Everything about Complex analysis
Branch of mathematics studying functions of a complex variable
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. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Complex analysisA 5-minute orientation
- Skim a recent paper: A Critical Analysis on Complex Urban Systems and Complex Systems TheoryInfluential work since 2022
- Pick up a classic book: A course of modern analysisThe most-reprinted book on the subject
- Read the landmark paper: OLEX2 : a complete structure solution, refinement and analysis programCited 32,778 times
- Go sideways: Cauchy–Riemann equationsA closely related topic
- Go sideways: Holomorphic functionA closely related topic
đź“– Definitions
Noun The branch of mathematics that studies holomorphic functions.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
OLEX2 : a complete structure solution, refinement and analysis program
An analysis of variance test for normality (complete samples)
Complex seismic trace analysis
Human complex sound analysis*
Curvature and complex analysis
Advanced Complex Trait Analysis
Complexity in Complex Analysis
Complex analysis and differential topology on complex surfaces
🆕 Influential since 2022
đź“š Books worth reading
A course of modern analysisE. T. Whittaker, G. N. Watson · 1902
Advances in Swarm IntelligenceYing Tan · 2012
Multivariable calculusJames Stewart · 1989
Complex AnalysisLars Valerian Ahlfors · 1953
Thinking in systemsDonella H. Meadows, Diana Wright · 2008
Crusaders for American liberalismLouis Filler · 1939
Complex analysisSerge Lang · 1977
Introduction to complex analysisH. A. Priestley · 1985
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Cauchy–Riemann equations In mathematics, the Cauchy–Riemann equations are two partial differential equations that characterize differentiability of complex functions. The equations…
- Holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood…
- Cauchy's integral theorem In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard…
- Cauchy's integral formula In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a…
- Morera's theorem In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic…
- Riemann mapping theorem In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane ℂ which is not…
- Analytic function In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex…
- Looman–Menchoff theorem In the mathematical field of complex analysis, the Looman–Menchoff theorem states that a continuous complex-valued function defined in an open set of the…