A Modern Introduction to Mathematical Analysis
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Beschreibung
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.
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.
Features an original approach to the exponential and circular functions Explains all the main analysis theory in only 400 pages Presents the Kurzweil-Henstock integral
Autor*in
Alessandro Fonda
Themen in »A Modern Introduction to Mathematical Analysis«
Kurzweil-Henstock Integral Modern Mathematical Analysis Stokes-Cartan Theorem Differential Calculus ODE
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“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)
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