【2015新书】A Course in Real Analysis
Book 图书名称：A Course in Real Analysis
Author 作者：Hugo D. Junghenn
Publisher 出版社：A Chapman & Hall/CRC
Page 页数：581
Publishing Date 出版时间：Feb 13, 2015
Language 语言：English
Size 大小：4 MB
Format 格式：pdf 文字版
ISBN:9781482219272, 9781482219289
Edition: 第1版 搜索过论坛，没有该文档
Covers both single variable functions and multivariable functions, making the book suitable for one- and two-semester courses
Provides a detailed axiomatic account of the real number system
Develops the Lebesgue integral on Rn from the beginning
Gives an in-depth description of the algebra and calculus of differential forms on surfaces in Rn
Offers an easy transition to the more advanced setting of differentiable manifolds by covering proofs of Stokes’s theorem and the divergence theorem at the concrete level of compact surfaces in Rn
Summarizes relevant results from elementary set theory and linear algebra
Contains over 90 figures that illustrate the essential ideas behind a concept or proof
Includes more than 1,600 exercises throughout the text, with selected solutions in an appendix
Solutions manual available upon qualifying course adoption
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book’s material has been extensively classroom tested in the author’s two-semester undergraduate course on real analysis at The George Washington University.
The first part of the text presents the calculus of functions of one variable. This part covers traditional topics, such as sequences, continuity, differentiability, Riemann integrability, numerical series, and the convergence of sequences and series of functions. It also includes optional sections on Stirling’s formula, functions of bounded variation, Riemann–Stieltjes integration, and other topics.
The second part focuses on functions of several variables. It introduces the topological ideas (such as compact and connected sets) needed to describe analytical properties of multivariable functions. This part also discusses differentiability and integrability of multivariable functions and develops the theory of differential forms on surfaces in Rn.
The third part consists of appendices on set theory and linear algebra as well as solutions to some of the exercises. A full solutions manual offers complete solutions to all exercises for qualifying instructors.
With clear proofs, detailed examples, and numerous exercises, this textbook gives a thorough treatment of the subject. It progresses from single variable to multivariable functions, providing a logical development of material that will prepare students for more advanced analysis-based courses.
== Table of contents ==
Part I: Functions of One Variable
Chapter 1: The Real Number System
Chapter 2: Numerical Sequences
Chapter 3: Limits and Continuity on R
Chapter 4: Differentiation on R
Chapter 5: Riemann Integration on R
Chapter 6: Numerical Infinite Series
Chapter 7: Sequences and Series of Functions
Part II: Functions of Several Variables
Chapter 8: Metric Space
Chapter 9: Differentiation on R^n
Chapter 10: Lebesgue Measure on R^n
Chapter 11: Lebesgue Integration on R^n
Chapter 12: Curves and Surfaces in R^n
Chapter 13: Integration on Surfaces
Part III: Appendices
Appendix A: Set Theory
Appendix B: Linear Algebra
Appendix C: Solutions to Selected Problems
Bibliography
Back Cover
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