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.

Description

It is useful in many branches of mathematics, including:

• Algebraic geometry
• Number theory
• Applied mathematics

It is used in many branches of physics and engineering, including:

• Hydrodynamics
• Thermodynamics
• Nuclear engineering
• Aerospace engineering
• Mechanical engineering
• Electrical engineering

Murray R. Spiegel described complex analysis as "one of the most beautiful as well as useful branches of Mathematics".

Complex analysis is particularly concerned with analytic functions of complex variables (or, more generally, meromorphic functions).

Because the separate real and imaginary parts of any analytic function must satisfy Laplace's equation, complex analysis is widely applicable to two-dimensional problems in physics.

See also

• Complex number
• Laplace's equation
• Mathematical analysis
• Mathematics

External links

• Complex analysis @ Wikipedia