文档介绍：Page iii
Applications of Lie's Theory of Ordinary and Partial Differential
Equations
Lawrence Dresner
Oak Ridge, Tennessee, USA
Institute of Physics Publishing
Bristol and Philadelphia
Page iv
O IOP Publishing Ltd 1999
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Committee of Vice Chancellors and Principals.
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-7503-0530-4 (hardback)
0-7503-053 1-2 (paperback)
Library of Congress Cataloging-in-Publication Data are available
Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London
Institute of Physics Publishing, Dirac IIouse, Temple Back, Bristol BS1 6BE, UIC
US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 South
Independence Mall West, Philadelphia, PA 19106, USA
Typeset by Digital by Design, Cheltenham
Printed in the UK by J W Arrowsmith Ltd, Bristol
Contents
Preface -ix
Conventions Used in this Book -xii
Dedication
1
One-Parameter Groups
Groups of Transformations
Infinitesimal Transformations
Group Invariants
Invariant Curves and Families of Curves
Transformation of Derivatives: the Extended Group
Transformation of Derivatives (continued)
Invariant Differential Equations of the First Order
Notes
Problems for Chapter 1
2
First-Order Ordinary Differential Equations
Lie's Integrating Factor
The Converse of Lie's Theorem
Invariant Integr