Objectives
We provide an introduction to complex analysis. Complex analysis is a branch of mathematics that involves functions of complex numbers. It provides an extremely powerful tool with an unexpectedly large number of applications, including applied mathematics, physics, and electrical engineering
Course program
Complex Numbers - Complex functions- Limits, continuity, differentiation - Harmonic functions - Curves, contours and simply connected domains - Complex integration - Cauchy's Theorem - Cauchy's integral formula - Maximum modulus principle - Power series - Taylor's series - Laurent's series - Analytic functions - Zero of Analytic functions - Analytic continuation - Singularities and poles - Cauchy's residue theorem.
