Mathematical Physics

Course Description

This is a one-semester graduate course on mathematical physics, centered on special functions and the differential equations that produce them. Following Novak and Fox’s Special Functions of Mathematical Physics: A Tourist’s Guidebook, the course covers complex analysis, Gamma/Beta/Zeta functions, Frobenius series, Sturm-Liouville theory, Bessel functions, Hankel transforms, spherical harmonics, and classical orthogonal polynomials.

Course Material

The primary textbook is Kyle A. Novak with Laura J. Fox, Special Functions of Mathematical Physics: A Tourist’s Guidebook. A free PDF is available from Equal Share Press.

References

The following references are recommended:

[1] K. A. Novak with L. J. Fox, Special Functions of Mathematical Physics: A Tourist’s Guidebook, Equal Share Press, 2018.
[2] G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 7th ed., Academic Press, 2013.
[3] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, 1965.
[4] F. W. J. Olver et al., eds., NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/.
[5] N. N. Lebedev, Special Functions and Their Applications, Dover, 1972.
[6] C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer, 1999.