SECOND-YEAR TECHNICIAN MATHEMATICS

Transcription

1 SECOND-YEAR TECHNICIAN MATHEMATICS

2 Other books in this series First-year Technician Mathematics: Rhys Lewis Third-year Technician Mathematics and Applications: Rhys Lewis Books by the same author Electronic Systems for Radio, Television, and Electronics Mechanics Books of related interest Linear Electronic Circuits and Systems: G.D. Bishop Digital Electronic Circuits and Systems: Noel M. Morris Essential Formulae for Electronic and Electrical Engineers: Noel M Morris Electrical Circuits and Systems: Noel M Morris The Electrical Principles of Telecommunications: R. Lowe and D. Nave Basic Electrotechnology: H. Cotton

3 SECOND-YEAR TECHNICIAN MATHEMATICS for Electrical, Electronics and Telecommunications Students RHYS LEWIS B.Sc. Tech., C.Eng., M.LE.E. Senior Lecturer, Openshaw Technical College, Manchester

4 Rhys Lewis 1975 All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission. First published 1975 by THE MACMILLAN PRESS LTD London and Basingstoke Associated companies in New York Dublin Melbourne Johannesburg and Madras SBN ISBN ISBN (ebook) DOI / This book is sold subject to the standard conditions of the Net Book Agreement. The paperback edition of this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser.

5 Contents Preface vii Arithmetic and Aids to Calculation Systems of numbers The binary system - basic arithmetical processes in the binary system - non-integral numbers: binary fractions Use of logarithms 12 Review of basic theory of logarithms - use of common logarithms - natural logarithms - antilogging of natural logarithms - logarithms to any base in terms of common logarithms Further use of the slide rule 25 Powers of e - natural logarithms - powers of any number - reciprocals 2 Algebra Indices Summary of definitions and rules Transposition of formulae Simultaneous linear equations Quadratic equations Solution of quadratic equations 3 Graphs Graphical solution of quadratic equations Use of straight-line graphs for non-linear relationships Laws of the form y = Axn Use of logarithmic graph paper

6 vi Second -Year Technician Mathematics 4 Mensuration 92 The mid-ordinate rule 93 Average value of a varying quantity.~ average height of a curve Simpson's rule for area determination 96 Root-mean-square values 97 Areas and volumes of regular bodies 108 Spheres ~ cylinders ~ cones ~ pyramids 5 Trigonometry 122 Functions of angles greater than Functions of angles between quadrants Equations of sinusoidal functions 128 Phase relationships between time-varying quantities 131 Phase relationships between sinusoidal functions Trigonometric identities 139 Trigonometric equations 142 Solution of triangles 144 The sine rule ~ the cosine rule ~ areas of triangles 6 Vectors and Phasors 154 Vector diagrams 156 Phasor diagrams 156 Summation of vectors and phasors using parallelograms 159 Problems involving more than two vectors 165 Vector and phasor resolution ~ vector or phasor subtraction Use of phasor diagrams in electrical circuit problems Geometry 178 Circles: vocabulary of terms 178 Thwrems 1~ Test Papers 199 Answers to Exercises 211 Answers to Test Papers 215

7 Preface This book is the second in a series of three books covering the mathematical syllabuses of courses leading to Electrical and Electronic Technician status and ultimately to Technician Engineer status. At the present time these courses include the City and Guilds of London Institute courses 280, 281,285,270 and 272. The titles of the books, breaking the total syllabuses into four years, stem from the organisation of these courses. With the advent of the Technician Education Council, and subsequent reorganisation of courses, it may be found that the breakdown by year may change; however, it is anticipated that the total content of all three volumes will more than adequately cover the total syllabus content of all electrical and electronic technician courses both present and proposed. All three books contain a large number of worked examples and exercises for the students to complete and end with a number of typical examination papers covering the content of each volume. The assistance and advice of Mr Noel M. Morris, the series editor, is gratefully acknowledged. In addition, I would particularly like to thank Mrs L. J. E. Jones for typing the manuscript and, as always, my wife for her help and encouragement. Openshaw, Manchester RHYS LEWIS