Introduction to Real Analysis 4th Edition by Robert G. Bartle, Donald R. Sherbert – Ebook PDF Instant Download/Delivery: 0471433316, 978-0471433316
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Product details:
ISBN-10 : 0471433316
ISBN-13 : 978-0471433316
Author: Robert G. Bartle, Donald R. Sherbert
This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations, and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with additional examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: Introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.
Introduction to Real Analysis 4th Table of contents:
CHAPTER 1 PRELIMINARIES
1.1 Sets and Functions
1.2 Mathematical Induction
1.3 Finite and Infinite Sets
CHAPTER 2 THE REAL NUMBERS
2.1 The Algebraic and Order Properties of R
2.2 Absolute Value and the Real Line
2.3 The Completeness Property of R
2.4 Applications of the Supremum Property
2.5 Intervals
CHAPTER 3 SEQUENCES AND SERIES
3.1 Sequences and Their Limits
3.2 Limit Theorems
3.3 Monotone Sequences
3.4 Subsequences and the Bolzano-Weierstrass Theorem
3.5 The Cauchy Criterion
3.6 Properly Divergent Sequences
3.7 Introduction to Infinite Series
CHAPTER 4 LIMITS
4.1 Limits of Functions
4.2 Limit Theorems
4.3 Some Extensions of the Limit Concept
CHAPTER 5 CONTINUOUS FUNCTIONS
5.1 Continuous Functions
5.2 Combinations of Continuous Functions
5.3 Continuous Functions on Intervals
5.4 Uniform Continuity
5.5 Continuity and Gauges
5.6 Monotone and Inverse Functions
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Tags: Introduction, Real Analysis, Robert Bartle, Donald Sherbert