Complex Analysis

Course Objectives: This course aims to introduce the basic ideas of analysis for complex functions in complex variables with visualization through relevant Practicals. Particular emphasis has been laid on Cauchy’s theorems, series expansions and calculation of residues. Course Learning Outcomes: The completion of the course will enable the students to: i) Understand the significance of differentiability of complex functions leading to the understanding of Cauchy-Riemann equations. ii) Evaluate the contour integrals and understand the role of Cauchy-Goursat theorem and the Cauchy integral formula. iii) Expand some simple functions as their Taylor and Laurent series, classify the nature of singularities, find residues and apply Cauchy Residue theorem to evaluate integrals. iv) Represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem.