Selected Topics in Mathematical Physics
Selected Topics in Mathematical Physics. Instructor: Professor V. Balakrishnan, Department of Physics, IIT Madras. A basic course in mathematical methods used in physics. Analytic functions of a complex variable. Calculus of residues, Linear response; dispersion relations. Analytic continuation and the gamma function. Mobius transformations. Multivalued functions; integral representations. Laplace transforms. Fourier transforms. Fundamental Green function for the Laplacian operator. The diffusion equation. Green function for the Helmholtz operator; nonrelativistic scattering. The wave equation. The rotation group and all that. (from nptel.ac.in)
|Lecture 01 - Analytic Functions of a Complex Variable (Part I)|
Complex numbers. Equations to curves in the plane in terms of z and z*. The Riemann sphere and stereographic projection. Analytic functions of z and the Cauchy-Riemann conditions. The real and imaginary parts of an analytic function.
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