PHYS 705 - Mathematical Physics

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The second course in a two-semester mathematical physics sequence. Functions of a Complex Variable: Singularities, multivalued functions, principal branch and branch cuts. Differentiability and Cauchy-Riemann equations, analyticity and the Laurent expansion. Contour integration and the calculus of residues. Analytic Continuation, integral transforns, and the Gamma function. Applied Statistics and Probability: Sets, combining sets, independent and conditional probability, Bernnoulli trails, the Central Limit Theorem, the Law of large numbers, Bayes theorem, Random variables, distributions, correlations Stochastic processes, stationary processes, spectral analysis (Fourier analysis), Markoff processes, noise and an introduction to detection theory, Sampling, error propagation, curve fitting, hypothesis testing.