- Domain (complex analysis)
In
complex analysis a domain usually means an open connectedsubset of thecomplex plane or of .
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Domain (complex analysis)
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Domain (mathematical analysis) — In mathematical analysis, a domain is any connected open subset of a finite dimensional vector space. This is a different concept than the domain of a function, though it is often used for that purpose, for example in partial differential… … Wikipedia
Complex analysis — Plot of the function f(x)=(x2 1)(x 2 i)2/(x2 + 2 + 2i). The hue represents the function argument, while the brightness represents the magnitude. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch … Wikipedia
Antiderivative (complex analysis) — 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 the antiderivative … Wikipedia
Pole (complex analysis) — The absolute value of the Gamma function. This shows that a function becomes infinite at the poles (left). On the right, the Gamma function does not have poles, it just increases quickly. In the mathematical field of complex analysis, a pole of a … Wikipedia
Liouville's theorem (complex analysis) — In complex analysis, Liouville s theorem, named after Joseph Liouville, states that every bounded entire function must be constant. That is, every holomorphic function f for which there exists a positive number M such that | f ( z )| ≤ M for all… … Wikipedia
Domain coloring — plot of the function ƒ(x) =(x2 − 1)(x − 2 − i)2/(x2 + 2 + 2i). The hue represents the function argument, while the saturation represents the magnitude. Domain coloring is a technique for… … Wikipedia
Domain — may refer to: General Territory (administrative division), a non sovereign geographic area which has come under the authority of another government Public domain, a body of works and knowledge without proprietary interest Eminent domain, the… … Wikipedia
Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics … Wikipedia
analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… … Universalium
Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… … Wikipedia
