## 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 16 - Multivalued Functions; Integral Representations (Part III) |

Contour integral representations for the beta function and the Riemann zeta function. Connection with Bernoulli numbers. Zeroes of the zeta function. Statement of the Riemann hypothesis.

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