KUK - LMS

Syllabus

MODULE NO / UNIT	COURSE SYLLABUS CONTENTS OF MODULE	NOTES
Course Code: PHY 101 Course Name: Mathematical Physics
1	Group Theory (14 hrs.) Fundamentals of Group theory: Definition of a group and illustrative examples, Group multiplication table, rearrangement theorem, cyclic groups, sub-groups and cosets, permutation groups, conjugate elements and class structure, normal devisors and factor groups, isomorphism and homomorphism, class multiplication. Group representation: Reducible and irreducible representations, great orthogonality theorem (without proof) and its geometric interpretation, character of a representation, construction of character table with illustrative examples of symmetry groups of equilateral triangle, rectangle and square. Decomposition of reducible representation, the regular representation. The elements of the group of Schrodinger equation.
2	Fourier Series and Integral Transforms (12 hrs.) Fourier series, General properties, Advantages and applications, Gibbs phenomenon, Development of the Fourier integral, Inversion theorem, Fourier transform, Fourier transform of derivatives, Momentum representation, Laplace transform, Laplace transform of derivative, Properties of Laplace transforms, Faltungs theorem, Inverse Laplace transformation.
3	Special Functions (12 hrs.) Bessel Functions: Bessel functions of the first kind Jn(x), Generating function, Recurrence relations, Expansion of Jn(x) when n is half an odd integer, Integral representation; Legendre Polynomials Pn(x): Generating function, Recurrence relations and special properties, Rodrigues' formula, Orthogonality of Pn(x); Associated Legendre polynomials, Spherical harmonics, Addition theorem for spherical harmonics, Hermite and Laguerre Polynomials: generating function & recurrence relations only.
4	Functions of a complex variable and calculus of residues (10 hrs.) Complex algebra, Functions of a complex variable, Cauchy’s integral theorem, Cauchy's integral formula; Taylor and Laurent expansions; Singularities; Cauchy's residue theorem, Cauchy principle value, Singular points and evaluation of residues, Jordan's Lemma; Evaluation of definite integrals of the type: ∫_0^2π▒〖f(sin⁡〖θ,cos⁡〖θ) dθ〗〗〗; ∫_(-∞)^∞▒f(x)dx; ∫_(-∞)^∞▒〖f(x) e^iax dx〗 using Cauchy’s residue theorem. Exercises in this unit are at the level of those given in book at Ref. No. 2.