MA6651 SYLLABUS FOR VIVA-VOCE
Basic Definitions, Examples and Theorems associated with the following topics
Bases and Dimension, Rank-Nullity Theorem, Matrix representation of linear transformations, Diagonalizability, Gram-Schmidt Orthogonalization.
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.
Group Actions, Sylows Theorems, Prime and Maximal Ideals, Principal Ideal Domain.
Analytic functions, Radius of convergence of power series, Cauchy integral formula, Laurents theorem.