Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of a complex variable of complex numbers.

Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with …

Nov 10, 2025 · Complex variables are variables that can take on complex numbers as values. A complex number is a number that can be expressed in the form z = x + iy, where x and y are real …

Most of the course will be devoted to adapting the notions of calculus to functions of a complex variable. In doing so, we will revisit familiar ideas (such as limits, derivatives, and integrals), but we shall also …

These notes are about complex analysis, the area of mathematics that studies analytic functions of a complex variable and their properties. While this may sound a bit specialized, there are (at least) two …

Complex numbers are pairs of real numbers (x, y) written as z = x + iy. When x, y run a real line R, corresponding complex number z runs a complex plane C. We have a one-to-one correspondence …

Complex variable, In mathematics, a variable that can take on the value of a complex number. In basic algebra, the variables x and y generally stand for values of real numbers. The algebra of complex …

Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Complex analysis is a basic tool in many mathematical theories. By …

An essential connection between the algebra and geometry of complex numbers is revealed by polar forms of complex multiplication and division. The polar form of the complex number z = x + yi results …

Complex Variables, Francis Flannigan, Dover, 1983. This course is an introduction to the study of functions of a complex variable.