I think it's a matter of personal preference. I, personally, tend to be more of a "witness stenographer" when taking notes with pen and paper. Because I can type faster than I can write, using a computer allows me more opportunities in class to stop and ponder the material.

I don't think there's any hard and fast rule that says that paper is better than computers or vice versa. Forcing students into using what the professor finds more helpful handicaps students who want to find the method which works best for them.

That study only compared students who doodle to students who daydream in class. They failed to consider that some students actually pay attention and take notes in class -- I think we'd agree that students who pay attention tend to focus better.

I'm replying to this post simply because this one actually intends to answer the original question.

When I took partial differential equations, we used "Advanced Engineering Mathematics" by Erwin Kreyszig.Of course, this is a mathematics book, so about 90% of it is "pure mathematics"... but being a physics student, I felt that it was quite applicable to my taste (physics). It does contain useful physics -- such as the heat equation, wave equation, etc. (Keep in mind that I knew most of the physics already when taking my class in PDEs... so I can't say for sure that someone who doesn't know physics would appreciate the physics discussed in this book).

If you want something that's the opposite of the book I mentioned above -- that is, it assumes you already know differential equations and simply want the physics, I'd recommend "Analytical Mechanics" by Fowles and Cassiday. This book just uses ODEs (not PDEs), but it's filled with examples which use ODEs to solve physics problems.

I'd recommend reading Analytical Mechanics to get yourself acquainted with how physicists use differential equations to solve physics problems, then reading Advanced Engineering Mathematics to see more advanced physics problems. Or maybe Analytical Mechanics would be enough... being that I don't have your PDE textbook ;), I'm not sure if Advanced Engineering Mathematics is any better than your math textbook as far as explaining the physics.