Tensors in Physics: Tensor Algebra, Vectors on manifolds, the fundamental tensors, Tensors in non-relativistic Physics, Tensor calculus, Kinematics in Riemannian space, Riemann-Christoffel tensor.

Boundary value Problem and Green’s Functions: Boundary value problems in physics, Non-homogeneous boundary value problems and Green’s functions, Green’s functions for one dimensional problems, Eigen function expansion of Green’s function, Construction of Green’s functions, Green’s function in higher dimensions, Quantum mechanical scattering problems.

Integral equations: Classifications of integral equations, Neumann-series solutions, The Fredholm alternatives, Fredholm and Volterra equations, integral equations and Green’s functions.

Group theory: Groups, Invariant subgroups and factor groups, Group representation, Character of a representation, Character tables, Decomposition of a reducible representation into irreducible ones, Lie groups and Lie algebras, The special unitary groups SU(2) and SU(3), Irreducible representation of SO(3) and SU(3), Some applications of group theory in physics.

Recommended Text:
1. G. B. Arfken, “Mathematical Methods for Physicists”, Academic Press Inc. (1995).
2. M. L. Boas, “Mathematical Methods in Physical sciences”, John Wiley and Sons, New York (1989).
3. P. K. Chattopadhyay, “Mathematical Physics”, Wiley eastern Limited, New Delhi (1990).
4. H. Cohen, “Mathematics for Scientists and Engineers”, Prentice Hall international Inc., New Jersey (1992).
5. E. Kreyszig, “Advanced Engineering Mathematics”, John Wiley and Sons, 7th edition (1993).