Introduction to complex numbers. Algebraic properties, conjugate, absolute value, geometric representation. Powers and roots.



Functions of complex variables. Introduction to limit, continuity and derivatives. Analytic function, the Cauchy-Riemann equation, Rational functions, polar form and zeros. Basic conformal mapping, basic Riemann surface.



Complex integration, fundamental theorem, Cauchy integral formula, local properties of analytic function. Residues.



Infinite sequence, convergence, uniform convergence. Power series, radius of convergence, Taylor series, Laurent series, partial fraction and factorization, infinite multiplication and total function.




References:

1. Antimirov, M.A., Kolyshkin, A.A. & Vaillancourt, R. (1998). Complex Variables. Academic Press.

2. Brown, J.W. & Churchill, R.V. (2004). Complex Variables and Applications (7th Edition). McGraw Hill.

3. Derrick, W.R. (1984). Complex Variables and Applications (2nd Edition). Wadsworth Inc.