Course No

P602

Credit

4

Approval

Syllabus

- Vectors and Tensors (index notation,vector analysis in curvilinear coordinates. Cartesian tensors and four vectors, General tensors).
- Review of Linear Algebra with emphasis on applications to physical problems (linear transformations + Matrix representations, Eigen values + Eigen Vectors, Innner product spaces).
- Review of complex analysis with applications (Cauchy-Riemann equations, Complex integration, Cauchy theorems, Contour integration, Branch points and branch cuts, Applications to integrals, series etc.)
- Hilbert Space methods, special functions (hilbert space, Orthonormal series expansions in Hilbert space especially Fourier series, Special functions
- Ordinary and partial differential equations (Analysis of second order OFE’s Sturm-Liouville system, Boundary value problems for Laplace Diffusion (Heat) and wave equations)
- Integral transforms, its applications and generalized functions (Laplace and Fourier transform, Dirac delta and other generalized functions, Green’s functions of ODE and PDE)
- Group theory (introduction using various groups occuring in physics, its algebra, Representation of groups, Characters)
- Probability and Statistics (probability distributions, Stochastic processes like Brownian motion, Error analysis for experiments, Statistical inference)

Reference Books

- Arfken and Weber, Mathematical Methods
- C.Harper, Mathematical methods
- T L Chow, Mathematical method for physicists.