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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.
Über den Autor / die Autorin
Alessandro Fonda ha conseguito il dottorato di ricerca presso la Scuola Internazionale Superiore di Studi Avanzati (SISSA-Trieste) nel 1988, sotto la supervisione di Jean Mawhin. Successivamente è stato ricercatore in Belgio, a Louvain-la-Neuve, prima di tornare in Italia, presso l'Università di Trieste, dove ricopre la carica di professore ordinario dal 2002.
Ha ricevuto due premi dall'Académie Royale de Belgique per le sue monografie "Periodic solutions of scalar second order differential equations with a singularity" nel 1993 e "Playing around resonance. An invitation to the search of periodic solutions for second order ordinary differential equations" nel 2017.
È stato invitato a tenere conferenze plenarie in numerosi convegni in Europa e negli Stati Uniti.
I suoi interessi di ricerca si concentrano principalmente sull'esistenza e molteplicità delle soluzioni per problemi ai limiti relativi alle equazioni differenziali. Recentemente ha dato un contributo importante allo studio delle soluzioni periodiche per i sistemi hamiltoniani, fornendo diverse generalizzazioni del Teorema di Poincaré-Birkhoff, nel caso planare e in dimensioni superiori. Ha inoltre studiato problemi relativi alle inclusioni differenziali, alla persistenza nei sistemi dinamici e al comportamento globale delle soluzioni di sistemi planari.
Zusammenfassung
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.
Zusatztext
“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)
Bericht
This well-written book brings together the classical topics of mathematical analysis normally taught in the first two years of a university course. It provides a pleasant narrative of the topics. It is self-contained. In my opinion, the fundamental results and the foundations of analysis are nicely covered here, and I would surely recommend this text to anybody already involved or ready to become involved in such a beautiful and fruitful theory as mathematical analysis. (Emma D Aniello, zbMATH 1564.26002, 2025)
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)
