Complex analysis

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Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that studies complex-valued functions of one or more complex variables. It is used in many branches of mathematics, including functional analysis, algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. It also has applications in engineering fields, such as nuclear, aerospace, mechanical, and electrical engineering. Complex analysis primarily studies holomorphic functions, which are differentiable functions of a complex variable. In contrast with a differentiable real function, a holomorphic function is always infinitely differentiable and equal to the sum of its Taylor series in some neighborhood of each point of its domain. This makes methods and results of complex analysis significantly different from those of real...

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