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Complex Variables and Applications, McGraw-Hill, 1st edition 1948, 2nd edition 1960, The 3rd (1974) and later editions were co-authored with James Ward Brown; Fourier Series and Boundary Value Problems, McGraw-Hill, 1941, 2nd edition 1963 [4] Modern Operational Mathematics in Engineering, McGraw-Hill, 1944 [5]
It is also called Osgood–Brown theorem is that for holomorphic functions of several complex variables, the singularity is a accumulation point, not an isolated point. This means that the various properties that hold for holomorphic functions of one-variable complex variables do not hold for holomorphic functions of several complex variables.
As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, holomorphic functions. The concept can be extended to functions of several complex variables.
The path C is the concatenation of the paths C 1 and C 2.. Jordan's lemma yields a simple way to calculate the integral along the real axis of functions f(z) = e i a z g(z) holomorphic on the upper half-plane and continuous on the closed upper half-plane, except possibly at a finite number of non-real points z 1, z 2, …, z n.
In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators [1]), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives ...
The definition of a complex analytic function is obtained by replacing, in the definitions above, "real" with "complex" and "real line" with "complex plane". A function is complex analytic if and only if it is holomorphic i.e. it is complex differentiable. For this reason the terms "holomorphic" and "analytic" are often used interchangeably for ...
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves.
Many titles on advanced topics are also available, such as complex variables and topology, but these may be harder to find in retail stores. Schaum's Outlines are frequently seen alongside the Barron's "Easy Way" series and McGraw-Hill's own "Demystified" series. The "Demystified" series is introductory in nature, for middle and high school ...
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