What are some good PDE books that can used for an independent study with a professor. My background includes:
- Linear Algebra at the level of Axler's Linear Algebra Done Right and Friedberg, Insel and Spence's Linear Algebra;
- Abstract Algebra at the level of Dummit and Foote's Abstract Algebra;
- Complex Analysis at the level of Bak and Newman's Complex Analaysisl
- Real Analysis at the level of Rudin's PMA and Pugh's Real Mathematical Analysis.
- Multivariable Differential Calculus at the level of Edwards' Advanced Calculus of Several Variables.
I'm also currently revising some of the aforementioned subjects. I also know a bit of measure theory, and I'll be taking a course on it the fall. I don't know functional analysis as of yet. I also don't know a lot about Multivariable Integral/Vector Calculus (theory). I haven't also taken any theory course on ODE's. I suppose I can pick up the basics of Fourier Series, Fourier Transforms etc. during the course of my independent study.
I'm looking for two textbooks that I can keep side by side to introduce myself to the basics of PDE's at the graduate level, as I'll be an incoming graduate student in the fall.
The standard suggestions seem to be Walter Strauss Partial Differential Equations (for a first course) and Lawrence Evans' Partial Differential Equations (for a second course). Does it seem like a reasonable for me to keep these two books side by side?
Is the theory of ODE's is an absolute pre-requisite for a course on PDE's taught from any book (at the advanced undergraduate/graduate level)? If not, is there any way I can skirt around it? I don't mind learning measure theory and functional analysis in a self-contained manner from a textbook that covers PDE's