Complex Analysis (2版)

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書名：Complex Analysis 2/E 作者：STEWART 出版社：Cambridge 出版日期：2018/10/00 ISBN：9781108436793 內容簡介 ●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 目錄 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...

Real and complex analysis (3版)

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【簡介】 Description This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. 【目錄】 Table of Contents Chapter 1: Abstract Integration Chapter 2: Positive Borel Measures Chapter 3: Lp-Spaces Chapter 4: Elementary Hilbert Space Theory Chapter 5: Examples of Banach Space Techniques Chapter 6: Complex Measures Chapter 7: Differentiation Chapter 8: Integration on Product Spaces Chapter 9: Fourier Transforms Chapter 10: Elementary Properties of Holomorphic Functions Chapter 11: Harmonic Functions Chapter 12: The Maximum Modulus Principle Chapter 13: Approximation by Rational Functions Chapter 14: Conformal Mapping Chapter 15: Zeros of Holomorphic Functions Chapter 16: Analytic Continuation Chapter 17: Hp-Spaces Chapter 18: Elementary Theory of Banach Algebras Chapter 19: Holomorphic Fourier Transforms Chapter 20: Uniform Approximation by Polynomials