An introduction to differentiable manifolds and Riemannian geometry (2nd Ed), Volume 120, Second Edition (Pure and Applied Mathematics)

The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields This is a revised printing of one of the classic mathematics texts published in the last 25 years. This revised edition includes updated references and indexes and error corrections and will continue to serve as the standard text for students and professionals in the field. Differential manifolds are the underlying objects of study in much of advanced calculus and analysis. Topics such as line and surface integrals, divergence and curl of vector fields, and Stokeand#39;s and Greenand#39;s theorems find their most natural setting in manifold theory. Riemannian plane geometry can be visualized a In this chapter, we establish some preliminary notations and give an intuitive, geometric discussion of a number of examples of manifolds-the primary objects of study throughout the book. An introduction to differentiable manifolds and Riemannian geometry (2nd Ed)