Editing Mathematical analysis (section)

=== Complex analysis ===
{{Main|Complex analysis}}

Complex analysis (traditionally known as the "theory of functions of a complex variable") is the branch of mathematical analysis that investigates [[Function (mathematics)|functions]] of [[complex numbers]].<ref name="Ahlfors_1979"/> It is useful in many branches of mathematics, including [[algebraic geometry]], [[number theory]], [[applied mathematics]]; as well as in [[physics]], including [[hydrodynamics]], [[thermodynamics]], [[mechanical engineering]], [[electrical engineering]], and particularly, [[quantum field theory]].

Complex analysis is particularly concerned with the [[analytic function]]s of complex variables (or, more generally, [[meromorphic function]]s). Because the separate [[real number|real]] and [[imaginary number|imaginary]] parts of any analytic function must satisfy [[Laplace's equation]], complex analysis is widely applicable to two-dimensional problems in [[physics]].