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Introduction to Real Analysis, 4th Edition

Introduction to Real Analysis, 4th Edition

Robert G. Bartle, Donald R. Sherbert

ISBN: 978-0-470-91181-5

Feb 2011

416 pages

Select type: E-Book



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.

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  • Several new examples have been added to this edition to make the text more up-to-date and relevant
  • New exercises have been added throughout to give students more material to practice and solidify their understanding of the material
  • Coverage of the Darboux integral has been added in Section 7.4
  • Treatment of Basic Theory of Functions: Detailed and rigorous treatment of the basic theory of functions of one real variable.
  • Pacing: Accessible and user-friendly because concepts are developed in a reasonably paced manner with many examples to illustrate the theory.
  • Examples and Solutions: Every concept is illustrated by examples and special cases. There is also a wide range of exercises, and hints for some of them are provided in the back of the text.
  • Approximation Methods and Numerical Calculation: These are emphasized whenever appropriate, making this text suitable for computer science students.