[Math] How to properly prepare for a graduate level PDE course using the books by Evans and Strauss

fourier seriespartial differential equationssoft-questionwave equation

For my undergrad background, I have Calculus 1-3, Linear Algebra, one semester of ODE, one semester of real analysis. Never had any PDE before. Thus I know this background is hardly enough to do well in a graduate PDE.

My plan during this coming 3 weeks of winter break is trying to have some PDE tricks before hand. I will use the Haberman's book "Applied PDE with Fourier series and boundary value prob" to prepare since it is used to teach undergrad PDE.

If any of you are familiar with the topics and the three PDE's books of Evans,Strauss and Haberman, please advice which Haberman's chapter that I need to read. Or if you have a better reference, comment on how to strengthen my background please do so. Many thanks in advance, sorry for lengthy post.

At my school, the 1st course in graduate level PDE will cover Evans 's PDE book chapter 2 and Strauss's chapter 4,5

Here is Evans's pde list:

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Here is Strauss 's pde list :

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Here is the contents of Haberman's pde :

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Best Answer

This is partly a matter of opinion, but a course that consists of "Evans' chapter 2 and Strauss 4,5" is not a graduate-level PDE course. Strauss' book is mostly an undergraduate textbook for first course in PDE, although the disconnect between the text and exercises makes going through it more difficult than it should be. Evans', of course, is a graduate-level book, but its Chapter 2 is introductory.

So, what you described is an undergraduate-level course, for which studying from Haberman's book means studying the material before studying the material (as Artem said).

By the way, an undergraduate course in PDE is not necessarily the best preparation for a graduate course in PDE. In a UG course based on Haberman's book students will spend an entire semester separating variables and writing down solutions in a form of an explicit series. This is not at all what a real PDE course on a graduate level will be about.

have some PDE tricks before hand

The most important tricks to have beforehand are not those taught in PDE courses. They are: multivariable chain rule, integration by parts, fundamental integral formulas of vector calculus, integral inequalities of real analysis (Cauchy-Schwarz etc), the skill of estimating things using the triangle inequality.

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