Overview
- Offers teachers the possibility to choose two different approaches a more basic and a more sofisticated one
- Covers a wide variety of examples and applications
- Addressed to students at a university level
Part of the book series: UNITEXT (UNITEXT, volume 137)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzelà theorem, the regularity of convex functions in R^n, L^p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions.
The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlesslydetermine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect.The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
Authors and Affiliations
About the authors
Paolo Marcellini is Emeritus Professor of Mathematical Analysis at University of Florence. His research interests are in calculus of variations and regularity theory for partial differential equations. He was Dean of the Faculty of Sciences at University of Florence and President of GNAMPA (National Group for Mathematical Analysis, Probability and their Applications). He was visiting professor at University of California, Berkeley; Collège de France, Paris; Institute for Advanced Study, Princeton; Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh; Mathematical Institute, University of Oxford; University of Texas, Austin and Institut Mittag-Leffler, Stockholm. Carlo Sbordone is Emeritus Professor of Mathematical Analysis at University of Naples “Federico II”, member of Accademia dei Lincei and was President of the Italian Mathematical Union (UMI). His research interests regard calculus of variations, Sobolev maps and function spaces. He was visiting professor at Scuola Normale Superiore in Pisa; Collège de France, Paris; Institut für Mathematik, Universität Zürich; Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh; University of California, Berkeley; Mathematical Institute, University of Oxford and University of Helsinki.
Bibliographic Information
Book Title: Mathematical Analysis
Book Subtitle: Functions of Several Real Variables and Applications
Authors: Nicola Fusco, Paolo Marcellini, Carlo Sbordone
Translated by: Simon G. Chiossi
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-031-04151-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-04150-1Published: 02 January 2023
eBook ISBN: 978-3-031-04151-8Published: 01 January 2023
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: X, 675
Number of Illustrations: 1 b/w illustrations
Topics: Numerical Analysis