Physics for Math Majors: Advice for Applying Math to Physical Problems

[epr2008]

Ok, so last year was my junior year in applied mathematics, and I decided to declare a second major in physics. My problem has never been the math at all, but rather its physical interpretations. University physics was a breeze, however, even then I did notice that towards the end conceptually I was lost at some points. I took a course in Modern Physics last semester which was heavily conceptual, and although I received a B, I really didn't feel like I earned it. This semester I am taking classical mechanics, astrophysics, and thermal dynamics and statistical mechanics.

Now, I have taken tons of math courses: calc sequence up to real and some functional analysis, abstract algebra, complex analysis, ODE, PDE, numerical methods, stats sequence, and I have self taught my way through a point-set topology and an algebraic topology book. And this semester I'm taking an applied math course that focuses on biological processes and modeling so really its more of a course in difference equations and non-linear differential equations.

I have two major problems. First of all even after learning all of those techniques from all of those math courses, I don't really know when to apply them in physics. Sometimes I don't even know where to begin on a problem at all. And I also have a difficult time inferring the physical meanings of the equations.

For example, in classical mechanics, most of the material covered would be a lot simpler and the equations more concise if you used complex variables instead of vectors, such as circular motion, motion of charged particles, etc. I mean realistically any vector quantity can be described in terms of a complex variable even if in some cases its not efficient to do so. My problem is that I was never taught how to do such a thing.

The weird thing is that in my applied math class I do know when and what techniques to apply which is basically the same thing in a different setting. So I was thinking that maybe I am just having trouble understanding it from a physicists point of view? There are plenty of math methods for physicists books that I have looked at, but all of them say they have applications which turns out to be like one chapter on one specific physical phenomenon. And what they really are is a condensed encyclopedia on solving different types of equations.

So I was wondering could anyone help me out by either recommending a book or some guidance in general?

Thanks in advance.

 

[intwo]

When I took introductory physics I applied equations instead of thinking the problems though. It really hit me when I got to classical mechanics and all I could do was glare at the pages and wonder how I could set up the problem. It sounds like you might be in a similar scenario.

I ended up going back through the mechanics sections in my introductory physics textbook and taking the time to understand what the equations actually meant and where they were applicable.

 

[Broccoli21]

You might like this:
https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20