This is a course on complex functions. The treatment is rigorous. Starting from complex numbers, we study some of the most celebrated theorems in analysis, for example, Cauchy's theorem and Cauchy's integral formulae, the theorem of residues and Laurent's theorem. The course lends itself to various applications to real analysis, for example, evaluation of definite integrals and finding the number of zeros of a complex polynomial in a region. Edited by Michael Singer, professor of mathematics at University College London.

## Cauchy's Theorem and its Consequences

## Cauchy's Theorem and Green's Theorem