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What Mathematics would be useful for Applied Physics?

  1. Jun 25, 2011 #1
    I am an undergraduate working towards a degree in Engineering Physics at Berkeley and I want to go to graduate school in Applied Physics, probably specializing in electronics.

    I have plenty of math major friends and they tell me all the time about how they keep running into physics majors in their classes. I was wondering what mathematics courses would be useful for someone planning to head in the direction I am heading in?

    I have completed calculus up to mulitvariable, lower division linear algebra and differential equations (They are lumped together in one semester at my school), and a year of math methods for physical scientists (First semester was things like complex numbers, applications of taylor series, and fourier series and transform. Second semester was basic PDE's: variational calculus, basic attempts at symmetry solutions, forbenius series, eigenvalue problems and the like).

    My math major friends tell me I should take upper division linear algebra and real analysis. One even suggests abstract algebra because his professor says it is crucial to quantum field theory. I personally feel very comfortable with not needing linear algebra after taking Quantum Mechanics but I'm not sure about the others.

    Just for the sake of being thorough, the classes that I am currently considering are:
    -Real Analysis (It is mandatory for the ODE course and I hear it is necessary for graduate PDE. Also a prereq for differential geometry and complex)
    -Linear Algebra (People say it is very hard to get by in the more rigorous upper division math classes without this class)
    -Numerical Analysis
    -Complex Analysis
    -Metric Differential Geometry (I don't know much about it but from what I can gather it is more or less an advanced geometry course which seems useful)
    -Optimization (Like I said I'm doing applied physics, and this seems useful for applied majors)
    -PDE (Basic PDE course, it studies PDE a little more rigorously than the mathematical physic course I've already taken)

    I definitely do not plan on taking all of these!

    If you had actually read all that, I feel like I should give you a prize but I'm afraid I can only offer my sincerest thank you.
     
  2. jcsd
  3. Jun 25, 2011 #2

    ZapperZ

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    If you do a search on here for "Mary Boas", you'll find a very strong recommendation for her book "Mathematical Methods in the Physical Sciences".

    Get this book. The mathematics that you will need will most probably be covered in this book. And it is designed for someone at the undergraduate level, and can also be used as a self-study.

    Zz.
     
  4. Jun 25, 2011 #3
    I actually have boas's book. The material is more undergraduate though. I am thinking more about what would be useful in graduate school and in the field. I've looked through other books such as Arfken and Vaughn and they cover plenty of material that is not present in boas or that boas doesn't cover in very much depth. I have time now to take more math, so i figure I might as well make my life easier later by taking things that would be helpful.
     
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