This book presents a collection of methods and techniques through problem-solving in fundamentals of Mathematical Analysis. In particular, emphasis is given to the computation and/or existence of limits of sequences, series and fractional part integrals.
It is the first book of its kind to give emphasis on the fractional part of functions which are involved in convergence, differentiation and integration problems.
The book provides an extensive presentation of a wide collection of problems on three selected topics of Mathematical Analysis: limits, series, and fractional part integrals. Emphasis is given to a variety of methods and techniques which apply to the solution of special computational problems. These problems are mainly oriented to undergraduate and beginning graduate students, who wish to be prepared for various problems-solving mathematical competition including the Putnam exam. The book will be particularly useful to teachers of Calculus and Real Analysis courses who wish to enrich their class with challenging problems, some of which require special skill and ingenuity.
Some of the problems appear for the first time in this book and have been introduced by the author or other mathematicians.
The book is highly recommended for libraries as well as for personal use.