Introduction to Vector and Tensor Analysis
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
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algebraic arrow associated axes axis basis calculus Cartesian coordinate system Cartesian vector Chapter Christoffel symbols coefficients cofactor completes the proof Compute consider constant contravariant valence contravariant vector corresponding covariant and contravariant covariant vector cross product defined determinant dr|dt dt dt elements Euclidean space Example expression fact function fundamental metric tensor geodesic given indicated introduced invariant line integral linear linearly independent magnitude mathematical matrix metric tensor multiplication n-tuples notation obtain orthogonal Cartesian parallel parametric equations partial derivatives perpendicular physical plane Problem properties reader real numbers rectangular Cartesian coordinate rectangular Cartesian system relation representation represented respect result Riemannian space rotation scalar field Section Show skew symmetric ſº space curve Suppose surface tangent vector theory three-space transformation equations transformation group transformation law triple vector concept vector field zero