Course: MAT 377 3.0 Complex Variables (Compulsory)
Course content: Complex Numbers and Elementary Functions: Complex numbers and their properties, Elementary functions, Limits and continuity; Analytic Functions: Differentiation of complex functions, Analytic functions, The Cauchy-Riemann equations, Harmonic functions, Singularities; Integration of Complex Functions: Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Morera’s theorem, and Maximum-modulus theorems; Sequences and Series of Complex Functions: Sequences and series, Taylor and Laurent series; Calculus of Residue: Cauchy’s residue theorem, Compute some definite integrals and sum of series, The argument principle and Rouche’s theorem.
Recommended Readings:
Foundation of Complex Analysis by S. Ponnusamy, Complex variables – Schaum’s Outline Series