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Complex Analysis

Complex analysis, i.e. the analysis of functions involving one complex-valued variable, definitely deserves a separate part of BookofProofs. One reason for this is that the material dealt with in this part has various applications in mathematics and in particular physics. But probably the most astonishing reason for this is that analysis of functions with complex-valued variables allows getting a deeper understanding of the analysis of functions with real-valued variables. That’s why complex analysis is often referred to as the function theory.

Function theory is a self-closed theory with a kind of mathematical beauty, not least because of it has many vivid geometrical interpretations, in particular of the behavior of points in the complex plane under certain complex-valued functions. The key concept of function theory is that of a holomorphic function. Holomorphy is a property of a function with far-reaching and astonishing consequences. These include:

Theoretical minimum (in a nutshell)

In order to start studying function theory, you should be acquainted with:

Concepts you will learn in this part of BookofProofs

| | | | created: 2014-02-20 20:26:15 | modified: 2020-02-29 10:08:59 | by: bookofproofs

1.Topological Aspects

2.Geometric Aspects

3.Properties of Complex Functions

4.Types of Complex Functions

5.Laurant Series

6.Isolated Singularities

7.Meromorphic Functions

8.Residue Theorem

9.Discrete Fourier Transform (DFT)

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)