Tensors and manifolds : with applications to physics / Robert H. Wasserman.

Includes bibliographical references and index.

Vector spaces -- Multilinear mappings and dual spaces -- Tensor product spaces -- Tensors -- Symmetric and skew-symmetric tensors -- Exterior (Grassmann) algebra -- The tangent map of real Cartesian spaces -- Topological spaces -- Differentiable manifolds -- Submanifolds -- Vector fields, 1-forms and other tensor fields -- Differentiation and integration of differential forms -- The flow and the lie derivative of a vector field -- Integrability conditions for distributions and for Pfaffian Systems -- Pseudo-Riemannian manifolds -- Connection 1-forms -- Connection on manifolds -- Mechanics -- Additional topics in mechanics -- A spacetime -- Some physics on Minkowski spacetime -- Einstein spacetimes -- Spacetimes near an isolated star -- Nonempty spacetimes-- Lie groups. -- Fiber bundles -- Connections on fiber bundles -- Gauge theory.

"This book is a new edition of Tensors and Manifolds: With Applications to Mechanics and Relativity which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanses modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline.

The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics."--Jacket.

Online resource; title from PDF title page (EBSCO, viewed June 15, 2017).

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