Complex Analysis

A new edition of a classic textbook on complex analysis with an emphasis on translating visual intuition to rigorous proof.

Ian Stewart (Author), David Tall (Author)

9781108436793, Cambridge University Press

Paperback / softback, published 23 August 2018

402 pages, 195 b/w illus. 2 tables
24.7 x 17.5 x 2 cm, 0.82 kg

This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy's theorem and Cauchy's residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.

Preface to the first edition
Preface to the second edition
The origins of complex analysis, and its challenge to intuition
1. Algebra of the complex plane
2. Topology of the complex plane
3. Power series
4. Differentiation
5. The exponential function
6. Integration
7. Angles, logarithms, and the winding number
8. Cauchy's theorem
9. Homotopy versions of Cauchy's theorem
10. Taylor series
11. Laurent series
12. Residues
13. Conformal transformations
14. Analytic continuation
15. Infinitesimals in real and complex analysis
16. Homology version of Cauchy's theorem
17. The road goes ever on
References
Index.

Subject Areas: Geometry [PBM], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Calculus [PBKA]