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The Big Book of Real Analysis From Numbers to Measures

This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus. Beginning with some basic proof techniques and the noti...

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Bibliographic Details
Main Author: Johar, Syafiq
Format: eBook
Language:English
Published: Cham Springer Nature Switzerland 2023, 2023
Edition:1st ed. 2023
Subjects:
Measure Theory
Functions Of Real Variables
Mathematical Analysis
Sequences, Series, Summability
Analysis
Real Functions
Measure And Integration
Sequences (mathematics)
Mathematics
Differential Equations
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • 1. Logic and Sets
  • 2. Integers
  • 3. Construction of the Real Numbers
  • 4. The Real Numbers
  • 5. Real Sequences
  • 6. Some Applications of Real Sequences
  • 7. Real Series
  • 8. Additional Topics in Real Series
  • 9. Functions and Limits
  • 10. Continuity
  • 11. Function Sequences and Series
  • 12. Power Series
  • 13. Differentiation
  • 14. Some Applications of Differentiation
  • 15. Riemann and Darboux Integration
  • 16. The Fundamental Theorem of Calculus
  • 17. Taylor and MacLaurin Series
  • 18. Introduction to Measure Theory
  • 19. Lebesgue Integration
  • 20. Double Integrals
  • Solutions to the Exercises
  • Bibliography
  • Index

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