TL;DR
This book provides a comprehensive introduction to univariate real analysis, covering fundamental concepts, theorems, and various types of integrals, suitable for students and researchers.
Contribution
It offers a detailed, structured presentation of univariate real analysis topics, including new insights into advanced integration methods.
Findings
Introduces the Henstock-Kurzweil integral as an extension of Riemann integral
Provides solutions to exercises for deeper understanding
Covers applications of integrals in various contexts
Abstract
Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Real numbers; 2. Limits of real sequences; 3. Series; 4. Limits of real functions. 5. Elementary functions; 6. Continuous functions; 7. Derivatives; 8. Mean value theorems; 9. Taylor polynomials; 10. Real analytic functions; 11. Newton integral; 12. Riemann integral; 13. Henstock-Kurzweil integral; 14. Applications of integrals; A. Auxiliary notions and notation; B. Solutions to exercises
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