Objectives : To introduce to students the basic techniques of mathematical Physics to pose and solve physical problems.
Course Contents : 1. Vecotrs and Tensors Vector calculus and tensors in index notation.
2. Linear Algebra Linear vector spaces, Dirac notation. Basis sets, Inner Products. Orthonormality and completeness. Gram-schmidt orthonormalization process. Linear operators, Matrix algebra, similarity transforms, diagonalization, orthogonal, Hermitian and unitary matrices. Spaces of square summable sequences and square integrable functions, generalized functions, Dirac delta function and its represenations. Differential operators, Fourier series.
3. Ordinary Differential Equations Power series solutions for second-order ordinary differential equations. singular poinrts of ODEs. Sturm-Liouville problems. Hermite, Legendre, Laugerre and Bessel fucntions. Recurrence relations and generating functions. Spherical harmonics. Addition theorem, Gamma, beta and error functions.
4. Probability theory and Random variables Probablity distributions and probability densities. Standard discrete and continous probablility distributions. Moments and generating fucntions. Central Limit Theorem (Statement and applications)
1 Schaum's outline series, Mcgraw Hill (1964):
(i) Vector and tensor analysis (ii) Linear Algebra
(iii) Differential Equations, (iv) Probability, (v) Statistics
2. M. Boas, Mathematical Methods in Physics Sciences, 2nd Edition, Wiley International Edition, (1983).
3. E. Kreyszig, Advanced Engineering Mathematics, Wiley Eastern, 5th Edition (1991).
4. E. Kreyszig, Introductory Fucntional Analysis and Applications, John Wiley, (1978)
5. P. R. Halmos, Finite Dimensional Vector Spaces, Prentice-Hall India. (1988).