Subject: Mathematical Physics
Subject Code: 09020101
|S.N||Topic||Domain||Hours as per UGC|
|1||VECTOR SPACES, TENSORS AND MATRICES
· Vector spaces: Introduction, definition of linear vector space
· linear independence, basis and dimension, scalar product, orthonormal basis,
· Gram-Schmidt Orthogonalization process, Linear operators,
· Covariant and Contravariant tensors,
· symmetric and skew-symmetric tensor,
· product of tensors,
· Metric tensors, Matrices,
· Orthogonal, Unitary and Hermition Matrices,
· Eigen values & Eigen vectors,
· Matrix diagonalization.
|2||DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS
· First order equation, second order equation with variable coefficients.
· ordinary point, singular point, series solution around an ordinary point and regular singular point,
· solution of Legendre equation,
· solution of Bassel’s equation,
· solution of Hermite & Lageurre equations.
· Definitions and properties of special functions:
· Bessel functions,
· Legendre polynomials,
· Hermite polynomials and
· Lageur repolynomials along with Recurrence relations.
· Function of complex variable,
· limit, continuity and differentiability of function of complex variables,
· Analytic function, Cauchy-Riemann conditions,
· Cauchy s integral theorem,
· Cauchy s Integral formula,
· Taylor s and Laurent s series,
· singular points, residues, evaluation of residues,
· Cauchy’s residue theorem,
· Jordan s lemma,
· evaluation of real definite integrals
Nice to know
· Fourier series, Dirichlet’s conditions,
· Fourier series of arbitrary period,
· Half-wave expansions, development of the Fourier integral,
· Fourier integral theorem,
· Fourier transforms, Properties of Fourier transform, Convolution theorem,
· Fourier transform of Dirac Delta function,
· Laplace transform, first and second shifting theorem,
· Laplace transforms of derivatives and integral of a function, convolution theorem,
· Inverse Laplace transform by partial fraction and by using convolution theorem,
· application of Laplace transform in solving differential equations.
Nice to know
1. G. Arfken and H.J. Weber. Mathematical Methods for Physicists. San Diego: Academic Press.
2. A.W. Joshi. Matrices and Tensors in Physics. New Delhi: Wiley Eastern.
3. P.K. Chatopadhyay. Mathematical Physics. New Delhi: Wiley Eastern.
4. C. Harper. Introduction to Mathematical Physics. New Delhi: Prentice Hall of India.
5. M.L. Boas. Mathematical Methods in the Physical Sciences. New York: John Wiley.
6. L .Pipes and L.R. Horwell. Applied Mathematics for Engineers and Physicists.
7. Mary L. Boas. Mathematics for Physicists.
8. B.S. Rajput. Mathematical Physics.
9. A. K. Ghatak and I. C. Goyal. Mathematical Methods for Physicists.