Elementary Real Analysis

Abstract

Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Five numeric domains; 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

Currently 400 pages. Chapter 1 is now basically complete. It develops in 70 pages, finally in a satisfactory way, the five numeric domains ${\mathbb{N}}_0$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, and ${\mathbb{R}}^{\ast }$. It is a fundament for the rest of the book. I wrote it in June and July 2026

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