Introduction to Complex Analysis

by Priestley, H. A.

• ISBN13: 9780198525622
• ISBN10: 0198525621
• Edition: 2nd
• Format: Paperback
• Copyright: 2003-10-30
• Publisher: Oxford University Press

Summary

Complex analysis is a classic and central area of mathematics, which is studies and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much-awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter.

Table of Contents

Complex numbers

Geometry in the complex plane

Topology and analysis in the complex plane

Holomorphic functions

Complex series and power series

A menagerie of holomorphic functions

Paths

Multifunctions: basic track

Conformal mapping

Cauchy's theorem: basic track

Cauchy's theorem: advanced track

Cauchy's formulae

Power series representation

Zeros of holomorphic functions

Further theory of holomorphic functions

Singularities

Cauchy's residue theorem

Contour integration: a technical toolkit

Applications of contour integration

The Laplace transform

The Fourier transform

Harmonic functions and holomorphic functions

Bibliography

Notation index

Index

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