Course Contents

1. Complex variables 2. Vector analysis 3. Group theory

Course Synopsis

1. COMPLEX VARIABLES: Function of complex variable, Cauchy Reimann condition, analytic function, Cauchy integral formula, Taylor and Laurent series, calculus of residues of 1st, 2nd, 3rd, 4th types. 2. VECTOR ANALYSIS: Differentiation of vector field, line integral, surface integral, Green theorem, Gauss's divergence theorem, Gauss's divergence theorem for simple and non simple surface, Stroke's theorem, curvilinear coordinates, differential equation in Physics, related problems. 3. GROUP THEORY: Group, subgroup, cyclic group, langrange theorem, and its application.

Course Learning Outcomes

◆ To learn the complex variables in detail including Cauchy Reimann, Cauchy integral formula, analytic function ◆ To learn Taylor and Laurent series ◆ To different types of Residues ◆ To learn vector analysis in detail and apply them to solve various problems in Physics ◆ To learn the importance of group theory and its basic concept to solve the various problems in Physics.