University of Arizona 3 credits Mathematics
Complex Analysis: variables; functions; analyticity; integrals; residue calculus; saddle-point method. Fourier Analysis: Fourier transform; Fourier series; delta-function; Riemann-Lebesgue lemma; Gibbs phenomenon. Ordinary Differential Equations: parameter variations; integrals of motion; phase portraits; perturbative analysis; Green's functions; Sturm-Liouville theory. Partial Differential Equations: method of characteristics; classification of second order linear (elliptic, hyperbolic, parabolic); separation of variables for boundary value problems; nonlinear examples. Other topics as chosen by the instructor.
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