PDEs for EEs: Signal Processing R&D

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kdinser
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This is kind of an off shoot of another thread, but figured it would be better to start my own rather then hijack someone else's :).

What does PDE cover and would it be useful to an EE looking to get into signal processing research and development? If so, could someone recommend a good book on the subject that is aimed more at the engineer then the math major? I don't mind rigorous mathematics when it's called for, but I get annoyed when it overlaps to much with common sense,
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Well, if you want to get into signal processing you can never have enough math. Hell, you can never have enough math, period.

PDE is an essential subject to be well versed in no matter what you go into. Right now I am studying tensor analysis on my own (dual major in EE and physics) so I can be prepared to study GR properly, but the next subject I plan to cover on my own is PDE.