG" id="generatedImage330" path=".\HMWK1_images/IMG0019_7553687.PNG" style="width: 48.75pt;height: 12.75pt;"></img></div><div id="mc-region-331" style="position: absolute; top: 738pt; left: 36pt; width: 237pt; "><a name="" /><img border="0" src=".\HMWK1_images/IMG0021_7553687.PNG" id="generatedImage331" path=".\HMWK1_images/IMG0021_7553687.PNG" style="width: 237pt;height: 197.25pt;"></img></div><div></div></body></html>