How Can I Bridge the Gap Between Undergraduate and Graduate Level PDEs?

[Gwely Mernans]

Hi,

I have completed an undergrad introductory PDEs course using the Strauss text and am now transitioning to graduate PDEs using the Evans text. Though the first parts of these texts treat (generally) the same subjects, there is a vast gap between them in terms of 'mathematical maturity.'

I was wondering if anyone familiar with the subject of PDEs and the Evans text specifically has any suggestions (ie other books, online lecture notes, etc) that might help smooth the transition between these texts.

My background:

Completed Calc I-III and ODEs (obviously), linear algebra, introductory real analysis course, undergrad PDEs performing well in all courses. Comfortable with proofs (up to the level of math I have seen).

Also, yes, I realize that measure and functional analysis are necessary for a truly rigorous examination of PDEs. However in our class these subjects aren't mandatory for the limited material we cover.

Thank you, in advance, for any suggestions.

 

[zhentil]

Fritz john has an excellent book which covers roughly the same material