Courses Catalogue

Methods Of Mathematical Physics

COURSE CODE: PHY7101
COURSE CREDIT UNIT: 4
ACADEMIC PROGRAMME: Physics, Masters
COLLEGE/SCHOOL/FACULTY: School of Natural and Applied Sciences
STATUS: Core
PROGRAMME TYPE: Postgraduate

Course Content and Outline

Linear Vector Spaces  (12 HOURS)

Linear operators - Representation of vectors and operators in a basis - Linear independence, dimension -Inner product - Schwarz inequality - Orthonormal basis -Gram-Schmidt Process.

Linear Differential Equations and Green’s Function  (12 HOURS)

Second order linear differential equations - Sturm - Liouville Theory – Orthogonality of eigen functions - Illustration with Legendre, Laguerre, Hermite, and Chebyshev differential equations - Location of zeros of these polynomials - Wronskian, ordinary and singular points.

Green‘s function – Eigen function expansion of the Green‘s function - Reciprocity theorem - Sturm – Liouville type equations in one dimension and their Green‘s function.

Complex Variables  (12 HOURS)

Functions of a complex variable - Single and multivalued functions - Analytic functions - Cauchy - Riemann conditions- Singular points - Cauchy‘s theorem and integral formulae- Taylor and Laurent expansions - Zeros and poles – Residue theorem and its applications.

Laplace and Fourier Transforms (12 HOURS)

Laplace transforms - Solution of linear differential equations with constant coefficients - Fourier integral - Fourier transforms, Fourier sine and cosine transforms - Convoltion theorems - Applications.

Group Theory (12 HOURS)

Basic definitions - Lagrange‘s Theorem – Invariant subgroup - Homomorphism and Isomorphism between groups - Representation of a group - unitary representations -Schur‘s lemmas - Orthogonality theorem - Character table- Simple applications to symmetry groups and molecular vibrations.

MODE OF DELIVERY

  • Lectures and discussions
  • Reading and problem assignments

 INSTRUCTIONAL MATERIALS AND / OR EQUIPMENT

  • Whiteboard and Markers
  • Flip Charts
  • LCD Projectors
  • CDs, DVDs and Tapes