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Complex Analysis

  • John M. Howie

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

Table of contents

  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
  5. John M. Howie
    Pages 51-78
  6. John M. Howie
    Pages 79-106
  7. John M. Howie
    Pages 107-117
  8. John M. Howie
    Pages 119-136
  9. John M. Howie
    Pages 137-152
  10. John M. Howie
    Pages 153-181
  11. John M. Howie
    Pages 183-194
  12. John M. Howie
    Pages 195-215
  13. John M. Howie
    Pages 217-224
  14. John M. Howie
    Pages 225-253
  15. Back Matter
    Pages 255-260

About this book

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 Springer Book Archive
  • 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
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