Higher Calculus

This book is intended for students who have completed an elementary course of calculus and are taking the subject further, more particularly, perhaps, on account of its applications in physics and engineering. It covers the ground of a calculus course at first-year level in universities and colleges of technology for students majoring in mathematics. It thus fills a gap between the numerous introductory texts and those on advanced analysis in which this material is embedded in a great deal of other matter. The emphasis is on essentials. Principles are treated rigourously while avoiding unnecessary difficulties for the student for whom mathematics is an ancillary subject. An original feature is the prominence given to the asymptotic property of the Taylor formula. The large number of examples has been carefully chosen to bring out the main points rather than to test manipulative ability; answers are given.

Preface; 1. Functions; 2. Differentiation; 3. Successive differentiation; 4. Taylor's theorem; 5. Partial derivatives; 6. Implicit functions; 7. Successive partial differentiation; 8. Maxima and minima; 9. Integration; 10. Infinite integrals; 11. Indefinite integrals; 12. Double integrals; Examples; Answers to Examples; Index.