Course: MAT 377 3.0 Complex Variables (Compulsory)
Course content:
Complex numbers and their properties, Elementary functions, Limit, continuity, and uniform continuity Complex differentiations, Analytic functions, The Cauchy-Riemann equations and Cauchy’s theorems, Harmonic functions, Liouville’s theorem, Morera’s theorem and maximum modules theorem, Sequences and series, Taylor and Laurent series, Singularities, Residual Theory, Cauchy Residue theorem, Using residue theory to compute some definite integrals, Schwarz lemma, Rouche’s theorem
Recommended Readings:
- Gamelin,T.W. (2001). Complex Analysis. Spring.
- Philips, E.G. (1940). Complex Variables. Dover Books.
- Conway, John B. (1973). Functions of one complex variable. Spring.