Bijan Davvaz - Examples and Problems in Advanced Calculus: Real-Valued Functions

This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.

The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

This book is a result of the experience of teaching general mathematics (calculus) from 1990 to the present time at Yazd University, Iran. I had the idea of writing this book from many years ago but began working on it seriously about three years ago. The book is intended to serve as a textbook of calculus exercises with solutions for calculus courses that are usually taken by first-year students. Indeed, it can be used by all students of mathematics, statistics, computer science, engineering and basic sciences. A total of 501 problems have been selected from 20,000 problems in different books. In choosing problems, three major criteria have been considered, to be challenging, interesting and educational. Therefore, most issues have technical and educational aspects. Over the years, while teaching general mathematics, I have encountered many challenging exercises which have been solved with much time. Most of these exercises have been collected over the last thirty years from different references. Although references that have been used are listed at the end of the book, I do not know the sources and the main creators of most exercises and problems. Therefore, it is my duty to thank everyone who has designed these issues for the first time. The book is based on problems andregardless of the assumption that readers have prior knowledge of classical contents from other textbooksthe beginning of each chapter includes necessary definitions, concepts and theorems. Moreover, as the reader will soon see, there are many exercises at the end of each chapter. They are divided into two categories: easier and harder. The purpose of these exercises is to allow students to test their assimilation of the material, challenge their mathematical ingenuity, and be a means of developing mathematical insight, intuition and techniques.

The book is composed of seven chapters. Chapter , we investigate how to compute the area, length of a curve, volume of a solid and area of a surface of revolution. Problems related to sequences and series are presented in the last chapter. A study of this chapter should give the reader a thorough understanding of miscellaneous methods about convergence of sequences and series.

Finally, I hope readers enjoy this book and find this issue informative and helpful.