[Math] Prerequisites for Studying a Book on PDE’s

book-recommendationreference-requestsoft-question

I'm taking a course on Electromagnetism that will cover the boundary-value problems — the solutions to Laplace's and Poisson's equations for various symmetries, ranging from cartesian to spherically symmetric (or more cases which I'm not aware of).

To that end, I am looking to go through a book on PDE's to keep up to date with various PDEs and their solutions on the side. I think this exercise will help me better keep apace with the course. I came across the following resource:

Partial Differential Equations: An Introduction by Walter A. Strauss (Amazon link)

The preface to the textbook states:

The main prerequisite is a solid knowledge of calculus, especially multivariate.
The other prerequisites are small amounts of ordinary differential
equations and of linear algebra, each much less than a semester’s worth. However,
since the subject of partial differential equations is by its very nature not
an easy one, I have recommended to my own students that they should already
have taken full courses in these two subjects.

I haven't taken a course in ODE's, so I'm not sure if I should be tackling this textbook. On the other hand, the last thing I'd want is to start tackling a 500+ page textbook on ODE's that'll take a whole semester to finish. For instance, I came across the following book on ODE's:

Ordinary Differential Equations by Tenenbaum and Pollard (Amazon link)

It'd be great if someone could answer:

  1. whether or not the aforementioned books on ODEs and PDEs suit my needs at the moment;

  2. should I bother first going through a text on ODEs? If not, why not? If yes, what topics should I be covering from the aforementioned book on ODEs to get sufficient background to start with PDEs. For example, the author mentions "…prerequisites are small amounts of ordinary differential
    equations."     I'm not so sure how much of knowledge of ODEs are required (for my purposes).

Thanks in advance.

Best Answer

For basic knowledge in PDE it will be good for you to read "Elements of Partial Differential Equations: Ian N Sneddon." and for BVP's in PDE you can read from either "Advanced Engineering Mathematics: Erwin Kreyszig Amazon link" or "Elementary Differential Equations and Boundary Value Problems: William E. Boyce, Richard C. Diprima Amazon link". It is nicely explained there.

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