several complex variables
Several complex variables is a branch of mathematics that studies functions of multiple complex numbers. Unlike single-variable complex analysis, which focuses on functions of one complex variable, this field explores how these functions behave when more than one complex variable is involved. It has applications in various areas, including theoretical physics, engineering, and applied mathematics.
In this area, mathematicians analyze properties such as continuity, differentiability, and singularities of functions. The study often involves concepts like holomorphic functions, Cauchy-Riemann equations, and Riemann surfaces. Understanding several complex variables can lead to insights in both pure and applied mathematics, enhancing our grasp of multidimensional phenomena.