**PH-601 Methods of Mathematical Physics**

- Fourier series: introduction and general properties, convergence of trigonometric series, Gibbs phenomenon, Parseval’s theorem, applications to various phenomena.
- Integral transform, development of the Fourier integral, Fourier transform, inversion theorems, Fourier transform of derivatives, convolution theorem, momentum representation, transfer functions.
- Complex arguments in Fourier transforms. Laplace transform, Laplace transform of derivatives, convolution products and Faltung’s theorem, inverse Laplace transform.
- Partial differential equations. Separation of variables in three dimensions, method of characteristics. Boundary value problems.
- Integral transforms, generating functions, Neumann series, separable (degenerate) kernels, Hilbert–Schmidt theory, integral equations.
- Calculus of variations: dependent and independent variables, Euler-Lagrange equation and applications, several independent and dependent variables, Lagrange multipliers, variational principle with constraints, Rayleigh–Ritz variational technique, application to discrete mesh.
- Nonlinear methods and chaos, the logistic map, sensitivity to initial conditions and parameters, nonlinear differential equations.
- Probability: definitions and simple properties, random variables, binomial distribution, Poisson distribution, Gauss's normal distributions, statistics.

**Recommended texts:**

*Mathematical Methods for Physicists*, Arfken & Weber (Academic Press, 6th edition, 2005).*Mathematical Methods for Physicists,*Tai L. Chow (Cambridge University Press, 2002).