The Early Period of the Calculus of Variations
This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange,
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The Early Period of the Calculus of Variations
The Early Period of the Calculus of Variations
Paolo Freguglia Mariano Giaquinta •
The Early Period of the Calculus of Variations
Mariano Giaquinta Scuola Normale Superiore Pisa Italy
Paolo Freguglia Department of Pure and Applied Mathematics Università di L’Aquila L’Aquila Italy
ISBN 978-3-319-38944-8 DOI 10.1007/978-3-319-38945-5
ISBN 978-3-319-38945-5
(eBook)
Library of Congress Control Number: 2016939938 Mathematics Subject Classification (2010): 49-03, 49-01, 01A45, 01A50, 01A75 © 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 book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com)
We dedicate this book to our respective grandchildren Michela, Gabriele and Andrea
Preface
In the current state of analysis we may regard these discussions [of past mathematics] as useless, for they concern forgotten methods, which have given way to others more simple and more general. However, such discussions may yet retain some interest for those who like to follow step by step the progress of analysis, and to see how simple and general methods are born from particular questions and complicated and indirect procedures.1 J.L. Lagrange, Leçons sur le calcul des fonctions, Paris 1806, p. 436.
The early history of the Calculus of variations is a well-beaten track; for instance, we refer the reader to • The last two chapters of the Calcul des functions of Lagrange [152]; • A Treatise on Isoperimetrical Problems and the Calculus of Variations by R. Woodhouse, reprinted by Chelsea with the title A History of the Calculus of Variations in the Eighteenth century, [202]; • The surveys by C. Carathéodory (1) (2) (3) and
The beginning of research in the Calculus of variations, [48], Basel und der Begin der Variationsrechnung, [49], Einführung in Eulers Arbeiten
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