Complements of Higher Mathematics
This book highlights the remarkable importance of special functions, operational calculus, and variational methods. A considerable portion of the book is dedicated to second-order partial differential equations, as they offer mathematical models of variou
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Complements of Higher Mathematics
Complements of Higher Mathematics
Marin Marin Andreas Öchsner •
Complements of Higher Mathematics
123
Marin Marin Department of Mathematics and Computer Science Transilvania University of Brasov Brasov Romania
Andreas Öchsner Faculty of Mechanical Engineering Esslingen University of Applied Sciences Esslingen am Neckar Germany
ISBN 978-3-319-74683-8 ISBN 978-3-319-74684-5 https://doi.org/10.1007/978-3-319-74684-5
(eBook)
Library of Congress Control Number: 2017964238 © Springer International Publishing AG, part of Springer Nature 2018 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
It is our belief that this book will help many students and researchers with mastering applied problems from different fields. The material presented here stems from courses and seminars on special topics in mathematics given by the authors for many years at universities, especially at technical, engineering, and economics faculties. We limit our considerations in this chapter to the basic notions and results of each domain of mathematics considered in this volume due to the diversity of the included chapters. Chapter 1 is devoted to complex functions. Here, emphasis is placed on the theory of holomorphic functions, which facilitate understanding the role played by the theory of complex variables in mathematical physics, especially in the modeling of plane problems. Furthermore, we consider the remarkable importance that the theories of special functions, operational calculus, and variational calculus have. A great part of the book is dedicated to second-order partial differential equations, since they are wide
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