New Tertiary Mathematics. Further Applied Mathematics

PERGAMON INTERNATIONAL LIBRARY of Science, Technology, Engineering and Social Studies The 1000-volume original paperback library in aid of education, industrial training and the enjoyment of leisure Publisher: Robert Maxwell, M.C. NEW TERTIARY MATHEMATICS Volume 2 Part 2 Further Applied Mathematics THE PERGAMON TEXTBOOK INSPECTION COPY SERVICE A n inspection copy of any book published in the Pergamon International Library w i l l gladly be sent t o academic staff w i t h o u t obligation for their consideration for course a d o p t i o n or recommendation Copies may be retained for a period of 6 0 days from receipt and returned if not suitable W h e n a particular title is adopted or recommended for a d o p t i o n for class use and the recommendation results in a sale of 12 or more copies, the inspection copy may be retained w i t h our compliments The Publishers w i l l be pleased to receive suggestions for revised editions and new titles to be published in this important International Library Some other Pergamon titles of interest C. PLUMPTON & W. A. TOMKYS Sixth Form Pure Mathematics Volumes 1 & 2 Theoretical Mechanics for Sixth Forms 2nd SI Edition Volumes 1 & 2 D. T. E. MARJORAM Exercises in Modern Mathematics Further Exercises in Modern Mathematics Modern Mathematics in Secondary Schools D. G. H. B. LLOYD Modern Syllabus Algebra E. Œ. WOLSTENHOLME Elementary Vectors 3rd SI Edition NEW TERTIARY MATHEMATICS C. Plumpton Queen Mary College, London P. S. W. Macllwaine Volume 2 Part 2 Further Applied Mathematics PERGAMON PRESS Oxford ■ New York ■ Toronto ■ Sydney ■ Paris ■ Frankfurt UK Pergamon Press Ltd., Headington Hill Hall, Oxford OX3 OBW, England USA Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523, U.S.A. CANADA Pergamon of Canada, Suite 104, 150 Consumers Road, Willowdale, Ontario, M2J 1P9, Canada AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., P.O. Box 544, Potts Point, N.S.W. 2011, Australia FRANCE Pergamon Press SARL, 24 rue des Ecoles, 75240 Paris, Cedex 05, France FEDERAL REPUBLIC O F GERMANY Pergamon Press GmbH, 6242 Kronberg-Taunus, Hammerweg 6, Federal Republic of Germany Copyright © 1981 C. Plumpton and P. S. W. Macllwaine All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers First edition 1981 British Library Cataloguing in Publication Data Plumpton, Charles New tertiary mathematics. - (Pergamon international library). Vol. 2, Part 2: Further Applied mathematics 1. Mathematics- 1961 — I. Title II. Macllwaine, Patrick Sydney Wilson 510 QA36 80-49934 ISBN ISBN ISBN ISBN 0-08-025037-8 0-08-025026-2 0-08-025036-X 0-08-021646-3 Hardcover Flexicover Flexicover (non-net) (4 volume set, hard only) Printed in Great Britain by A. Wheaton & Co. Ltd. Exeter Preface IN this volume, the basic "Applied Mathematics" of Volume 1 Part 2 is extended and developed to cover almost all the topics of Theoretical Mechanics and Probability included in Advanced Level Applied Mathematics and Further Mathematics syllabuses of the seven Examining Boards. The aim of the book is to provide an adequate course and source book for mathematical pupils in Sixth Forms of Schools, Sixth Form Colleges, Colleges of Further Education and Technical Colleges, and students engaged in private study. Chapters 7-10 on Theoretical Mechanics are strongly "vector-based", wherever this is appropriate. Chapter 7 extends the statics of Volume 1 to the analysis of systems of forces in three dimensions, c