When working with PDEs and variational methods it is not advised to identify H^1_0 with its dual H^{-1}, because you lose some subtleties. The space L^2 is sometimes called the pivot space and is sort of in the middle in terms of regularity, i.e. functions in L^2 are first derivatives of...
@NumericalFEA
Well, I had already considered that and decided that I want to do a PhD. It is now a matter of where, and whether it is advisable to get a loan to do it.
@micromass
When they interviewed me, they told me that they were interested in having me as a student, but the University as...
Hi guys! I applied to a DPhil program on PDEs at the University of Oxford and recently got an offer without funding. I would love to attend this program, but as you may know, the tuition fees for international students are really high. My government could help me with 2/3 of the tuition + a (not...
In my opinion the way to go is to use distribution theory. In the book Applied Functional Analysis - Applications to Mathematical Physics by Eberhad Zeidler there is a discussion of the electrostatics case (page 183). Maybe you can try to use similar arguments to prove the magnetostatics case.
There is a book on mathematical modelling written by Eck, Garcke & Knabner that I like a lot, but there is one little problem: It is written in german and I don't know if it has been translated. If this poses no problem for you then check it out...
There is an article focusing on eigenvalue problems in the Volume 2 of the Handbook of Numerical Analysis written by I. Babuška and J. Osborn (I don't know if this qualifies as a simple introduction though...)
https://www.amazon.com/dp/0444703659/?tag=pfamazon01-20
Right, I would start with courses, which is why I thought it wouldn't be that helpful to contact faculty, but I guess it can't hurt...
Oh I didn't know that; in my intended programs there are no obligatory courses and I get to choose whatever I want. Maybe this is just for mathematics though...
OK, I will try to change that, thanks for the feedback.
I've been thinking about it and I am not sure how to do it (I've never contacted a professor this way). Do you have any tips? I fear that my email might be too generic...
Well, as an exchange student I had total freedom to choose my...
Thanks for the reply!
Do you mean that there is superfluous information? Or that the sentences are too long?
Actually I did, but I didn't think it would be appropriate to write that...
I wrote it because the university specifically asks us to state whether we know or are in contact with...
Hi guys, I've been a long time reader of these forums, but this is the first time I create a thread. In the next weeks I will be applying to some masters programs in Europe (in math) and as part of the application process I must write a statement of purpose. Since english is not my first...
I like Spivak, but I don't think it is suitable for self-study (it is VERY concise). I always recommend:
-Fleming - Functions of Several Variables
https://www.amazon.com/dp/0387902066/?tag=pfamazon01-20
-Munkres - Analysis on Manifolds
https://www.amazon.com/dp/0201315963/?tag=pfamazon01-20...
Just a quick note: The space \{u\in C^2[a,b]\} : u(a)=u(b)=0\} with the inner product (u,v)_{L^2} = \int_a^b uv is not a Hilbert space (it is not complete). In this case we should work on a so called Sobolev space, in this case the space H_0^1(a,b) = \{u\in L^2(a,b) : u'\in L^2,u(a)=u(b)=0\} ...
I always recommend these 3:
-Edwards. Advanced Calculus of Several Variables
https://www.amazon.com/dp/0486683362/?tag=pfamazon01-20
-Fleming. Functions of Several Variables
https://www.amazon.com/dp/0387902066/?tag=pfamazon01-20
-Munkres. Analysis on Manifolds...
What Terandol said. The thing is that the Euler-Lagrange equations are a necessary condition. If you look closely, what the theorem actually says, is that if the minimizer exists, then it has to satisfy the E-L equations.