Inverse Laplace Transforms

Pre-College Topics High School Life
1

<p>Does Homework Help include just general questions about a subject area? I don't care about specific questions on my homework.</p>

<p>I'd really like an explanation of how to solve inverse Laplace Transforms where the denominator is a non-factorable polynomial. I can't use partial fractions, and I really don't want to use the convolution integral (especially since this is for the section before that topic is introduced).</p>

<p>On a related note, I'm also curious if there's a quick way to solve a 5-variable system of equations.</p>

2

<p>cramer’s rule,
and you can simplify determinants by using the determinant-simplifying rules,
or you could just use gaussian elimination,
it isn’t that bad</p>

3

<p>So you have to use matrices? Because I haven’t learned that yet (I’m taking Diff Eq’s before Multivariable and Linear Algebra). I guess it’s not that important right now, since the professor’s not going to be putting anything time consuming on the test tomorrow.</p>

4

<p>^Umm Cramer’s Rule/Matrices/Gaussian Elimination was like Algebra 2/PreCalc stuff…how do you not know that, and you’re taking Diff. Eq?</p>

5

<p>I’m the bomb at inverse Laplace.</p>

<p>Do you have that table that tells you what everthing simplifies to?</p>

6

<p>

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<p>They crammed it in in the last few weeks of Algebra 2. That was 3 years ago.</p>

7

<p>Try this: L^-1{s/(s^2 + 4s +5)}</p>

<p>Maybe I’m missing something obvious.</p>

8

<p>You’ll have e^-1{aF(s)+bG(s)}=ae^-1{F(s)}+be^-1{G(s)}, I think, it’s been a few months.</p>

<p>You take the inverse transform of the two individual transforms and put any a or b constants back in and +/- the constants back. </p>

<p>If you can’t factor the denominator, first try completing the square on the denominator? Then you can check and see if it’s a sine or cosine. Cosine needs an s in the numerator with at most a multiplicative constant, while a sine needs only a constant and no s in the numerator.</p>

9

<p>I’m not sure completing the square would help. That lets you solve for s, but that’s not what I need to do.</p>

<p>Yes, the answer does include cosine.</p>

10

<p>^nevermind</p>

<p>s^2 + 4s + 5 –> (s+2)^2 + 1</p>

<p>Now I can solve it.</p>