An Introduction to Real Analysis
eBook - PDF

An Introduction to Real Analysis

The Commonwealth and International Library: Mathematical Topics

  1. 324 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

An Introduction to Real Analysis

The Commonwealth and International Library: Mathematical Topics

Book details
Table of contents
Citations

About This Book

An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.

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Information

Publisher
Pergamon
Year
2014
ISBN
9781483158969
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Front Cover
  2. An Introduction to Real Analysis
  3. Copyright Page
  4. Table of Contents
  5. PREFACE
  6. INTRODUCTION. THE PURPOSE OF REAL ANALYSIS
  7. CHAPTER 1. SETS, RELATIONS, AND FUNCTIONS
  8. CHAPTER 2. NUMBERS
  9. CHAPTER 3. SEQUENCES
  10. CHAPTER 4. SERIES
  11. CHAPTER 5. FUNCTIONS OF A REAL VARIABLE
  12. CHAPTER 6. THE DERIVATIVE
  13. CHAPTER 7. SOME IMPORTANT FUNCTIONS AND EXPANSIONS
  14. CHAPTER 8. THE RIEMANN INTEGRAL
  15. ANSWERS AND HINTS
  16. INDEX