The Absolute Differential Calculus (calculus of Tensors)Written by a distinguished mathematician, this classic examines the mathematical material necessary for a grasp of relativity theory. Covers introductory theories, fundamental quadratic forms, absolute differential calculus, and physical applications. 1926 edition. |
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The Absolute Differential Calculus: Calculus of Tensors Tullio Levi-Civita No preview available - 2005 |
Common terms and phrases
analogous angle arbitrary calculate Cartesian co-ordinates Chapter coefficients coefiicients condition congruence consider contravariant components corresponding covariant derivatives covariant differentiation curve defined definition denote determinant differential equations direction Einstein’s equivalent Euclidean space expression fact field finally find finite first approximation first derivatives first kind fixed follows formula functions of position geodesic geodesic curvature geometrical give given hence hypersphere hypothesis identity increments independent variables indices infinitely infinitesimal integral interchanging invariant left-hand side linear combinations Lorentz transformation manifold material particle metric motion multilinear form multiplying obtained ordinary orthogonal parallel displacement parameters parametric equations partial differential equations particular plane quadratic form quadric quantities reciprocal reduces reference relation represent result Riemann’s symbols Riemannian curvature satisfied significance simple system solution spacelike specified substituting summing with respect suppose surface tangential tensor theorem tions transformation values vanish vector velocity versor world line zero