An Introduction to Real Analysis by John K. Hunter
An Introduction to Real Analysis - Table of Contents
- 1. Sets and Functions
- 2. Numbers
- 3. Sequences
- 4. Series
- 5. Topology of the Real Numbers
- 6. Limits of Functions
- 7. Continuous Functions
- 8. Differentiable Functions
- 9. Sequences and Series of Functions
- 10. Power Series
- 11. The Riemann Integral
- 12. Properties and Applications of the Integral
- 13. Metric, Normed, and Topological Spaces
What You Will Learn in An Introduction to Real Analysis
An Introduction to Real Analysis by John K. Hunter is a comprehensive, rigorous lecture-note style textbook developed for upper-division undergraduate mathematics students at the University of California, Davis. The text bridges intuitive calculus with formal mathematical rigor, covering core analytical topics such as The Completeness of the Real Numbers and Open Sets, Sequences, Subsequences, and Limits, Continuity and Differentiability of Functions, and Sequences of Functions and Riemann Integration.
This book serves as an invaluable guide for mathematics undergraduates and theoretical science students who want to build a deep, logical foundation for advanced mathematical analysis. Hunter combines concise theoretical explanations with crystal-clear proofs, ensuring readers develop strong analytical reasoning and proof-writing skills.
Due to its pedagogical precision and open-access availability, it is widely recognized as an outstanding digital reference for learning rigorous single-variable analysis. Rather than relying on heuristic shortcuts, it equips learners with the formal epsilon-delta tools necessary for modern mathematical analysis, advanced topology, and applied mathematics.
Book Details & Specifications
Title:
An Introduction to Real Analysis by John K. Hunter
Publisher:
University of California Davis
Year:
2014
Pages:
305
Type:
PDF
Language:
English
ISBN-10 #:
B007N3I766
ISBN-13 #:
N\A
License:
External Educational Resource
Amazon:
Amazon
About the Author: John Kelso Hunter
The author John Kelso Hunter
is a distinguished professor of mathematics at the University of California, Davis, renowned for his research and teaching in partial differential equations, analysis, and fluid mechanics.
Through An Introduction to Real Analysis, Hunter successfully distilled complex analytical concepts into accessible yet rigorously structured lecture notes. His clear mathematical exposition makes this text a masterpiece resource for undergraduate real analysis.
Read or Downloadable An Introduction to Real Analysis
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