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: