PREFACE 



FOR the past nine years I have been lecturing in this subject to 

 students taking courses in Mechanical and Electrical Engineering 

 at the Woolwich Polytechnic, and this book is based on the work 

 done by the senior students there. So as not to make the book 

 too cumbersome for a text-book, a preliminary knowledge of the 

 fundamental principles of Algebra, Trigonometry, and Mensuration, 

 and the use of Logarithms and squared paper, has been assumed, 

 this being well within the scope of the elementary student. The 

 book is meant to cover a two- or three-years' course, and it is 

 roughly divided into three sections : 



(1) Algebra and Trigonometry. 



(2) The Differential and Integral Calculus. 



(3) The application of the subject-matter of the two previous 



sections to concrete examples. 



The work in Section I has been carefully selected in such a 

 way as to help the student with the later work in the Calculus. 

 There is no doubt that after the idea of the Calculus has been 

 thoroughly grasped, a great many of the so-called difficulties 

 which arise out of the work are entirely due to a weakness in the 

 knowledge of the fundamental principles of Algebra and Trigono- 

 metry. For instance, many students fail in the integration of 

 sin 2 x, not because they do not knofa how to integrate, but because 

 they fail to see or fail to remember that 



sin 2 x = - (1 cos 2x) 







Again, many fail to integrate algebraic functions because they 

 have such weak notions of partial fractions and simple substitu- 

 tions. Section I has been written with the idea of removing this 

 weakness. 



The Calculus has been treated as thoroughly as the size of the 

 book allows. It might be said that this part of the work has 

 been elaborated too much for the practical side of Mathematics ; 

 but it must be remembered that the Calculus cannot be success- 

 fully applied to the problems which occur in actual practice 

 until the student has become thoroughly familiar with its under- 



