# Complex Analysis

• John M. Howie
Textbook

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

1. Front Matter
Pages i-xi
2. John M. Howie
Pages 1-18
3. John M. Howie
Pages 19-34
4. John M. Howie
Pages 35-49
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Pages 51-78
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Pages 183-194
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Pages 195-215
13. John M. Howie
Pages 217-224
14. John M. Howie
Pages 225-253
15. Back Matter
Pages 255-260

### Introduction

Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

### Keywords

Analysis Complex analysis Complex numbers Functions of a complex variable Residue theorem calculus contour integration

#### Authors and affiliations

• John M. Howie
• 1
1. 1.School of Mathematics and Statistics, Mathematical InstituteUniversity of St AndrewsNorth Haugh, St Andrews, FifeUK

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-0027-0
• Copyright Information Springer-Verlag London 2003
• Publisher Name Springer, London
• eBook Packages
• Print ISBN 978-1-85233-733-9
• Online ISBN 978-1-4471-0027-0
• Series Print ISSN 1615-2085
• Series Online ISSN 2197-4144
• Buy this book on publisher's site