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【2015】 A Course in Analysis - Volume I: Introductory Calculus, Analysis of Functions of One Real Variable

Book 图书名称： A Course in Analysis - Volume I: Introductory Calculus, Analysis of Functions of One Real Variable
Author 作者：      Niels Jacob, Kristian P Evans
Publisher 出版社： World Scientific Publishing
Page 页数：746
Publishing Date 出版时间： Nov 22, 2015                        
Language 语言： English
Size 大小： 6 MB
Format 格式： pdf 文字版
ISBN: 9814689084, 978-9814689083
Edition: 第1版 搜索过论坛，没有该文档

Volume I covers the content of two typical modules in undergraduate course for mathematics:
    Part 1: Introductory calculus
    Part 2: Analysis of functions of one variable
These two parts are divided into 32 chapters. Part 1 begins with an overview of a set of real numbers: rational and irrational. This is accompanied by a discussion of arithmetic rules, inequalities, absolute values. Doing this, the authors, in a clever way, introduce elements of a set theory using Cantor's approach. This is followed by the definition of a function and discussion of operations on functions. From this they move to differential and integral calculus and their applications.

Part 2 contains rigorous proofs of theorems from Part 1. In particular, they introduce the order structure on a real line using axioms of an ordered field. It is worth mentioning that Part 2 contains elements of topology obviously on real line and a good insight on convex functions. The convex functions relate Analysis to linear spaces equipped with norm. Finally, to close Part 2 the authors supply a number of Appendices, among them Appendices on logic, set theory and Peano axioms.

•         Remarkably, Volume I contains 360 problems with complete solutions.
•         Readership: Undergraduate students in mathematics.
  

== Table of contents ==
n/a


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