This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory.

In addition to the standard results of advanced calculus, the book contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis.

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

This book therefore extends and complements the geometrical symbolism Guénon employs in several of his other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science.

"The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions.

Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations.

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation.