Peter Olver Vs Strauss for an introduction to PDEs

[Hamza M khan]

I have just finished my sophomore year as a physics major and am trying to teach myself Partial differential equations. My focus is primarily the various techniques of solving PDEs, but I would like to use a text that is rigorous to a certain extent. (For example, I would at least like statements and conditions for the various convergence theorems, if not their proofs). Among the plathora of PDE texts, the two that seem to align with my goals are "Introduction to Partial Differential equations by Peter Olver" and "Partial Differential Equations: An introduction" by Strauss. The text by Strauss seems to be widely used but some users mention that it is vague and "sloppily written". The text by Olver seems to have good reviews as well, but it is fairly new.

Does anyone have any experience with these (or any other similar texts) ? I would really appreciate some guidance, as I am trying to learn PDEs for the first time and, as such, cannot decide on what text to adopt. The fact that I am self-studying makes it all the more important that I settle on a text and stick to it, lest I get carried away.

 

[MidgetDwarf]

I used Strauss, and I did not find it sloppy. However, you need to work it out with pen and paper as you go along reading it.
Moreover, you have to think about why every line follows. That is true for all books, but there is less hand holding , compared to say calculus and intro ode books.

If you want a rigorous pde book, then you need at the minimum functional analysis / measure theory.

The first foray into pdes is typically learning methods to solve the transport, wave, heat, and laplace equation.

As a physics sophmore, I doubt you have the mathematical background for a text such as Evans or even Folland for a rigorous treatment.

 

[MidgetDwarf]

Im not familiar with Peters book.
But i found this one useful when first learning the subject

https://www.amazon.com/gp/aw/d/0070048509?tag=pfamazon01-20

I read Strauss and this one together. Its also cheap. So maybe get both if money is not an issue?

 

[Hamza M khan]

I used Strauss, and I did not find it sloppy. However, you need to work it out with pen and paper as you go along reading it.
Moreover, you have to think about why every line follows. That is true for all books, but there is less hand holding , compared to say calculus and intro ode books.

If you want a rigorous pde book, then you need at the minimum functional analysis / measure theory.

The first foray into pdes is typically learning methods to solve the transport, wave, heat, and laplace equation.

As a physics sophmore, I doubt you have the mathematical background for a text such as Evans or even Folland for a rigorous treatment.

Hi. Thank you for your reply. You are right in that I definitely don't have a proper background to study something like Evans. I meant rigorous in the sense using precise terminology and stating the theorems and their conditions (without proofs).

I will try out Strauss. I don't really mind working out the details in a text as long as the content is well written. How did you find the problems in Strauss' book?

 

[MidgetDwarf]

I found them doable but challenging for, say 1/3 of the problems in each each section.

Granted , I do not use solution manuals. So experience can vary if you plan to look at solutions.

Other book worth mentioning, is the one by Bleeker.

Haberman is also widely used, and is considered to be easier than Strauss.

I own a copy of Haberman, but never read it.Older editions are very cheap.

Bleeker, I like but Strauss is more "concise".