A Modern Introduction to Mathematical Analysis
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0,99 €
| Verlag | Springer |
| Auflage | 2023 |
| Seiten | 431 |
| Format | 15,5 x 2,8 x 23,5 cm |
| Gewicht | 846 g |
| Artikeltyp | Englisches Buch |
| ISBN-10 | 3031237129 |
| EAN | 9783031237126 |
| Bestell-Nr | 03123712A |
This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem.
The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics.
The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools - no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.
Inhaltsverzeichnis:
- Part I The Basics of Mathematical Analysis. - 1. Sets of Numbers and Metric Spaces. - 2. Continuity. - 3. Limits. - 4. Compactness and Completeness. - 5. Exponential and Circular Functions. - Part II Differential and Integral Calculus in R. - 6. The Derivative. - 7. The Integral. - Part III Further Developments. - 8. Numerical Series and Series of Functions. - 9. More on the Integral. - Part IV Differential and Integral Calculus in RN. - 10.The Differential. - 11. The Integral. - 12. Differential Forms.
Rezension:
"A Modern Introduction to Mathematical Analysis, by Alessandro Fonda, is a well-written text that provides an enjoyable narrative of the major results of (advanced undergraduate or elementary graduate) analysis. ... The text is self-contained ... . I would recommend it to anyone needing a refresher on the fundamental results and foundations in Analysis, or for those looking for a different perspective on the material." (John Ross, MAA Reviews, January 28, 2024)