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100+1 Problems in Advanced Calculus

Paolo Toni, Pier Domenico Lamberti, and Giacomo Drago
Publication Date: 
Number of Pages: 
Problem Book
[Reviewed by
Andrzej Sokolowski
, on
The book 100+1 Problems in Advanced Calculus by P.Toni, D. Lamberti, and G. Drago provides one-hundred problems on various calculus topics. It consists of eight chapters whose content complexity gradually increases following, to a certain extent, 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.
Starting with a review of fundamental theorems and definitions of, e.g., sets, sequences, and functions, it concludes with differential and integral calculus. Finally, the reader will find Rolle’s, LaGrange’s, Cauchy’s, and L’Hospital’s theorems as they apply to various function representations, mainly graphs and functions.
Each chapter presents a short theoretical introduction of the concepts embedded in carefully developed problems. All problems are accompanied by detailed solutions whose lines of inquiry correspond with their theoretical presentation. 
Unquestionable attributes of this book are multiple representations of discussed ideas ranging from algebraic and geometric to graphical. In some cases, however, when, for example, function concavity and points of inflection are introduced, graphical representations are not presented in the theoretical background. Similarly, function asymptotes are introduced rigorously using abstract algebraic symbols without a direct link to their graphical embodiments. Graphical representations are used more often to support solutions. 
While the book is suggested to help first-year undergraduates in mathematics, physics, and engineering courses, it does not offer real-life application problems that would reach beyond purely abstract algebraic functions. However, 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, Ph.D., is the author of several books on developing students’ mathematical reasoning skills to enhance their understanding of science. He is also a mathematics and physics professor at Lone Star College, TX, USA.