Real Analysis - An Introduction
eBook - ePub

Real Analysis - An Introduction

Mathematical Arguments and Elementary Proof Techniques

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

Real Analysis - An Introduction

Mathematical Arguments and Elementary Proof Techniques

About this book

Designed for a broad spectrum of mathematics majors, not only those pursuing graduate school, this book also provides a thorough explanation of undergraduate Real Analysis. Through a developmentally appropriate narrative that integrates informal discussion, motivation, and basic proof writing approaches with mathematical rigor and clarity, the aim is to assist all students in learning more about the real number system and calculus theory.

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Yes, you can access Real Analysis - An Introduction by Michael Cullinane in PDF and/or ePUB format. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2025
eBook ISBN
9783111429946
Edition
0

Table of contents

  1. Title Page
  2. Copyright
  3. Contents
  4. Frontmatter
  5. Contents
  6. 1 Algebraic and order properties of the real numbers
  7. 2 Absolute value and distance
  8. 3 The natural numbers, the integers, and the rational numbers
  9. 4 The completeness of the real numbers
  10. 5 Finite sets and infinite sets
  11. 6 The nested intervals property
  12. 7 Limit points, closed sets, and open sets
  13. 8 Connected sets and compact sets
  14. 9 An introduction to sequences and sequential convergence
  15. 10 More about sequences and convergence
  16. 11 Subsequences
  17. 12 Limits of functions
  18. 13 An introduction to continuous functions
  19. 14 More about continuity
  20. 15 The derivative
  21. 16 The mean value theorem
  22. 17 Taylor polynomials
  23. 18 The Riemann integral
  24. 19 Criteria for integrability
  25. 20 The fundamental theorem of calculus
  26. 21 Approximating the value of an integral
  27. 22 Infinite series
  28. 23 Absolute convergence and conditional convergence
  29. 24 Regroupings and rearrangements of series
  30. 25 Sequences and series of functions
  31. 26 Uniform convergence
  32. 27 More about power series and Taylor series
  33. 28 The trigonometric functions
  34. 29 Two remarkable results of Weierstrass
  35. Index
  36. Subject Index