Brief and physics-oriented (?) resource for PDEs

[etotheipi]

Hey, I realized there are some parts (okay, a lot of parts) of Physics that I can't learn more about until I actually get a bit of practice solving PDEs. I'll cover it 'properly' next year but for now I'm just interested to learn about the most common solution techniques, types of boundary conditions, Green's functions and all that stuff.

If there are some decent lecture notes or problem sets available online that anyone can vouch for, that'd be neat. Nothing that you think would be far too difficult, please . Thanks!

 

[jasonRF]

The free text by Nearing has a short chapter on PDEs
Mathematical Tools for Physics (miami.edu)

Many "math methods for physics" types of books have brief treatments. Springer has some books available free during the pandemic, including the undergraduate and graduate books by Hassani
Mathematical Methods | SpringerLink

Mathematical Physics | SpringerLink

jason

 

[etotheipi]

Thanks, Nearing's chapter on separation of variables looks nice.

There's a lot of content available on PDEs and the tricky thing for me is to try and figure out what's worth spending my time on

 

[hutchphd]

I would suggest choosing a few PDE you know and love and then beating them to death with each technique. For the big picture `I am a fan of Schaum's outlines in general but don't know specifically for PDE

 

[jasonRF]

I think I understand - there really are a lot of treatments available. I listed the online resources I knew since libraries and such are less available these days.

The easiest text to learn PDEs from that I am aware of is the one by Farlow:
Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics): Stanley J. Farlow: 8601234581253: Amazon.com: Books
It is not free, but it is not expensive. The first section on the heat equation introduces you to separation of variables and integral transform techniques, which you will see over and over in applications. Lesson 9 uses eigenfunction expansions to solve non-homogenous equations, which is one standard way of deriving Green's functions. The book does not cover some of the theory that is important (eg Sturm-Liouville theory is briefly covered in a short comment) but your upcoming class should include the theory you need.

Note that the graduate level "mathematical physics" book by Hassani I linked is not easy reading and probably not the best choice, but it does include a lot on Green's functions. Not all undergraduate treatments include that topic.

jason

 

[Frabjous]

Your going to be taught standard PDE’s. I would suggest looking at a couple of adjacent topics, Fourier analysis and green’s functions that are commonly not taught in depth.

I have used these, but I am not sure if these are the best references
Bracewell Fourier Transform and its Applications (it is affordable used)
Greenberg applications of green’s functions (dover)

This popped up when I was looking for the references so I cannot speak to it’s quality
Bell Special Functions for Scientists and Engineers (dover)
Here you would learning about the properties of the solutions to various PDE’s

 

[etotheipi]

Nice, thanks everyone

 

[vanhees71]

As anything by Sommerfeld,

A. Sommerfeld, Lectures on Theoretical Physics, vol. 6 (Partial Differential Equations),

but particularly this volume of his lectures, is a masterpiece.

 

[atyy]

http://u.arizona.edu/~sgralla/teaching.html
Samuel Gralla has YouTube lectures on partial differential equations.