- List of complex analysis topics
-
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.
Contents
Overview
- Complex numbers
- Complex functions
- Complex derivative
- Holomorphic functions
- Harmonic functions
- Elementary functions
- Polynomial functions
- Exponential functions
- Trigonometric functions
- Logarithmic functions
- Inverse trigonometric functions
- Residue theory
Related fields
- Number theory
- Hydrodynamics
- Thermodynamics
- Electrical engineering
Local theory
- Holomorphic function
- Antiholomorphic function
- Cauchy-Riemann equations
- Conformal mapping
- Power series
- Radius of convergence
- Laurent series
- Meromorphic function
- Entire function
- Pole (complex analysis)
- Zero (complex analysis)
- Residue (complex analysis)
- Isolated singularity
- Removable singularity
- Essential singularity
- Branch point
- Principal branch
- Weierstrass-Casorati theorem
- Landau's constants
- Holomorphic functions are analytic
- Schwarzian derivative
- Analytic capacity
- Disk algebra
Growth
- Bieberbach conjecture
- Borel-Carathéodory theorem
- Hadamard three-circle theorem
- Hardy space
- Maximum modulus principle
- Nevanlinna theory
- Picard's theorem
- Paley-Wiener theorem
- Value distribution theory of holomorphic functions
Contour integrals
- Line integral
- Cauchy integral theorem
- Cauchy's integral formula
- Residue theorem
- Liouville's theorem (complex analysis)
- Examples of contour integration
- Fundamental theorem of algebra
- Simply connected
- Winding number
- Principle of the argument
- Rouché's theorem
- Bromwich integral
- Morera's theorem
- Mellin transform
- Kramers–Kronig relation
Special functions
- Exponential function
- Beta function
- Gamma function
- Riemann zeta function
- Elliptic function
- Elliptic modular function
- J-function
- Modular function
- Modular form
Riemann surfaces
- Analytic continuation
- Riemann sphere
- Riemann surface
- Riemann mapping theorem
- Carathéodory's theorem (conformal mapping)
- Riemann-Roch theorem
Other
- Antiderivative (complex analysis)
- Bôcher's theorem
- Cayley transform
- Complex differential equation
- Harmonic conjugate
- Hilbert's inequality
- Method of steepest descent
- Montel's theorem
- Periodic points of complex quadratic mappings
- Pick matrix
- Runge approximation theorem
- Schwarz lemma
- Weierstrass factorization theorem
- Mittag-Leffler's theorem
Several complex variables
- Analytization trick
- Biholomorphy
- Cartan's theorems A and B
- Cousin problems
- Edge-of-the-wedge theorem
- Several complex variables
History
Main article: History of complex analysisPeople
- Augustin Louis Cauchy
- Leonhard Euler
- Carl Friedrich Gauss
- Jacques Hadamard
- Kiyoshi Oka
- Bernhard Riemann
- Karl Weierstrass
Outlines - General reference
- Culture and the arts
- Geography and places
- Health and fitness
- History and events
- Mathematics and logic
- Natural and physical sciences
- People and self
- Philosophy and thinking
- Religion and belief systems
- Society and social sciences
- Technology and applied sciences
Categories:- Mathematics-related lists
- Complex analysis
- Outlines
Wikimedia Foundation. 2010.