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. PREFACE 5 PREFACE TO THE THIRD EDITION 7 CONTENTS 9 INTRODUCTION 15 CHAPTER I. SPEED AND LIMITS 26 CHAPTER II. THE DERIVATIVE OF A FUNCTION 33 CHAPTER III. RULES AND FORMULAS FOR DIFFERENTIATION 40 CHAPTER IV. DIFFERENTIALS, DIFFERENTIAL EQUATIONS AND ANTI-DIFFERENTIALS 50 CHAPTER V. THE DEFINITE INTEGRAL 64 CHAPTER VI. THE TRANSCENDENTAL FUNCTIONS 85 CHAPTER VII. RELATED RATES, MAXIMA AND MINIMA, CURVE PLOTTING 108 CHAPTER VIII. DISPLACEMENT, VELOCITY AND ACCELERATION. APPLICATIONS OF RATES OF CHANGE. FIRST MOMENTS, WORK, AND PRESSURE 126 CHAPTER IX. FURTHER METHODS OF DETERMINING ANTI-DIFFERENTIALS 153 CHAPTER X. ROLLE'S THEOREM, MEAN VALUE THEOREM, PARAMETRIC EQUATIONS, ARC LENGTH, SURFACE OF REVOLUTION, CURVATURE, SECOND ORDER DIFFERENTIAL EQUATIONS, L'HOSPITAL'S RULE 171 CHAPTER XI. FUNDAMENTAL THEOREMS 203 CHAPTER XII. INFINITE SERIES 215 CHAPTER XIII. PARTIAL DERIVATIVES, MULTIPLE INTEGRATION, MOMENTS OF INERTIA 234 CHAPTER XIV. VECTORS AND SOLID GEOMETRY 266 CHAPTER XV. DETERMINANTS MATRICES AND LINEAR EQUATIONS 279 CHAPTER XVI. LINEAR RELATIONS AMONG VECTORS 289 CHAPTER XVII. VECTOR PRODUCTS APPLICATIONS OF VECTORS 295 CHAPTER XVIII. QUADRIC SURFACES 303 INDEX 311
