Five year integrated MSc Degree Course in Photonics.pdf

Tensors- Tensor Analysis - Definition, law of transformations, rank of tensor, covariant and
contravariant tensors, algebra of tensors, lowering and raising of indices, contraction of tensors,
fundamental tensors, metrics.
Cartesian tensors, Stress, strain and Hooke's law and moduli of elasticity, Piezo electricity and
dielectric susceptibility.
MODULE 2
Vector space - Field, definition of vector space, innerproduct, norm, dual vectors and dual space,
Bra and ket notations, linearly independent and dependent vectors, orthonormal vectors. Schmidt's
othogonalisation . basis, dimension, change of basis, linear operator, adjoint and hermitian
operators, matrix representation of operators, similarity and unitary transformations. eigen value
and eigen vectors, projection operator, function space. Hilbert space.
MODULE 3
Partial Differential equations- Separation of variables technique. Laplace's equation in
rectangular, cylindrical and spherical polar coordinates.
Differential equations- Series solution, ordinary and singular points. examples, Frobenius
method, examples. Green's function technique to solve differential equations.
MODULE 4
Sturm -Liouville Problem- Hermitian differential equations. Orthogonal functions. Legendre,
Bessel and Hermite differential equations and their solutions, Legendre, Bessel and Hermite
functions and their properties , Spherical Harmonics .
Fourier Series. Beta and gamma functions. Properties of beta and gamma functions. Laplace
transform, Laplace Transforms of some simple functions. Solving differential equations using
LT.
REFERENCES
25
Vector analysis with an introduction to tensor analysis- Murray R Speigel, Tata McCraw
Hill (1975)
Matrices and tensors for physicists- A W Joshi, New Age International (1995)
Linear vector space - Hamos
Mathematics for physicists and engineers-G B Arfken, Academic Press (2001)
Mathematics for Physicists - Dennery and Kerzywiki
Mathematical Methods for Physicists -GB Arfken, H J Weber, Academic Press (2001)
A textbook of Mathematical Physics - P K Chakrabarti. SN Kundu Books and Allied Pub,
Calcutta (1996)
Mathematical Methods in Classical and Quantum Physics Tulsi Dass. S K Sharma;
University Press (1896)
Mathematical Physics- Differential equations and Transform Theory, A K Ghatak, 1C Goyal.
S J Chua McMillan India Ltd. (2002)
Mathematical Physics (Parts 1.2 and 3)- J D Anand, P K Mittal, A Wadhwa Har, Anand
Publications, ( 2003)
CENTRE OF EXCELLENCE IN LASERS AND OPTOELECTRONICS SCIENCES