Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including 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. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.^[1]

Not to be confused with Complexity theory.

As a differentiable function of a complex variable is equal to 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.

Complex geometry

Hypercomplex analysis

Vector calculus

List of complex analysis topics

Monodromy theorem

Real analysis

Riemann–Roch theorem

Runge's theorem

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Ablowitz, M. J.

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Henrici, P.

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Theory of Functions of a Complex Variable, (Prentice-Hall, 1965). [Three volumes.]

Markushevich, A. I.

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Marsden

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