### MA6651 SYLLABUS FOR VIVA-VOCE

#### Course Details

Basic Definitions, Examples and Theorems associated with the following topics

Linear Algebra:

Bases and Dimension, Rank-Nullity Theorem, Matrix representation of linear transformations, Diagonalizability, Gram-Schmidt Orthogonalization.

Real Analysis:

Continuous functions, Completeness, Connectedness, Uniform convergence.

Ordinary Differential Equations:

Exact solutions of first order ODE, The method of successive approximations, Existence and Uniqueness of solutions of initial value problem, Wronskian, Method of variation of parameters.

Algebra I:

Group Actions, Sylows Theorems, Prime and Maximal Ideals, Principal Ideal Domain.

Complex Analysis:

Analytic functions, Radius of convergence of power series, Cauchy integral formula, Laurents theorem.

#### Course References: