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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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    $\begingroup$ You need courses in undergraduate real analysis, Lesbegue integration, and functional analysis before tackling a graduate PDE course. $\endgroup$
    – Potato
    Nov 21, 2013 at 20:08
  • $\begingroup$ @Potato But note that this course only covers chapter 2 of Evans. And Strauss doesn't require much analysis. $\endgroup$
    – littleO
    Nov 21, 2013 at 20:11
  • $\begingroup$ @littleO I didn't realize the second book was more applied. I suppose he could get by, but it still seems unwise me to. $\endgroup$
    – Potato
    Nov 21, 2013 at 20:12
  • $\begingroup$ Sorry to mention , I have one real analysis course in undergrad and currently in a measure theory course . $\endgroup$
    – Peter
    Nov 21, 2013 at 20:13
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    $\begingroup$ There is no point to study Haberman before Strauss book, they are approximately on the same level and cover very similar topics, albeit Haberman's text is much more wordy and does not cover some of the topics from Strauss book. I am not sure this is a universally good advice (not enough information), but I would suggest to a get a copy of Farlow's PDE and work through it. Three weeks is more than enough for this. $\endgroup$
    – Artem
    Nov 21, 2013 at 20:18

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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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  • $\begingroup$ Hi @sandwich, so, should I just start reading out of Evans' book to prepare for a PhD level introductory PDE course that I plan to take this coming fall semester? I have also heard that undergraduate courses, books, and notes spend a lot of time separating variables and doing stuff that is not exactly a "pre-req" to the PhD course -- and also that spending a lot of time learning ODE theory is not a pre-req to PDE theory. What do you think? (I have no experience with PDEs yet.) Thanks, $\endgroup$
    – User001
    May 19, 2016 at 23:05
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    $\begingroup$ Ask the professor teaching that course. $\endgroup$
    – user147263
    May 20, 2016 at 0:10

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