Sequences and Series
A sequence is a function whose domain is a set of the form \(\{n\in \mathbb {Z}\ : \ n\ge m\}\) ; m is usually 1 or 0. Thus, a sequence is a function that has a specified value for each integer \(n\ge m\) . It is customary to denote a sequence by a latter
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Examples and Problems in Advanced Calculus: Real-Valued Functions
Examples and Problems in Advanced Calculus: Real-Valued Functions
Bijan Davvaz
Examples and Problems in Advanced Calculus: Real-Valued Functions
123
Bijan Davvaz Department of Mathematics Yazd University Yazd, Iran
ISBN 978-981-15-9568-4 ISBN 978-981-15-9569-1 https://doi.org/10.1007/978-981-15-9569-1
(eBook)
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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
Preface
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 sou
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