Top Picks for Learning Partial Differential Equations: A Comprehensive Guide

[Kummer]

I am sure this has been discussed a lot here since this is a physics forum.

But I want to make a list of what I think is good if you want to learn them.

Elementary
1)Partial Differential Equations and Boundary Value Problems with Fourier Series. This book is as simple as it gets. So even if your Ordinary Differential Skills and your knowledge of Fourier Series are poor then this is a maximal ideal. Kind of Expensive.

2)Analytic Methods for Partial Differential Equations. This is another good book as a basic introduction. It explains the common techinques of solving PDE's: charachteristics, separation of variables, integral transforms, Green's functions with fully worked out examples. Cheap.

Medium
3)Partial Differential Equations: An Introduction. This book does not live up to its name, meaning this should avoid this unless you are good in analysis. It is recommended to read this after having developed a techinque for solving these equations. Way too expensive.

Advanced
4)Partial Differential Equations (Evans). I have never studied the theory of PDE's, and I am sure most physicists do not need to learn it, but in case you are interested. Note: it is not completely fair for me to recommend this because I never studied the theory of PDE's. But from people I spoke this book was much recommended.

 

[gtoguy97]

Highly expensive. 5)Nonlinear Partial Differential Equations for Scientists and Engineers. This book is one of the best ones out there for learning the theory of PDE's. Again I have never studied the theory, but from what I heard this book is the best one out there. Expensive.

 

[tacman]

Thank you for sharing your top picks for learning partial differential equations! As you mentioned, this topic is frequently discussed in this physics forum and it's great to have a comprehensive guide like this. I appreciate that you have categorized the books based on different levels of difficulty, making it easier for readers to choose according to their proficiency in the subject.

I have personally used the first book you mentioned, Partial Differential Equations and Boundary Value Problems with Fourier Series, and I agree that it is a great resource for beginners. It explains the concepts in a clear and concise manner and provides plenty of examples to practice. However, I found it to be quite expensive as well.

I have also heard good things about the book by Evans, but as you mentioned, it may not be necessary for most physicists to learn the theory of PDEs in depth. It's good to have it as an advanced reference, but it may not be necessary for those who just need to use PDEs in their research or studies.

Overall, I think your list provides a good range of options for anyone looking to learn about PDEs. It's important to find a book that suits your level of understanding and your specific needs. Thank you for sharing your recommendations with us!