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
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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.
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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.
原價:
1562
售價:
1484
現省:
78元
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