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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.

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  • $\begingroup$ You need at least the general understanding of ODEs to work with PDEs. It's common sense - you wouldn't start studying quadratic equations before learning about square roots first, right? But you surely don't need to spend a whole semester on ODEs. If you have good grasp on integrals, you won't have trouble with ODEs. You need to learn some key topics - Initial value problem, separation of variables. If you need to solve a particular kind of ODE this source has a great list of solutions $\endgroup$
    – Yuriy S
    Jan 25, 2017 at 10:11
  • $\begingroup$ In any case, I strongly recommend using multiple online sources (including textbooks), instead of spending money on paper books. I would like to remind you that MIT now has all of its courses online, including this $\endgroup$
    – Yuriy S
    Jan 25, 2017 at 10:14
  • $\begingroup$ @YuriyS Yeah, you're right. I have never taken a course on ODE's but I do have a working knowledge on how to solve various ODEs from my physics classes. So I'm a bit confused, what units should I be reading from a book to do enough to start off with PDEs. I'd ideally keep a book and not an online/video lecture resource as that'll involve my having to sit down and watch the lectures, whereas with a book I can go at my pace/selection of topics. Suggestions? $\endgroup$
    – Junaid Aftab
    Jan 25, 2017 at 10:46
  • $\begingroup$ Without an exposure to ODE, working with PDE may be a tall order. Vladimir Arnol'd has a book on ODE and one one PDE. I suggest looking through the first 1-2 chapters of the first, at least for an overview, and then looking through the first couple of chapters of the latter. You may be needing to come back to each book for a deeper look, but at least they are a quick way to get you into the subjects, as Arnol'd emphasized a connection with physics (as is evident from his article "On teaching mathematics"). $\endgroup$
    – avs
    Dec 3, 2020 at 3:08
  • $\begingroup$ You definitely cannot understand PDEs if you do not already understand ODEs. $\endgroup$
    – Clyde Kertzer
    Apr 5, 2022 at 21:59

1 Answer 1

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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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