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A FIRST COURSE IN MATHEMATICS FOB TECHNICAL STUDENTS HY P. J. HALEE, B. Sc., A. M. I. MECH. E., A. I. E. E. IIM I. K IVKKK IN I-M. 1NKKRIM1 Hl-HJKCTS I UK L. C C. IIACKNfcY IV lll AND A. H. STUART, B. Sc., F. R. A. S. LKfirUKH IN MVIHKMMKS AT TUB I-. C . HACKNEY INS1ITU1K LONDON W. B. CLIVE fg Cufortaf preec HIGH ST., NEW OXFORD ST., W. C. 1914 PREFACE. THIS little book is intended to meet the growing demand for a simple and practical course on the rudiments of mathematics suitable for students who are preparing for a course of technical study. It is modelled on a scheme covering all the usual requirements of a First Years Course in Preliminary Technical Classes. The authors have endeavoured to insure that the atmosphere of the workshop should pervade the whole book. Wherever possible the problems deal with concrete quantities which refer to actual working conditions. The necessary reference which the student must make to the drawings accompanying many of the problems should form a good introduction to the art of reading machine drawings, plans, etc. Graphical methods have been introduced into almost every chapter, as the necessity for the correlation of technical drawing and mathematics cannot be too strongly insisted upon. When studying the common solids it is important that the student should make paper models of them. Full instructions are given in the text. Special emphasis has been laid on the importance of approxi mate calculations. From the practical point of view it must be remembered that although accuracy is essential in all cases it differs in degree. The rough estimate may, in the end, be quite VI PREFACE. as near the truth as the calculation made at leisure, for in most cases the data are only approximate to begin with. The student should be encouraged to apply a rough check to every example he works. This rough mental estimate of a result is not only a useful check in itself, but it is invaluable as forming a habit essential to successful workshop practice. The scheme of work will be found to cover all the requirements of the first year examination in Mathematics in the Preliminary Technical Course of the Lancashire and Cheshire Union of Institutes, the Education Committee of the County Council of the West Riding of Yorkshire, the National Union of Teachers, and other similar examining bodies. As the authors are lecturers in the employment of the London County Council it is necessary for them in accordance with recent regulations to state explicitly that the London County Council are in no way responsible for the contents of this book and have taken no part in its publication. P. J. H. A. H. S. HACKNEY INSTITUTE, October 10, CONTENTS. CHAPTER 1 AUK I. MEASUREMENT DECIMAL FRACTIONS . . I II. VULUAR FRACTIONS Hi III. POWERS AND ROOTS ... .. . . ... . . 2 2 IV. USE OF JSgUAKED P PF, K KAPHS . ... JS V. RATIO AND PROPORTION ... 38 VI. ANGLES AND PLANK FKIUKKS ... .. . ... 48 VII. CIRCUMFERENCE AND AREA OF A OKCLK , r 6 VI1L USE OF FORMULAE 63 IX. ALCEBRAIC PROCESSKN .. 08 X. SIMPLE EQUATIONS . ... 84 XI. COMMON SOLIDS 92 XII. RELATIVE DENSITIES, WEICIITS, AND VOLUMKS 101 XIII. drRAPHS OF SlMPLE FUNCTIONS 109 XIV. SIMULTANEOUS KOUATIONS 114 ANSWERS 120 CHAPTER I. MEASUREMENT DECIMAL FRACTIONS. Measurement. If AVG were asked to determine the length of the line shown in Fig. 1, we should apply some kind of graduated scale to it. In this country we are accustomed to the length called an inch, and if an inch scale were applied to this line it would reveal the fact that the length lay between two inches Vie. I and three inches a length measured in inches, say three inches, is frequently written thus 3. If the inches were subdivided into quarters we could say that the required length lay between 2 and 2f
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A First Course In Mathematics For Technical Students
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