Identifiers: LCCN 2018037033 | ISBN 9781108424936 Subjects: LCSH: Geometry, Differential – Textbooks. Description: Cambridge New York, NY : Cambridge University Press, 2019. Title: A first course in differential geometry surfaces in Euclidean space / John Bolton (University of Durham), L.M. Library of Congress Cataloging-in-Publication Data Names: Bolton, John (Mathematics professor), author. Padstow, Cornwall 2019 A catalogue record for this publication is available from the British Library. First published 2019 Printed in the United Kingdom by TJ International Ltd. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. Woodward and John Bolton 2019 This publication is in copyright. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. BOLTON University of Durham © in this web service Cambridge University Press Cambridge University Press 978-3-6 - A First Course in Differential Geometry Lyndon Woodward, John Bolton Frontmatter More Information University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. © in this web service Cambridge University Press Cambridge University Press 978-3-6 - A First Course in Differential Geometry Lyndon Woodward, John Bolton Frontmatter More Information © in this web service Cambridge University Press Cambridge University Press 978-3-6 - A First Course in Differential Geometry Lyndon Woodward, John Bolton Frontmatter More Information A First Course in Differential Geometry Surfaces in Euclidean Space L. Between them, they have over 70 years’ teaching experience, being well regarded as enthusiastic, clear, and popular lecturers. They embarked on a long and fruitful collaboration, co-authoring over 30 research papers in differential geometry, particularly on generalisations of “soap film” surfaces. at the University of Liverpool and joined Durham University in 1970, where he was joined in 1971 by Lyndon Woodward, who obtained his D.Phil. It includes many exercises to test students’ understanding of the material, and ends with a supplementary chapter on minimal surfaces that could be used as an extension towards advanced courses or as a source of student projects. While the main topics are the classics of differential geometry – the definition and geometric meaning of Gaussian curvature, the Theorema Egregium of Gauss, geodesics, and the Gauss–Bonnet Theorem – the treatment is modern and student-friendly, taking direct routes to explain, prove, and apply the main results. It provides a thorough introduction by focussing on the beginnings of the subject as studied by Gauss: curves and surfaces in Euclidean space. This introductory textbook originates from a popular course given to third-year students at Durham University for over 20 years, first by the late Lyndon Woodward and then by John Bolton (and others). It is also the language used by Einstein to express general relativity, and so is an essential tool for astronomers and theoretical physicists. It is a mainstay of undergraduate mathematics education and a cornerstone of modern geometry. Citation previewĬambridge University Press 978-3-6 - A First Course in Differential Geometry Lyndon Woodward, John Bolton Frontmatter More Information A First Course in Differential Geometry Surfaces in Euclidean Space Differential geometry is the study of curved spaces using the techniques of calculus. Hints or answers to some exercises Index.
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