Publisher's Synopsis
From the PREFACE.
The favorable reception accorded the two volumes on the Calculus in this series shows that they have been serviceable in supplying a real need. A general demand has arisen for a similar treatment of the subjects in briefer form, suitable for use in shorter and more elementary courses. Accordingly, in response to numerous requests and suggestions, the present volume has been prepared.
The part on the Differential Calculus is of essentially the same character as the former separate volume (which will be referred to in the text as D. C), but the range of topics is restricted; various theorems have been put in less abstract form, and fewer alternative proofs have been given. The chapter on the expansion of functions has been so arranged that the remainder theorem may be omitted without marring the continuity of the subject. In the treatment of functions of two independent variables no use is made of an auxiliary variable.
The characteristic features of the larger book are retained. Some of these are as follows: --
1. The derivative is presented rigorously as a limit.
2. The process of differentiation is so arranged as to give the x-derivative of a function of u, in which u is a function of x; the resulting type forms being printed in full-face letters in the text and collected for reference at the end of the chapter.
3. Maxima and minima are discussed as the turning values in the variation of a function, with complete graphical representation.
4. The notions of rates and differentials are so presented as to grow naturally out of the idea of a derivative, and are not introduced until the student has become familiar with the process of finding the derivative and with its use in studying the variation of a function.
5. The related theories of inflexions, curvature, and asymptotes receive direct and comprehensive treatment....