Mathématiques 04

Complex analysis is a branch of mathematics that deals with complex numbers, their functions, and their calculus. In simple terms, complex analysis is an extension of the calculus of real numbers to the complex domain. We will extend the notions of continuity, derivatives, and integrals, familiar from calculus to the case of complex functions of a complex variable. In doing so we will come across analytic functions, which form the centerpiece of this introduction. In fact, to a large extent complex analysis is the study of analytic functions.