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PHYS 320: Mathematical Physics

Seth Major

Offering "...sparking Legendre magic in [your] soul" since at least 2001! (Thanks to Ryan Tamburrino)

Course information (pdf):

Course syllabus & info

Special functions presentation info

Questions, Problems and Reading (pdf):

Questions 1
Questions 2
Questions 3
Questions 4
Questions 5
Questions 6
Questions 7
Questions 8
Questions 9
Questions 10
Questions 11
Questions 12
Questions 13
Questions 14
Questions 15
Questions 16
Questions 17
QPS 3(revised)
Questions 18
Questions 19
Questions 20
Questions 21
Questions 22
Final QPS

Some recent topics:

  • Complex Numbers

  • Methods of solving Ordinary Diff. Equ's (ODEs)

    First order, linear second order equations, Laplace transformations, Green functions, series method, ...

  • Sturm-Liouville Theory

    The remarkable properties of solutions to self-adjount differential equations

  • Special Functions

    Gamma, Legendre, Hermite, Bessels, Laguerre, Chebyshev even Hypergeometric functions will be our delight

  • Fourier Series & Transforms

    A theorem, computation of coefficients, Fourier transform, Dirac delta-function

  • Partial Diff Equ's (PDEs)

    Waves, diffusion, Schrodinger, Laplace, separation of variables

  • Techniques of Complex Analysis

    Complex number review, analytic functions, integration, integral theorems

  • Tensors

    (Notes) definition and applications

  • Groups

    Introduction, examples, rotations in 3-space, representations, applications

Handy links:

The NIST Digital library of Mathematical Functions.

  • Wolfram Alpha (launches a new tab):

  • Referenced links:

    Curious to see more on the growth and energy discussion? I started with a article in Physics Today (July 2016). Tom's Murphy's Peak Oil piece on Tom's Do the Math blog - I am a fan.

    A more careful statement (pdf) of the existance and uniqueness of solutions.

    Here is pdf of the slope field example we discussed - but did not see! - in class.

    The mathematica intro document in pdf and nb forms.

    Here's a link to the carbon capture article about Climeworks I mentioned on Feb 12.

    Reading (3.9 MB pdf) on Sturm-Liouville theory from Arfken and Weber.

    Michael Berry's Physics Today article on Special Functions.

    Reading on the Frobenius method from Arfken. An example of the method starts on page 395.

    Dirac Notation Primer (There is also a little bit on the notation in Boas, see page 181.)

    The 2019 Special Functions presentation list.

    A video of standing waves on a soap film disk. The Bessel functions are identified. The background music may be safely ignored.

    Info on the cosmic microwave background radiation (CMBR) power spectrum. Here is some old COBE images and new Planck result including polarization data, WMAP (5 yr results). The black body spectrum from COBE which helped win the 2006 Nobel Prize

    BBC news on the Earth's geoid. Here's a page with the expansion of the Earth's gravitational potential in terms of associated Legendre polynominals.

    Lovely Simulations of hydrogenic orbitals from


    Math Methods Poetry (pdf):

    Spring 2017 Creations

    Spring 2009 Creations


    Last modified 10 May 2019

    link to Seth's Net Home link to Department of Physics link to archives link to gr-qc link to gr-qc/new link to archive form