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Hey, /sci/. I just got this email, and I was wondering if anyone had any books that could take me from knowing differential equations (and real analysis) to being able to do this.
I really would love an NSF fellowship, and I am working directly under this professor, so I think I could get this.
"BTW, if anyone knows of an undergraduate student capable of solving coupled non-linear second order partial differential equations in heterogeneous domains with discontinuous boundaries, please let me know. We would want to encourage this student to pursue an NSF fellowship."
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>>8457951
hmmm.... how much algebraic geometry do you know?
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>>8457959
I mean, not too much (i.e. nothing). Is that intimately related to a problem like this?
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>>8457970
Most definitely. If I were you I'd get started working my way through the exercises in Hartshorne's book.
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>>8457973
Okay, I will probably talk to the professor about it, and then start working on that tomorrow! Thanks!
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>>8457951
Does anybody else have any suggestions?
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>>8458017
Really any textbooks would be super helpful. This is just so specific that it's hard to know for me.
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>>8457951
Is this even something that an undergraduate could do?
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>>8457951
>coupled non-linear second order partial differential equations
Stuff of nightmares right there. How does one go from standard pdes to that?
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>>8458100
Right? I feel like this is unrealistic even for an NSF fellowship
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>>8457951
So this is two pendulums, each in their own box, sitting on a Tempur Pedic mattress and every once and a while, a monkey comes along and shakes one of the boxes.
You'll want to know the position of each pendulum at time T.
Yep! Sounds like a NSF grant!
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>>8457951
I would start with Evans PDE book. If you have already taken a standard undergrad PDEs course, skip right to chapter 5.
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>>8458152
I think it's in mathematical biology, but working with the professor, I had to sign an NDA. It simultaneously made me super uncomfortable and super important.
>>8458166
Thanks for the resource! I will definitely check that out now! I just feel like the number of specifications make it a pretty bizarre/niche problem.
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>>8457951
Is it implicit in any problem like this that it would be solved numerically? I can't imagine there is a pretty closed form for the majority of PDEs, let alone something this complicated.
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Advanced calculus of several variable.
Just skip to the Stokes theorem in the back.
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>>8459554
Is that really germane to this? Sorry if I am too much of a brainlet to understand why that would be helpful in this context.
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>>8459778
Well you need analysis in several variables to do PDEs obviously. But for the integration side of things, you should just skip right to the lebesgue theory.
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>>8459801
That's definitely helpful. Shouldn't be too hard to actually learn more Lebesgue theory, since it's legitimately fascinating.
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