PDE and Analysis Reference Request From Small College Grad

Question

I am in my final semester graduating from a liberal arts college (physics/math major) and intend to study high-energy theory in graduate school. Coming from a smaller college I have not had the opportunity to take courses in partial differential equations, integral equations, or numerical/computational methods.

What resources, in the aforementioned fields, might one recommend to a student looking to get sufficiently up to speed for graduate level coursework and research (n.b. I do solid math background, in general, including linear algebra and complex analysis, which might come in handy for such topis/learning)?

Answer 1

It's my understanding real analysis is helpful for physics Phd's. A good source for this is Principles of Mathematical Analysis (often referred to as baby Rudin's). I have heard this book is an excellent source for undergrads/grad students.

https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X

As for PDEs, a great resource I have used is an online website done by a professor at Lamar university. Notes go from calc 1 through PDEs, so it's a great resource.

http://tutorial.math.lamar.edu/Classes/DE/IntroPDE.aspx

As for actual texts, the book by Strauss is good for a first course (and for self-study).

http://rads.stackoverflow.com/amzn/click/0470054565