Complex Analysis (MAT 312)




Building on the first year introduction to complex numbers, this course provides a rigorous introduction to the theory of functions of a complex variable. After studying the geometry of the complex plane, it introduces and examines complex-valued functions of a complex variable and their limits, derivatives and integrals. In particular, great care is given to treat the theory of holomorphic functions and the theory of contour integrals in the complex plane.


Revision of complex numbers; geometry in the complex plane; complex differentiation and holomorphic functions; elementary holomorphic functions and their properties; branches of logarithmic functions; , integration in the complex plane; Cauchy's Theorem and integral formula; Taylor series; singularities of complex functions and Laurent series; Residue theory and applications.


ONE tutorial per week.


TWO class tests and ONE final examination.

Last Modified: Tue, 07 Jan 2014 12:03:36 SAST