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Calculus FOR Engineers % Tr.i.cJu o^^jr r.i^ LIBRARY OF THE UNIVERSITY OF CALIFORNIA. aass CALCULUS FOE ENGINEEES, QtambxiUQt: PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. : THE CALCULUS FOE ENGINEEES BY JOHN PERRY, M.E, RSc, F.R.S. WH. SCH., ASSOC. MEMB. INST. C.E., PROFESSOR OF MECHANICS AND MATHEMATICS IN THE ROYAL COLLEGE OF SCIENCE, LONDON: PRESIDENT OF "IBan^Xtsiil^^O^ OF ELECTRICAL ENGINEERS. FIFTH IMPRESSION. Honlron EDWARD ARNOLD, BEDFORD STREET. 37, lAll Rights reserved,] Engirie- ring Library .V^^ Digitized by tine IntemVt Arciiive in 2008 witftfanding from IVIicrosoft Corporation littp://www.arcliive.org/details/calculusforenginOOperrricli PEBFACB. This book describes what has for many years been the most important part of the regular course in the Calculus for Mechanical and Electrical Engineering students at the Finsbury Technical College. It was supplemented by easy work involving Fourier, Spherical Harmonic, and Bessel Functions which I have been afraid to describe here because the book is already much larger than I thought it would become. The students in October knew only the most elementary mathematics, many of them did not know the Binomial Theorem, or the definition of the sine of an angle. In July they had not only done the work of this book, but their knowledge was of a practical kind, ready for use in any such engineering problems as I give here. One such student, Mr Norman Endacott, has corrected the manuscript and proofs. He has worked out many of the exercises in the third chapter twice over. I thank him here for the care he has taken, and I take leave also to say that a system which has, year by year, produced many men with his kind of knowledge of mathematics has a good deal to recommend it. I say this through no vanity butbecause Iwishto encouragethe earnest student. Besides I cannot claim more than a portion of the credit, for I do not think that there ever before was such a complete 2/ 12b J VI PREFACE. harmony in the working of all the departments of an educational institution in lectures and in tutorial, labora- tory, drawing office and other practical work as exists in the Finsbury Technical College, all tending to the same end to give an engineer such a perfect acquaintance with ; his mental tools that he actually uses these tools in his business. Professor Willis has been kind enough to read through the proofs and I therefore feel doublysure thatno important mistake has been made anywhere. An experienced friendthinksthat I might with advantage have given many more illustrations of the use of squared paper just at the beginning. This is quite possible, but if a studentfollows my instructions he will furnish all this sort of illustration very much better for himself Again I might have inserted many easy illustrations of integration by numerical work such as the exercises on the Bull Engine and on Beams and Arches which are to be found in my book on Applied Mechanics. I can only say that I encourage students to find illustrations of this kind for themselves; and surely there must be some limit to spoon feeding. JOHN PERRY. EoYAL College of Science, London, 16th March, 1897.