Thus, for virtually all of this book, the only pre-requisites are a good working knowledge of Calculus (including partial differentiation), Vectors and Linear Algebra (including matrices and determinants). This topic contains some of the most beautiful results in Mathematics, and yet most of them can be understood without extensive background knowledge. Cover design: Deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (Preface The Differential Geometry in the title of this book is the study of the geometry of curves and surfaces in three-dimensional space using calculus techniques. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. Enquiries concerning reproduction outside those terms should be sent to the publishers. Toland University of Bath For other titles published in this series, go to Andrew Pressley Elementary Differential Geometry Second Edition 123 Andrew Pressley Department of Mathematics King’s College London Strand, London WC2R 2LS United Kingdom Springer Undergraduate Mathematics Series ISSN 1615-2085 ISBN 978-1-84882-890-2 e-ISBN 978-1-84882-891-9 DOI 10.1007/978-1-84882-891-9 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2009942256 Mathematics Subject Classification (2000): 53-01, 53A04, 53A05, 53A35 c Springer-Verlag London Limited 2010, Corrected printing 2012 ⃝ Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. MacIntyre Queen Mary, University of London L.C.G. Springer Undergraduate Mathematics Series Advisory Board M.A.J. Inner product spaces and self-adjoint linear maps. Table of contents : Elementary Differential Geometry.
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