This new edition of a classic textbook develops complex analysis using simple topological ideas to translate visual intuition into formal arguments. With numerous examples and exercises, clear and direct proofs, and three new chapters including a view to the future of the subject, this is an invaluable companion for any complex analysis course.
This new edition of a classic textbook develops complex analysis using simple topological ideas to translate visual intuition into formal arguments. With numerous examples and exercises, clear and direct proofs, and three new chapters including a view to the future of the subject, this is an invaluable companion for any complex analysis course.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Ian Stewart, FRS, is Emeritus Professor of Mathematics at the University of Warwick. He is author or co-author of over 190 research papers and is the bestselling author of over 120 books, from research monographs and textbooks to popular science and science fiction. His awards include the Royal Society's Faraday Medal, the Institute of Mathematics and its Applications (IMA) Gold Medal, the American Association for the Advancement of Science (AAAS) Public Understanding of Science Award, the London Mathematical Society (LMS)/IMA Zeeman Medal, the Lewis Thomas Prize, and the Euler Book Prize. He is an honorary wizard of the Discworld's Unseen University.
Inhaltsangabe
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.
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.
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