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Hi folks,

One of my older daughters has a maths assignment and is hoping for a little help, if possible. She has been to her tutorials and has asked her tutors plenty of questions, but there are still a couple of things she'd like some clarification on.

@square_25 or @kiana or @4KookieKids  Are any of you familiar with PDEs and Fourier transforms, by any chance?

 

Here are my daughter's questions:

When solving a PDE system with Fourier transforms (being allowed to use online tables of transforms and not having to do it by hand) does the rule for transforming a derivative also apply to the rule for transforming a partial derivative? Also, it was my understanding the integrals you'd end up with have a dx attached, so why does the solution I know I need to find have a dk as the term the integral is over? Finally, if I end up with integrals on one side of an equation, either added or multiplied, can they be combined into the one integral to simplify?
 
 
When scaling in terms of either length or velocity do you need to only scale terms that involve it? For instance, if there is a velocity term U somewhere in an equation alone, would it be ignored if I'm only concerned with scaling in terms of length H?
 

Thank you 🙂 

Edited by chocolate-chip chooky

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Oof. I did take PDEs, but last time I saw them was more than a decade ago. So I can't answer :-(. Sorry! 

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1 hour ago, square_25 said:

Oof. I did take PDEs, but last time I saw them was more than a decade ago. So I can't answer :-(. Sorry! 

Oof indeed! Her maths looks *scary*!

Thanks for your reply🌻

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1 hour ago, Arcadia said:

My Fourier transforms was in engineering school in 1991. See if links helps your daughter 

https://www.math.ubc.ca/~feldman/m267/pdeft.pdf

https://www.roe.ac.uk/japwww/teaching/fourier/fourier_lectures_part5.pdf

Arcadia, you're a gem. Thank you from the Chooky household 🌻

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