Graphical Methods In Applied Mathematics - A Course Of Work In Mensuration And Statics For …..
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Graphical Methods In Applied Mathematics - A Course Of Work In Mensuration And Statics For Engineering And Other Students
Graphical Methods In Applied Mathematics - A Course Of Work In Mensuration And Statics For Engineering And Other Students
By G. C. Turner
Publisher: Turner Press
Number Of Pages: 400
Publication Date: 2007-03-15
ISBN-10 / ASIN: 1406765724
ISBN-13 / EAN: 9781406765724
Binding: Paperback
Text extracted from opening pages of book: GRAPHICAL METHODS IN APPLIED MATHEMATICS PREFACE. THE importance of Graphics in modern mathematical training, and its numerous uses in practical work, render unnecessary any excuse for the publication of an elementary account of some of its applications, provided these applications are chosen with discretion and treated with clearness. The author is hopeful that competent judges will consider that the present book fulfils these requirements. It has not been written with a view to any particular examination ; but the easier parts will be found to meet the needs of secondary schools and of candidates in military and naval examinations ; while students in technical colleges and candidates in the examinations of the University of London will, it is believed, find most of the chapters of definite use to them. All sections and exercises marked with an asterisk should be omitted in a first reading of the volume ; students who wish further to curtail the course of work will find an easy First Course mapped out on page ix. Special attention is directed to the large number of concrete examples, worked out in detail, which are supplied in the various chapters. It is essential that the student should himself work out the graphical constructions according to the instruc tions given, and afterwards compare his results with those obtainable by measurement of the figures in the text. To avoid the tendency to produce very small figures, which characterise the work of almost all students, the instructions supplied will be found to determine large drawings in nearly all cases. An endeavour should be made so to construct the diagrams that all lengths are correct to at least three numerical figures ; it is hoped that this degree of accuracy has been attained in the answers given at the end of the book. Owing to slight, vi PREFACE. perhaps very slight, errors in construction the final result, obtained by measurement, will often be slightly incorrect in the third figure. The student is strongly urged not to confine himself to graphical methods only in statics and mensuration. The employment of calculation and graphics may be likened to the use of our two hands; no matter how highly developed one instrument may be, much more can be done with the two conjointly than with one alone. Of necessity, in this book analytical methods and calculations are only incidentally touched upon, but students with a knowledge of Trigonometry will see that even roughly drawn vector polygons can easily be used for purposes of calculation. This opportunity is gladly taken to acknowledge a debt of gratitude to Prof. Henrici, F. ES., of the Central Technical College, London to whom the author’s first knowledge of the true value of Graphics is due. His teaching showed Statics and Dynamics not merely as a branch of somewhat unsatisfying Mathematics, but as a real and interesting subject with important applications. Those acquainted with Prof. Henrici’s work and lectures will appreciate the author’s obligation to him. Thanks are also due to Mr. E. F. Witchell of the Central Technical and Goldsmiths’ Colleges for reading most of the proof sheets, suggesting improvements, and correcting some of the answers; to Prof. B. A. Gregory and Mr. A. T. Simmons for their unsparing trouble during the preparation of the MSS. and while the book was passing through the press; and finally to the Senate of the University of London and the Controller of H. M. Stationery Office for permission to make use of problems set in various University, Civil Service, Naval, Military, and Board of Education examinations. The source of each such problem, and the date when subsequent to 1902, has been given after the question. G. C, TfJENEK. SIDCUP, November, 1907- CONTENTS. CHAPTER I. PAGE GRAPHICAL ARITHMETIC,-1 Miscellaneous Examples /., 41 CHAPTER II. GRAPHICAL MENSURATION, - 43 Miscellaneous Examples IL, - - - 65 CHAPTER III. VECTORS AND THEIR APPLICATION TO VEL
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