Spivak M. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus

Addison Wesley, 1965. — 158 p. — ISBN 0-8053-9021-9.Michael Spivak's Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus is a short text treating analysis in several variables in Euclidean spaces and on differentiable manifolds.Mathematics has been expanding in all directions at, a fabulous rate during the past half century. New fields have emerged, the diffusion into other disciplines has proceeded apace, and our knowledge of I he classical areas has grown ever more profound. At the same time, one of the most striking trends in modern mathematics is the constantly increasing interrelationship between its various branches. Thus the present-day students of mathematics are faced with an immense mountain of material. In addition to the traditional areas of mathematics as presented in the traditional manner — and these presentations do abound — there are the new and often enlightening ways of looking at these traditional areas, and also the vast new areas teeming with potentialities. Much of this new material is scattered indigestibly throughout the research journals, and frequently coherently organized only in the minds or unpublished notes of the working mathematicians. And students desperately need to learn more and more of thie material.