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What (who) is complex analysis - definition

Complex analysis

BRANCH OF MATHEMATICS STUDYING FUNCTIONS OF A COMPLEX VARIABLE

Complex function; Theory of analytic functions; Complex variable; Function of a complex variable; Complex functions; Complex variables; Functions of a complex variable; Complex analytic; Complex-valued function; Complex map; Complex function theory; Complex variable analysis; Theory of complex variable; Complex Analysis; Theory of functions of a complex variable; History of 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, 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, aerospace, mechanical and electrical engineering.

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).

https://en.wikipedia.org/wiki/Complex_analysis

List of complex analysis topics

WIKIMEDIA LIST ARTICLE

Outline of complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.

https://en.wikipedia.org/wiki/List_of_complex_analysis_topics

König's theorem (complex analysis)

THEOREM ABOUT SIMPLE POLES OR SIMPLE ROOTS OF A MEROMORPHIC FUNCTION

Konig's theorem (complex analysis)

In complex analysis and numerical analysis, König's theorem, named after the Hungarian mathematician Gyula Kőnig, gives a way to estimate simple poles or simple roots of a function. In particular, it has numerous applications in root finding algorithms like Newton's method and its generalization Householder's method.

https://en.wikipedia.org/wiki/König's_theorem_(complex_analysis)

Examples of use of complex analysis

1. Therefore, Ivanov has recently been presented on television assort of an adviserto Putin, offering the president a complex analysis of the national economy.