Calculus Problems
This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. Each chapter starts with a summary of the main definitions and results, which
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Marco Baronti · Filippo De Mari Robertus van der Putten Irene Venturi
Calculus Problems
UNITEXT - La Matematica per il 3+2 Volume 101
Editor-in-chief A. Quarteroni Series editors L. Ambrosio P. Biscari C. Ciliberto M. Ledoux W.J. Runggaldier
More information about this series at http://www.springer.com/series/5418
Marco Baronti Filippo De Mari Robertus van der Putten Irene Venturi •
•
Calculus Problems
123
Marco Baronti Dipartimento di Matematica Università di Genova Genova Italy
Robertus van der Putten DIME Università di Genova Genova Italy
Filippo De Mari Dipartimento di Matematica Università di Genova Genova Italy
Irene Venturi Dipartimento di Matematica Università di Genova Genova Italy
ISSN 2038-5722 ISSN 2038-5757 (electronic) UNITEXT - La Matematica per il 3+2 ISBN 978-3-319-15427-5 ISBN 978-3-319-15428-2 (eBook) DOI 10.1007/978-3-319-15428-2 Library of Congress Control Number: 2016943794 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Die mathematische Analysis gewissermassen eine einzige Symphonie des Unendlichen ist (D. Hilbert, Über das Unendliche, 1927) In a certain sense, mathematical analysis is a symphony of the infinite (D. Hilbert, On the Infinite, 1927)
Preface
The aim of this book is to provide a practical working tool for students in Engineering, Mathematics, and Physics, or in any other field where rigorous Calculus is needed. The emphasis is thus on problems that enhance students’ skill in solving standard exercises with a careful attitude, encouraging them to devote an attentive eye to what may or may not be done in manipulating formulae or deriving correct conclusions, while maintaining, whenever possible, a fresh approach, that is, seeking guiding ideas. Every chapter starts with a summary of the main results that should be kept
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