Course Details

Subject {L-T-P / C} : MA2104 : Complex Analysis { 3-1-0 / 4}

Subject Nature : Theory

Coordinator : Sangita Jha

Syllabus

Module 1 (10 hours) Complex numbers, functions, algebra of complex numbers, limit, continuity, differentiability, analytic function, Cauchy Riemann equations, Laplace equation, Harmonic function.
Module 2 (8 hours) Branch point and branch cut, multivalued functions, Linear fractional transformations, Conformal mapping.
Module 3 (10 hours) Complex integration, line integral in the complex plane, Cauchy's theorem, Cauchy integral theorem, Cauchy integral formula, Liouville's theorem, Morera's theorem.
Module 4 ( 10) Sequence and series of complex functions, convergence test, power series, Taylor's, Maclaurin's and Laurent's series, uniform convergence, zeros, limit point of zeros, singularities, poles, residue theorem, evaluation of real integrals.

Course Objectives

Course Outcomes

CO1: Students will gather the knowledge of complex variables, complex functions, and multivalued functions.
CO2: They will learn to evaluate the complex integrals.
CO3: They will understand the Cauchy's theorem in different domains.
CO4: They will learn the singularities and zeros of complex functions and will be able to evaluate their residues.
CO5: They can compute the sum of complex series and real definite integrals. They will have the ability to use techniques from complex analysis and apply them to diverse fields in real-life problems.

Essential Reading

Supplementary Reading