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Optional Mathematics

  1. Jun 12, 2005 #1
    Well I wasted 15 minutes trying to write up a thread and unfortunately an error popped up so I had to close the window so I'll be brief.

    Real Analysis I
    Real Analysis II
    Complex Variables

    When does the material from these courses come up in upper division physics courses?

    Is a course in statistics recommended for QM?

    Mathematical physics courses won't suffice. I want the real deal.


    Damn that was short.
     
  2. jcsd
  3. Jun 12, 2005 #2
    What is covered in the real analysis courses?
    You'll definately need a course in complex analysis.

    Statistics could be useful in QM, but it depends on how the course is taught. If it includes measure theory I'd say take it, else drop it.
     
  4. Jun 12, 2005 #3
    Real Analysis I

    Numbers, sets, and functions: induction; supremum, infimum, and completeness; basic set theory; bejective and inverse functions; countable and uncountable sets.

    Sequences: convergence, Cauchy sequence, subsequence, Bolzano-Weierstress theorem, limsup, and liminf.

    Limits and continuity: basic theorems, intermediate value theorem, extreme value theorem, inverse function theorem, uniform continuity.

    Derivative: basic theorems, mean value theorem, Taylor's theorem, trigonometric functions, exponential functions, l'Hopital's rule.

    Riemann integral: basic definition and theorems, fundamental theorem of calculus.

    Real Analysis II

    Series: convergence tests, absolute convergence, conditional convergence, rearrangements, Cauchy product.

    Sequences and series of functions: pointwise and uniform convergence, Weierstress M-test, power series.

    Euclidean spaces: Basica topology, connectedness, compactness; metric spaces.

    Functions of several variables: limits and continuity.

    Derivative: linear transformations, differentiability, inverse function theorem, implicit function theorem.



    These all sound like content from Calculus I, II, & III but of course I have no idea what is actually taught in the class.

    Can you explain why a course in complex analysis is important and what physics courses would it apply in?

    I hope that clarifies things...
     
    Last edited: Jun 12, 2005
  5. Jun 12, 2005 #4

    cronxeh

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    Gold Member

    This has been covered before in this same section. Basically Real Analysis is a rigorous overview of Calculus and introduces more advanced ideas and introduces the student to proofs and analytical methods. How is this stuff useful for a Physicist? I'm not sure but I do believe that math can not hurt a Physics major, and as far as I know this course will be a prereq for partial diff eq of mathematical physics or something similar sounding - which would include something of this nature:

    As well as
    And
    You will note that Real Analysis 2 is listed as a prerequisite for all 3 of those courses (well at least in my University). Whether you'd like to get to know that material is your call.
     
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