Good Physics Books For a Math PhD Student?

An anonymous reader writes "As a third-year PhD math student, I am currently taking Partial Differential Equations. I'm working hard to understand all the math being thrown at us in that class, and that is okay. The problem is, I have never taken any physics anywhere. Most of the problems in PDEs model some sort of physical situation. It would be nice to be able to have in the back of my mind where this is all coming from. We constantly hear about the heat equation, wave equation, gravitational potential, etc. I'm told I should not worry about what the equations describe and just learn how to work with them, but I would rather not follow that advice. Can anyone recommend physics books for someone in my position? I don't want to just pick up a book for undergrads. Perhaps there are things out there geared towards mathematicians?"

Comments

Partial differential equations

[Animats]

First of all, "partial differential equations" should not be capitalized.

The general idea is straightforward. Partial derivatives are just the concept of a derivative generalized to higher dimensions. Just as a derivative is a tangent to a curve, a partial derivative is is a tangent plane to a surface.

There are many physical situations in which the physics gives you the partial derivative in the current situation, and if you want to predict what happens next, you have to integrate the partial derivative. For most real-world problems, this has to be done numerically, although for some special situations, like planetary orbits, there are analytical solutions.