|
Complex Antiderivative
In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function ''g'' is a function whose complex derivative is ''g''. More precisely, given an open set U in the complex plane and a function g:U\to \mathbb C, the antiderivative of g is a function f:U\to \mathbb C that satisfies \frac=g. As such, this concept is the complex-variable version of the antiderivative of a real-valued function. Uniqueness The derivative of a constant function is the zero function. Therefore, any constant function is an antiderivative of the zero function. If U is a connected set, then the constant functions are the only antiderivatives of the zero function. Otherwise, a function is an antiderivative of the zero function if and only if it is constant on each connected component of U (those constants need not be equal). This observation implies that if a function g:U\to \mathbb C has an antiderivative, then that antiderivative is unique up to addition of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear engineering, nuclear, aerospace engineering, aerospace, mechanical engineering, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is Analyticity of holomorphic functions, analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |