Sharpening Mathematical Analysis Skills

Alina Sîntămărian is a Professor of Mathematics at Technical University of Cluj-Napoca, Romania. She holds a PhD in Mathematics from Babeș-Bolyai University, Cluj-Napoca, Romania. Her research interests focus on non-linear operators, fixed point theory, multivalued operators, mathematical analysis, constants evaluation, asymptotic expansions. Ovidiu Furdui is an Associate Professor of Mathematics at Technical University of Cluj-Napoca, Romania. He has published more than 500 problems in journals, with a problem column, from all over the world and he is the author of Limits, Series, and Fractional Part Integrals and has co-authored Square Matrices of Order 2, both published by Springer.     

Preface.- Notations.- Sequences of Real Numbers.- Series of Real Numbers.- Power Series.- Derivatives and Applications.- Partial Derivatives and Applications.- Implicit Functions.- Challenges, Gems, and Mathematical Beauties.- An Artistry of Quadratic Series. Two New Proofs of Sandham-Yeung Series.- Solutions.- References.- Index.

"It should be of use to a variety of readers including, those teaching Calculus sequence, researchers who routinely deal with series, and mathematical laypeople who wish to enjoy some punchy, beautiful identities and revel at some mathematical jokes. ... the solutions are frequently high-quality step-by-step derivations. The book is more than a collection of problems." (Russel Jay, Hendel, MAA Reviews, May 23, 2022)

"Think of competition level problems like those of the Putnam competition or the Mathematical Olympaids like SEEMOUS. This book can be used to prepare for such contests both by potential participants as well as by those that have to set up the questions. ... This is a challenging, surprising, and interesting way to explore the classical topics in analysis clearly intended for the those who want to excel in mathematics." (Adhemar Bultheel, zbMATH1482.00001, 2022)