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:
- Arfken George B., Weber Hans J., Harris Frank E, Mathematical Methods for Physicists: A Comprehensive Guide, Academic Press.
- Lawson T., Linear Algebra, John Wiley & Sons.
- Churchill R. V. and Brown J.W., Complex Variables and Applications, McGraw-Hill.
- Harper Charlie, Introduction to Mathematical Physics, Prentice-Hall of India Pvt. Ltd.
- Boas Mary L., Mathematical Methods in Physical Sciences, John Wiley & Sons
- Wyld H.W., Mathematical Methods for Physics, Westview Press.
- Mathews and Walker, Benjamin W.A. Mathematical Methods of Physics
- Dennery P. and Krzywicki A., Mathematics for Physicists, Dover Publications.
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