Subject Code: PH5L002 Subject Name:  Mathematical Physics L-T-P: 3-0-0 Credit: 3
Pre-requisite(s):Nil
Vector Analysis: Gradient, divergence, and curl in curvilinear co-ordinate system; Tensor Analysis: Contraction, Direct Product, Quotient Rule, Pseudo-tensors, Dual tensors, General Tensors, Tensor Derivative Operators; Determinants and Matrices: Orthogonal, Hermitian and Unitary Matrices, Diagonalization of Matrices; Linear Algebra: Vector spaces, Inner products, Gram-Schmidt orthogonalization,  Linear transformations, eigenvalues and eigenvectors, Hilbert space; Complex analysis: Cauchy-Riemann conditions, Cauchy’s theorem, Taylor and Laurent series, Singularities, Calculus of residues, Conformal mapping; Differential Equations: Partial and First order equations, Series solution-Frobenius' method, Laplace equation, Separation of variables, Sturm-Liouville theory; Special Functions: Legendre, Bessel, Hermite and Laguerre functions; Integral Transforms: Fourier and Laplace transforms, applications; Probability: Random variables, binomial, Poisson and normal distributions, central limit theorem; Introductory Group theory: Lie groups, generators and representations.
Text/Reference Books:
  1. Arfken George B., Weber Hans J., Harris Frank E, Mathematical Methods for Physicists: A Comprehensive Guide, Academic Press.
  2. Lawson T., Linear Algebra, John Wiley & Sons.
  3. Churchill R. V. and Brown J.W., Complex Variables and Applications, McGraw-Hill.
  4. Harper Charlie, Introduction to Mathematical Physics, Prentice-Hall of India Pvt. Ltd.
  5. Boas Mary L., Mathematical Methods in Physical Sciences, John Wiley & Sons
  6. Wyld H.W., Mathematical Methods for Physics, Westview Press.
  7. Mathews and Walker, Benjamin W.A. Mathematical Methods of Physics
  8. Dennery P. and Krzywicki A., Mathematics for Physicists, Dover Publications.