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Revision of Complex analysis front page from Fri, 01/05/2009 - 12:57

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Complex analysis is the study of complex-differentiable functions. In a first course on complex analysis, these functions are normally defined on domains, that is, connected open subsets of \C. The definition of a complex-differentiable function looks just the same as the definition of a differentiable function from \R to \R, but this appearance is misleading: complex-differentiable functions are so unlike real-differentiable functions that they are given a different name. They are known as holomorphic functions. Holomorphic functions can also be defined on Riemann surfaces and complex manifolds. At a more advanced level, there are many connections between complex analysis and geometry. More generally, complex analysis is a tool that is used throughout mathematics.


A basic knowledge of the main theorems of complex analysis.

At the moment there are very few complex analysis articles on the Tricki, so here is a list of all of them. Later, it will almost certainly be necessary to add another level to the hierarchy. In fact, a start has been made on that process, by grouping together the first two articles.

To calculate a path integral, use theorems rather than direct calculation

Contour integration tricks