## Principles & applications of tensor analysis |

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### Contents

Basic Tensor Theory | 13 |

Christoffel Symbols and the Covariant Derivatives | 43 |

RiemannChristoffel Tensors | 69 |

Copyright | |

2 other sections not shown

### Common terms and phrases

associated tensors base vectors Chapter Christoffel symbols Christoffel tensor classical mechanics components contravariant metric tensor contravariant tensor corresponding covariant derivative covariant tensor curvature differential dimensional dot product dr d0 ds ds dt dt dynamics Equa equal to zero evaluated example force vector Frenet formula geodesic h dr illustrate Equation inertial system inner product intrinsic derivative invariant Jacobian Kronecker Delta Lagrange's equations Laplace's equation Laplacian line element dS2 Lorentz transformations Minkowski acceleration mixed tensor Newtonian gravitational potential orbit orthogonal cartesian co-ordinates orthogonal co-ordinate system partial derivatives particle polar co-ordinates position vector r2 sin2 rank and mixed relative tensor respect Ricci tensors Riemann second kind side of Equation space special theory Substituting Equation summation surface tensor analysis tensor equation tensor notation tensor Rank term in Equation theory of relativity tion two-body problem u1 and u2 values velocity vector yields the result