- K.F. Riley, M.P. Hobson and S.J. Bence
*Mathematical Methods for Physics and Engineering*. - D.A. McQuarrie
*Mathematical Methods for Scientists and Engineers*.

- G.B. Arfken and H.J. Weber
*Mathematical Methods for Physicists*. - J.J. Kelly
*Graduate Mathematical Physics*.

- Probability: distributions, generating functions, central limit theorem, stochastic processes.
- Complex Variables: analytic functions, complex integrals, residues, contour integration asymptotic expansions.
- Group Theory: definitions, examples, applications, representations, characters, product reps, Clebsch-Gordan coefficients, irreducible representations, irreducible Tensors, Wigner-Eckart.
- Fourier transforms, delta functions, convolution, correlation, power spectrum density.
- ODEs: exact solutions, series solutions, Legendre polynomials and functions, Frobenius method, Bessel functions, eigenfunctions, orthogonal functions, Sturm-Liouville theory, Green's functions, qualitative methods, numerical methods.
- PDEs: separation of variables, cylindrical coordinates (Bessel), spherical coordinates (Legendre and Spherical Harmonics), Green's functions, boundary problems.

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Copyright © 2009 Duke University

Copyright © 2009 Duke University