複變函數論

Complex Analysis 2/e

+作者:

Stewart

+年份:
2018 年2 版
+ISBN:
9781108436793
+書號:
MA0442P
+規格:
平裝/單色
+頁數:
404
+出版商:
Cambridge
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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.

●Using simple topological ideas of continuity and connectivity, this textbook explains the differences between real and complex analysis as a consequence of the richer geometry of the complex plane and teaches students to translate visual intuition into rigorous proof
●Introduces a simple formal definition of an extension field containing infinitesimal quantities to show the connection between pure and applied approaches - students grasp the continuing evolution of mathematical ideas
●Includes supplementary material showing in more detail the changes between the previous edition and this one

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.
David Tall is Emeritus Professor of Mathematical Thinking at the University of Warwick and is known internationally for his contributions to mathematics education. He is author or co-author of over 200 papers and 40 books and educational computer software, covering all levels from early childhood to research mathematics.

0. 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...