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.
Edit:
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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?
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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
Best Answer
Partial Differential Equations by Mikhailov introduces the necessary Lebesgue integration and functional analysis prerequisites in a 60-page preliminary chapter. However, the book presupposes acquaintance with the theory of ordinary differential equations. The preface states the following three prerequisites.
A Course of Mathematical Analysis (two volumes) by Nikolsky
Foundations of Linear Algebra by Mal'cev
Ordinary Differential Equations by Pontryagin