M. Sc Physics

Unit-I: Complex Analysis
Introduction. Complex Functions, Calculus of Complex Functions: Limits, Continuity
Differential Coefficients, C-R Equations, Analytic Functions- Applications to Flow
Problems. Transformations with Special Reference to Conformal Transformations
Integrations-Theorems, Series (without-proof) and Evaluation of Certain Integrals. Zeros,
Singular Points, Residues and Residue Theorem (without-proof).
Unit-II: Ordinary Differential Equations
Ordinary Differential Equations of the First Order and First Degree and Higher and their
Solutions. Linear Differential Equations with Constant Coefficients. Physical
Applications.
Unit-III: Discrete Mathematics:
Introduction to Various Types of Matrices, Matrix Arithmetic. Incidence, Adjacency,
Path and Circuit Matrix, Fundamental Circuit matrices A, B and C of Digraphs (Directed
graphs).
Unit IV: Special Functions
Gamma Function, Beta Function, Dirichlet’s Integral, Bessel’s Equation and its
Functions, Recurrence Formulae for Jn(x), Generating Function for Jn(x) Orthogonality,
Legendre’s Equation; Rodrigue’s Formula, Legendre Polynomials Pn, Generating
Function for Jn(x), Orthogonality of Legendre Polynomials, Laguerre’s Polynomials,
Hermite’s Polynomials.