Tensors and manifolds: with applications to mechanics and relativity

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Vector spaces Multilinear mappings and dual spaces Tensor product spaces Tensors Symmetric and skew-symmetric tensors Exterior (Grassman) algebra The tangent map of real cartesian spaces Topological spaces Differentiable manifolds Submanifolds Vector fields, 1-forms, and other tensor fields Exterior differentiation and integration of differential forms The flow, and the lie derivative of a vector field Integrability conditions for distributions of a vector field Integrability conditions for distributions and for Pfaffian systems Pseudo-riemannian geometry Connection 1-forms Connections on manifolds Mechanics Additional topics in mechanics A spacetime Some physics on Minkowski spacetime Einstein spacetimes Spacetimes near an isolated star Nonempty spacetimes.