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Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex ...
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers.It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable.
As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally, they are power series in the variables z i. Equivalently, they are locally uniform limits of polynomials; or locally square-integrable solutions to the n-dimensional Cauchy–Riemann equations.
Complex analysis is the branch of mathematics investigating holomorphic functions, i.e. functions which are defined in some region of the complex plane, take complex values, and are differentiable as complex functions. Complex differentiability has much stronger consequences than usual (real) differentiability.
Pages in category "Theorems in complex analysis" The following 110 pages are in this category, out of 110 total. This list may not reflect recent changes. A.
This is a glossary of concepts and results in real analysis and complex analysis in mathematics. In particular, it includes those in measure theory (as there is no glossary for measure theory in Wikipedia right now). See also: list of real analysis topics, list of complex analysis topics and glossary of functional analysis
Morera's theorem states that a continuous, complex-valued function f defined on an open set D in the complex plane that satisfies = for every closed piecewise C 1 curve in D must be holomorphic on D. The assumption of Morera's theorem is equivalent to f having an antiderivative on D .