Description

This unit provides an introduction to the theory of functions of a complex variable, the geometry of complex numbers and conformal transformations. Applications include a discussion on fractals such as Julia and Mandelbrot sets. The theory of functions of a complex variable is one of the most beautiful parts of mathematics which provides the foundations of very powerful techniques widely used in almost all areas of mathematics and physics and also in other science disciplines, engineering and technology. Topics include complex numbers and transformations in the complex plane; complex functions; analyticity; Cauchy's theorem; Cauchy's formula; method of residues; series expansion; conformal mappings; dynamics of quadratic polynomials of a complex variable—Julia and Mandelbrot sets.

For more info see : http://handbooks.uwa.edu.au/units/math/math3342