An Introduction to the Calculus

Abstract

THIS little volume has been designed as a first course in the calculus for Indian students. The treatment is the outcome of years of experiment and observation and the method followed is, as the author points out, rigorous in the long run. By this is implied that the refinements of modern rigour are gradually developed, as they should be, in accord with the fundamental principles of true teaching. This idea, which is not too frequently apparent in mathematical text-books, as distinct from those written especially for schools, has been well and consistently carried out. After a commendable foreword to the student, twelve instructive chapters follow which should ensure a firm foundation for future study of the calculus. Beginning with limits and continuity, occupying three chapters, the student is led to the derivative itself. The usual standard theorems concerning the differentiation of functions are then considered, together with sscond order derivatives, maxima, minima and the exponential and logarithmic functions. Integration is next introduced as the inverse of differentiation, its full significance being developed later in accordance with the aim of the writer. The final chapter, after summarizing a few of the more important standard results previously established, proceeds to discuss briefly Taylor's and Maclaurin's series, Rolle's theorem, partial fractions, hyperbolic functions and surface and volume integrals.