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All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

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Chapter 9

Complex Analysis

Basic Object:

The complex numbers

Basic Map:

Analytic functions

Basic Goal:

Equivalences of analytic functions

Complex analysis in one variable studies a special type of function (called analytic or holomorphic) mapping complex numbers to themselves. There are a number of seemingly unrelated but equivalent ways for defining an analytic function. Each has its advantages; all should be known.

We will first define analyticity in terms of a limit (in direct analogy with the definition of a derivative for a real-valued function). ...

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