Elements of real Analysis
This book is an introduction to mathematical analysis. It offers a self-contained treatment of some elementary and some advanced topics. After preliminaries concerning sets and functions, the authors describe real numbers (in an axiomatic way), sequences (Cauchy criterion, upper and lower limits, open and closed sets), infinite series, limits of a function, continuity (including compactness), differentiation (including Taylor’s theorem), the Riemann integral (the fundamental theorem of calculus and improper integrals), sequences and series of functions (uniform convergence and power series), the Lebesgue measure and Lebesgue integration (including convergence theorems). The course is clearly written; it starts with elementary topics and it finishes with the complicated theory of integration. The book contains a lot of solved examples and exercises. It can be used as an introductory course at the senior undergraduate level.