1987 • 952 Pages • 341.26 MB • English

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Engineering Mathematics

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The English Language Book Society is funded by the Overseas Development Administration of the British Government. It makes available low- priced, unabridged editions of British publishers' textbooks to students in developing countries. Below is a list of some other books on engineering published under the ELBS imprint. Bajpai, Mustoe and Walker Advanced Engineering Mathematics John Wiley Drabble Elementary Engineering Mechanics Macmillan Greer Statistics for Engineers Stanley Thomes Greer and Taylor Mathematics for Technicians New Levels I-III Stanley Thomes Hughes and Hughes Engineering Science Longman Jeffrey Mathematics for Engineers and Scientists Chapman & Hall Stephenson Mathematical Methods for Science Students Longman Stroud Further Engineering Mathematics Macmillan Zammit Motor Vehicle Engineering Science for Technicians Longman

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Engineering Mathematics Programmes and Problems Third Edition K.A. STROUD Fonnerly Principal Lecturer in Mathematics, Lanchester Polytechnic, Coventry English Language Book Society!Macmillan

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Macmillan Education Ltd Houndmills, Basingstoke, Hampshire RG21 2XS Companies and representatives throughout the world © K. A. Stroud 1970, 1982, 1987 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, mechanical, photocopying, recording or otherwise, without the prior written permission of the Publishers. First published 1970 Reprinted (with corrections) 1972, 1973, 1974, 1975,1977,1978,1979 (twice), 1980, 1981 (twice) Second edition 1982 Reprinted 1983, 1984, 1985 (twice), 1986 Third edition 1987 Reprinted 1987,1988,1990 ELBS edition first published 1990 ISBN 978-0-333-54454-9 ISBN 978-1-349-12153-3 (eBook) DOI 10.1007/978-1-349-12153-3

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CONTENTS Preface to the first edition xi Preface to the second edition xiii Preface to the third edition xiv Hints on using the book xv Useful background information xvi Programme 1: Complex Numbers, Part 1 Introduction: The symbol j; powers of j; complex numbers Multiplication of complex numbers Equal complex numbers Graphical representation of a complex number Graphical addition of complex numbers Polar form of a complex number Exponential form of a complex number Test exercise I Further problems I Programme 2: Complex Numbers, Part 2 37 Introduction Loci problems Test exercise II Further problems II Programme 3: Hyperbolic Functions 73 Introduction Graph$ of hyperbolic functions Evaluation of hyperbolic functions Inverse hyperbolic functions Log form of the inverse hyperbolic functions Hyperbolic identities Trig. identities and hyperbolic identities Relationship between trigonometric & hyperbolic functions Test exercise III Further problems III Programme 4: Determinants 101 Determinants Determinants of the third order Evaluation of a third order determinant Simultaneous equations in three unknowns Consistency of a set of equations v

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Properties of determinants Test exercise IV Further problems IV Programme 5: Matrices 141 Definitions; order; types of matrices Operations Transpose and inverse of a square matrix Solution of sets of linear equations Gaussian elimination method Eigenvalues and eigenvectors Revision summary Test exercise V Further problems V Programme 6: Vectors 189 Introduction: Scalar and vector quantities Vector representation Two equal vectors Types of vectors Addition of vectors Components of a given vector Components of a vector in terms of unit vectors Vectors in space Direction cosines Scalar product of two vectors Vector product of two vectors Angle between two vectors Direction ratins Summary Test exercise VI Further problems VI 219 Programme 7: Differentiation Standard differential coefficients Functions of a function Logarithmic differentiation Implicit functions Parametric equations Test exercise VII Further problems VII Programme 8: Differentiation Applications, Part 1 243 Equation of a straight line vi

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Centre of curvature Test exercise VIII Further problems VIII 271 Programme 9: Differentiation Applications, Part 2 Inverse trigonometrical functions Differentiation of inverse trig. functions Differential coefficients of inverse hyperbolic functions Maximum and minimum values (turning points) Test exercise IX Further problems IX Programme 10: Partial Differentiation, Part 1 299 Partial differentiation Small increments Test exercise X Further problems X Programme 11: Partial Differentiation, Part 2 325 Partial differentiation Rates of change problems Change of variables Test exercise XI Further problems XI Programme 12: Curves and Curve Fitting 345 Standard curves Asymptotes Systematic curve sketching Curve fitting Method of least squares Test exercise XII Further problems XII Programme 13: Series, Part 1 395 Sequences and series Arithmetic and geometric means Series ofpowers of natural numbers Infinite series: limiting values Convergent and divergent series Tests for convergence; absolute convergence Test exercise XIII Further problems XIII vii

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Programme 14: Series, Part 2 425 Power series, Maclaurin's series Standard series The binomial series Approximate values Limiting values Test exercise XIV Further problems XIV Programme IS: Integration, Part 1 455 Introduction Standard integrals Functions of a linear function Integrals of the form ff(x)./'(x)d.x etc. Integration of products - integration by parts Integration by partial fractions Integration of trigonometrical functions Test exercise XV Further problems XV Programme 16: Integration, Part 2 487 Test exercise XVI Further problems XVI Programme 17: Reduction Formulae 517 Test exercise XVII Further problems XVII Programme 18: Integration Applications, Part 1 533 Parametric equations Mean values R.m.s. values 5ummary sheet Test exercise XVIII Further problems XVIII Programme 19: Integration Applications, Part 2 555 Introduction Volumes of solids of revolution Centroid of a plane figure Centre ofg ravity of a solid of revolution Lengths of curves Lengths of curves - parametric equations Surfaces of revolution viii

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Surfaces of revolution - parametric equations Rules of Pappus Revision summary Test exercise XIX Further problems XIX Programme 20: Integration Applications, Part 3 581 Moments of inertia Radius of gyration Parallel axes theorem Perpendicular axes theorem Useful standard results Second moment of area Composite figures Centres of pressure Depth of centre of pressure Test exercise XX Further problems XX Programme 21: Approximate Integration 615 Introduction ApprOXimate integration Method 1 - by series Method 2 - Simpson's rule Proof of Simpson 's rule Test exercise XXI Further problems XXI Programme 22: Polar Co-ordinates System 637 Introduction to polar co-ordinates Polar curves Standard polar curves Test exercise XXII Further problems XXII Programme 23: Multiple Integrals 663 Summation in two directions Double integrals: triple integrals Applications Alternative notation Determination of volumes by multiple integrals Test exercise XXIII Further problems XXIII Programme 24: First Order Differential Equations 691 Introduction Formation of differential equations ix

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