## 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 18 - Laplace Transforms (Part I) |

Definition of the Laplace transform. The convolution theorem. Laplace transforms of derivatives. The inverse transform, Mellin's formula. The LCR series circuit. Laplace transform of the Bessel and modified Bessel functions of the first kind. Laplace transforms and random processes: the Poisson process.

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