An Introduction to Differentiable Manifolds and Riemannian Geometry : An Introduction to Differentiable Manifolds and Riemannian Geometry

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 book is intended to lead the student from a reasonable mastery of advanced multivariable calculus and a rudimentary knowledge of general topology and linear algebra to a solid fundamental knowledge of differentiable manifolds, including some facility in working with the basic tools of manifold theory: tensors, differential forms, Lie and covariant derivatives, multiple integrals, and so on An Introduction to Differentiable Manifolds and Riemannian Geometry