Principles of Mathematical Analysis, 3/e (2023 Edition)
暫譯: 數學分析原理（第三版，2023年版）
Walter Rudin
- 出版商: McGraw-Hill Education
- 出版日期: 2023-01-01
- 定價: $800
- 售價: 9.8 折 $784
- 語言: 英文
- 頁數: 342
- ISBN: 6269708117
- ISBN-13: 9786269708116
-
相關分類:
數值分析 Numerical-analysis
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商品描述
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.
商品描述(中文翻譯)
書籍描述
本書旨在作為高年級本科生或學習數學的一年級學生所修的分析課程的教材。
本版新內容
- 第9章中有關多變數函數的內容已大幅重寫，填補了許多細節，並增加了更多範例和動機。逆函數定理的證明透過有關收縮映射的固定點定理進行簡化。微分形式的討論也更加詳細。包含了幾個斯托克斯定理的應用。
- 第6章中的黎曼-斯蒂爾傑斯積分已稍作刪減。
- 第8章新增了一個簡短的自學部分，介紹伽瑪函數。
- 全書新增了大量練習題，大多數都有相當詳細的提示。
- 包含了幾篇出現在《美國數學月刊》和《數學雜誌》的文章參考，鼓勵學生養成查閱期刊文獻的習慣。
目錄大綱
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
目錄大綱(中文翻譯)
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
