David Tall Ian StewartCambridge University PressEdition: 2, 8/23/2018EAN 9781108436793, ISBN10: 110843679XPaperback, 402 pages, 24.7 x 17.5 x 2 cmLanguage: EnglishThis 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 editionPreface to the second editionThe origins of complex analysis, and its challenge to intuition1. Algebra of the complex plane2. Topology of the complex plane3. Power series4. Differentiation5. The exponential function6. Integration7. Angles, logarithms, and the winding number8. Cauchy's theorem9. Homotopy versions of Cauchy's theorem10. Taylor series11. Laurent series12. Residues13. Conformal transformations14. Analytic continuation15. Infinitesimals in real and complex analysis16. Homology version of Cauchy's theorem17. The road goes ever onReferencesIndex.
