I have only had a one hour lecture on these, so it is hard to think about these.

Show that

Printable View

- Feb 24th 2010, 05:42 PMArythLaplace Transform
I have only had a one hour lecture on these, so it is hard to think about these.

Show that - Feb 24th 2010, 07:33 PMchisigma
Integrating by parts we obtain...

(1)

... where we use the fact that if exists, then is...

(2)

Kind regards

- Feb 24th 2010, 07:37 PMAryth
I appreciate the help. Thanks.

- Feb 24th 2010, 09:28 PMAryth
I have one question with inverse transforms.

- Feb 24th 2010, 10:06 PMchisigma
Applying the residue theorem we find...

(1)

... where...

(2)

... so that is...

(3)

Kind regards

- Feb 24th 2010, 10:08 PMoblixps
for the inverse transform use partial fractions to split the expression up. you can check if i did it correctly but i got (1/2)/(s-3) + (1/2)/(s+1). so you should be able to recognize these as laplace transforms of the exponential function. so you should get (1/2)e^(3t) + (1/2)e^(-t).

- Feb 25th 2010, 04:34 PMoblixps
the laplace transform of te^(-t) should be 1/(s+1)^2, not 1.

- Feb 25th 2010, 04:46 PMAryth