ME565 Lecture 25: Laplace transform solutions to PDEs

ME565 Lecture 25
Engineering Mathematics at the University of Washington

Laplace transform solutions to PDEs

[chotirawee]

Hi, I have a question on the first example

For the first term of the solution u(x, t), Is the first term really independent of x?
I mean, before taking inverse Laplace transform, that term was a function of both s and x. Why does its inverse Laplace transform only a function of t

[federicogasparv]

Excellent class. I would like to ask If there is any chance to use Laplace transformation in both variables at the same time and if there is any example of this technique aplyied to PDE where you can not use separation of variables.

[gah]

Well worked and a good pace. Thanks.
I think the comment (31:40) about the u(x, t) term that disappears if no forcing term is present wasn't right. The first term would not disappear. The second term would disappear.
Also, fyi, the final inverse Laplace involves the 2nd shifting theorem, so can be done without a table lookup as relatively common.

[AshishPatel-yqxc]

The comment about the impulse function used to model acoustic signatures of studios is very relevant. There are commercial products that use this idea .have a look at Dirac 2 room correction . All DSP stuff but underlying math technique is I bet what u mention.