After Boas's Mathematical Methods?

[Twigg]

Hi all,

Is there a more advanced version of Mary Boas's Mathematical Methods? Specifically, these are some topics I would like to learn more about and work through problems on:

1. Uniqueness and Existence theorems boundary value problems with 2nd order PDEs of elliptic, parabolic, and hyperbolic type
2. Green's functions for general boundary value problems with 2nd order PDEs of elliptic, parabolic, and hyperbolic type, including the conditions for the Green's function on the boundary
3. Sturm-Liouville theory (I picked up the theorems, but I would like to test my knowledge on problems)
4. Differential forms
5. Group theory (for physicists)
6. Adjoints, exponential formulae like BCH, and all that jazz

I was thinking that maybe a combination of Arken for 3,4,5 and Jackson for 1,2. (I know Jackson is an E&M text, but I first learned about the general conditions to use a Green's functions in a given boundary value problem for Poisson's equation in a borrowed copy of that book, so I am hoping it might have a similar discussion of the wave equation, at least, from which I may be able to get the gist of the general case.) Should I be looking at Hilbert-Courant?

 

[Dr Transport]

1-3 are covered in Byron and Fuller as well as Courant and Hilbert.

Differential forms: I cannot tell you.

Group Theory, there is a multitude of threads here about that, I recommend Joshi, Tinkham then Wu Ki Tung in that order.

Adjoints etc: again not a clue

 

[Brian T]

I have several recommendations for differential geometry / forms:
For a classical dg text, you can try "Tensor Analysis on Manifolds".
For a more physics oriented text (specifically relativity), see "Differential Forms and the Geometry of General Relativity". This is a good book to see some computations with forms used in relativity
Lastly, a text I highly recommend for a lot of geometry used in physics is "Differential Geometry, Gauge Theories, and Gravity" (covers topics such as exterior algebra, differential forms, metrics, gauge theories, GR, manifolds, lie groups/algebras, and bundle theory)