topics in probability theory, complex analysis, asymptotic
expansions, group theory, Fourier analysis, Green functions, ordinary
and partial differential equations; and use of Mathematica.
Possible principal texts:
- 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.
Other texts to consider:
- G.B. Arfken and H.J. Weber
Mathematical Methods for Physicists.
- J.J. Kelly
Graduate Mathematical Physics.
Undergraduate courses in intermediate calculus (such as MTH
103 or equivalent) are required. Students must have some
familiarity with partial differentiation, multiple integrals,
infinite series, differential vector calculus (grad, div,
integral vector calculus (divergence and Stokes theorems),
coordinates (spherical and cylindrical),
matrices and determinants, simultaneous linear equations,
Fourier series, and
generating functions, central limit theorem,
residues, contour integration
definitions, examples, applications,
characters, product reps, Clebsch-Gordan coefficients,
irreducible representations, irreducible Tensors, Wigner-Eckart.
convolution, correlation, power spectrum density.
ODEs: exact solutions,
series solutions, Legendre polynomials and functions,
Frobenius method, Bessel functions,
separation of variables,
(Legendre and Spherical Harmonics),
Green's functions, boundary problems.
There is a
2009 Duke University