Introduction to Real Analysis, 4th Edition
by Bartle, Robert G.; Sherbert, Donald R.Edition: 4th
Format: Hardcover
Pub. Date: 2011-01-18
Publisher(s): Wiley
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Summary
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, analyse 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 addition 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.
Author Biography
Robert Gardner Bartle was an American mathematician specializing in real analysis. He is known for writing various popular textbooks.
Donald R. Sherbert is the author of Introduction to Real Analysis, 4th Edition, published by Wiley.
Table of Contents
| Preliminaries | |
| Sets and Functions | |
| Mathematical Induction | |
| Finite and Infinite Sets | |
| The Real Numbers | |
| The Algebraic and Order Properties of R | |
| Absolute Value and Real Line | |
| The Completeness Property of R | |
| Applications of the Supremum Property | |
| Intervals | |
| Sequences and Series | |
| Sequences and Their Limits | |
| Limit Theorems | |
| Monotone Sequences | |
| Subsequences and the Bolzano-Weierstrass Theorem | |
| The Cauchy Criterion | |
| Properly Divergent Sequences | |
| Introduction to Infinite Series | |
| Limits | |
| Limits of Functions | |
| Limit Theorems | |
| Some Extensions of the Limit Concept | |
| Continuous Functions | |
| Continuous Functions | |
| Combinations of Continuous Functions | |
| Continuous Functions on Intervals | |
| Uniform Continuity | |
| Continuity and Gauges | |
| Monotone and Inverse Functions | |
| Differentiation | |
| The Derivative | |
| The Mean Value Theorem | |
| L'Hospital's Rules | |
| Taylor's Theorem | |
| The Riemann Integral | |
| The Riemann Integral | |
| Riemann Integrable Functions | |
| The Fundamental Theorem | |
| Approximate Integration | |
| Sequences of Functions | |
| Pointwise and Uniform Convergence | |
| Interchange of Limits | |
| The Exponential and Logarithmic Functions | |
| The Trigonometric Functions | |
| Infinite Series | |
| Absolute Convergence | |
| Tests for Absolute Convergence | |
| Tests for Nonabsolute Convergence | |
| Series of Functions | |
| The Generalized Riemann Integral | |
| Definition and Main Properties | |
| Improper and Lebesgue Integrals | |
| Infinite Intervals | |
| Convergence Theorems | |
| A Glimpse into Topology | |
| Open and Closed Sets in R | |
| Compact Sets | |
| Continuous Functions | |
| Metric Spaces | |
| Logic and Proofs | |
| Finite and Countable Sets | |
| The Riemann And Lebesgue Criteria | |
| Approximate Integration | |
| Two Examples | |
| References | |
| Photo Credits | |
| Hints for Selected Exercises | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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