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Physics for math majors

  1. Feb 28, 2012 #1
    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.
     
  2. jcsd
  3. Feb 28, 2012 #2
    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.
     
  4. Mar 6, 2012 #3
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