A Friendly Approach to Complex Analysis (2版)

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The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text. The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained. Request Inspection Copy Sample Chapter(s) Overview Chapter 1: Complex numbers and their geometry Contents: Complex Numbers and Their Geometry Complex Differentiability Cauchy Integral Theorem Taylor and Laurent Series Harmonic Functions Solutions to All Exercises Readership: Undergraduate students in complex analysis.

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...

Introduction to Complex Analysis (2版)

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Complex analysis is a classic and central area of mathematics, which is studies and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much-awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter.