Vectors in classical physics: Differentiation of vectors, fields, Directional derivatives and gradients, Line integrals, Green’s theorem in the Plane, The divergence and divergence theorem, The Curl and Stoke’s theorem.

Differential equations in Physics: First and Second order linear differential equations, Homogeneous and Inhomogeneous solutions, series solution of Differential equations, Partial differential equations in physics, Sturm-Liouville systems, introduction to non linear systems.

Complex variables: Functions of complex variables, Cauchy Riemann conditions and analytic functions, Cauchy integral theorem and integral formula, Taylor and Laurent series, Calculus of residues, Complex integration.

Linear Vector Spaces and Matrices: Linear vector spaces, Gram-schmidt orthogonalization, Matrices, Eigen values and Eigen vectors of a matrix, Hilbert spaces, Orthogonalization.

Special functions: Bessel functions and Hankel functions, Spherical Bessel functions, Legendre Polynomials, Associated Legendre Polynomial, Laugerre Polynomial, Hermite Polynomial.

Integral Transforms: The Laplace transform, Application of Laplace transform, Fourier transform, Convolution and Parseval’s theorem, integral transform solution of partial differential equations, Dirac delta function.

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).