Principles of Mathematical Analysis 3/e 2023 Edition (3版)

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Principles of Mathematical Analysis 3/e 2023 Edition 作者：Walter Rudin ISBN：9786269708116 版次：3 年份：2023 出版商：McGraw-Hill 頁數/規格：342頁/平裝單色 Description This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics. NEW to This Edition The material on functions of several variables in Chapter 9 is significantly rewritten, with many details filled in, and with more examples and more motivation. The proof of the inverse function theorem is simplified by means of the fixed point theorem about contraction mappings. Differential forms are discussed in much greater detail. Several applications of Stokes' theorem are included. The Riemann-Stieltjes integral in Chapter 6 has been trimmed a bit. A short do-it-yourself section on the gamma function has been added to Chapter 8. There is a large number of new exercises throughout the book, most of them with fairly detailed hints. Several references to articles appearing in the American Mathematical Monthly and in Mathematics Magazine are included for students to develop the habit of looking into the journal literature. 目錄 Table of Contents Chapter 1: The Real and Complex Number Systems  Chapter 2: Basic Topology  Chapter 3: Numerical Sequences and Series  Chapter 4: Continuity  Chapter 5: Differentiation  Chapter 6: The Riemann-Stieltjes Integral  Chapter 7: Sequences and Series of Functions  Chapter 8: Some Special Functions  Chapter 9: Functions of Several Variables  Chapter 10: Integration of Differential Forms  Chapter 11: The Lebesgue Theory