Since first publication in 1954, this text has been widely used in North American universities in introductory courses in science and engineering. It is a streamlined text, in which essential ideas are not buried in endless detail. For science students and engineers the sine qua non is formal training in the techniques and manipulations which they will use in their regular engineering courses and in their professional work. But at the same time there is in every class a small group who have an interest in knowing the reasons back of their manipulative work. In Professor Jeffery's text, a framework of fundamental principles is always in sight and available. In the new edition, the study of the definite integral has been moved ahead from Chapter VII to Chapter V. The differential and the differential notation are introduced and used soon after the derivative has been defined. Some topics have been added—the chain rule for partial derivatives, directional derivatives, l'Hospital's rule, determinants, and linear dependence relative to vectors. More practice problems, especially in determining anti-differentials, have been added and where experience has shown it desirable, more detailed explanations have been given.