This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry.
| ISBN: | 9783319786308 |
| Publication date: | 24th May 2018 |
| Author: | Fabio Silva Botelho |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Hardback |
| Pagination: | 567 pages |
| Genres: |
Real analysis, real variables Integral calculus and equations Calculus and mathematical analysis |