Authors:
- Convenes problems in Advanced Calculus with solutions that favor creativity
- Covers all the classical topics seen in first-year Calculus and Mathematical Analysis courses
- Offers a theoretical background in every chapter, with relevant definitions and theorems for self-study
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (8 chapters)
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Front Matter
About this book
In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found atthe end of each chapter.
Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.
Reviews
“A sequence of a traditional textbook for an undergraduate calculus course. From this standpoint, this book can be used as a supplement to any conventional calculus text. … It is well known that students struggle with inducing abstract math concepts to gain insight into behavior in real-world phenomena to understand better those behaviors; including such examples is seen as a potential asset.” (Andrzej Sokolowski, MAA Reviews, August 1, 2022)
Authors and Affiliations
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Liceo Scientifico Statale Enrico Fermi, Padova, Italy
Paolo Toni
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Dipartimento di Tecnica e Gestione dei Sistemi Industriali (DTG), University of Padova, Vicenza, Italy
Pier Domenico Lamberti
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Istituto Tecnico Economico Calvi, Padova, Italy
Giacomo Drago
About the authors
Pier Domenico Lamberti is a Full Professor in Mathematical Analysis at the University of Padua, Italy. He got a PhD in Mathematics from the University of Padua (2003), and has been visiting researcher at the University of Cardiff, UK; University of Athens, Greece; and Complutense University of Madrid, Spain. His research interests lie in mathematical analysis, with focus on partial differential equations, spectral theory, theory of functions spaces, functional analysis, calculus of variations, and homogenization theory.
Giacomo Drago is a Teacher of Mathematics and Physics at Istituto Tecnico Economico Calvi in Padua, Italy. He obtained a Master degree in Mathematics (2011) from the University of Padua, Italy. As a student, he distinguished himself in the national finals of three consecutive editions (2004-2006) of the Kangourou Mathematics Competitions.
Bibliographic Information
Book Title: 100+1 Problems in Advanced Calculus
Book Subtitle: A Creative Journey through the Fjords of Mathematical Analysis for Beginners
Authors: Paolo Toni, Pier Domenico Lamberti, Giacomo Drago
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-030-91863-7
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
Hardcover ISBN: 978-3-030-91862-0Published: 09 March 2022
Softcover ISBN: 978-3-030-91865-1Published: 10 March 2023
eBook ISBN: 978-3-030-91863-7Published: 08 March 2022
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XVII, 220
Number of Illustrations: 171 b/w illustrations
Topics: Real Functions, Analysis