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Mathematics useful for Physics classes

  1. Apr 9, 2015 #1
    I'm not going to ask what mathematics are relevant to physics, I know the answer is all mathematics. I was hoping you guys could help me figure out which specific mathematics topics would be best to take concurrently or prior to certain physics topics, so that the order of my classes is most beneficial to my understanding (I'm a physics major, and I'm going to go a bit beyond a minor in math). I am going to be taking some 300-level differential equations and partial differential equations as well as vector analysis. I could go deeper into these topics or to more statistical/analysis topics, or more pure mathematics, or really anything you could think of including graduate level. I'm looking for the greatest connection to my upcoming physics classes however, which are (in approx. order):

    -Computational Physics
    -Intro to Condensed Matter Physics
    -Electricity and Magnetism 1&2
    -Intro to Quantum Mechanics 1&2
    -Elementary Particles

    Any suggestions? Also, take into consideration that I'm considering a more theoretical field likely involving heavy QM and perhaps particle/high-energy physics. I've already gotten the suggestion that a more advanced linear algebra that describes it more fundamentally would greatly benefit QM, and advanced algebra would benefit QFT specifically. This is such a complicated question though that I want to get as much input as possible.
  2. jcsd
  3. Apr 9, 2015 #2


    Staff: Mentor

    For undergrad:
    - multivariable calculus,
    - differential equations
    - linear algebra

    - complex analysis
    - boundary value problems

    - tensor analysis
    - group theory
    - differential forms
  4. Apr 9, 2015 #3
    E&M - vector analysis is useful to understand all the derivations
    Quantum - all kinds of integrals, linear algebra/matrices, spherical harmonics, Dirac notation
    Thermo - so far, a lot of partial derivatives
  5. Apr 10, 2015 #4


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    Staff Emeritus
    Science Advisor
    Education Advisor

    Check out the various threads that we have had on Mary Boas's text "Mathematical Methods in the Physical Sciences". For any undergraduate physics and engineering student, this should be a book to refer to, and at the basic level, the math that you will need to survive. For a physics majors, the chapter on Calculus of Variation alone is worth the price of the book!

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