## Tensor analysis: theory and applications to geometry and mechanics of continua |

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### Contents

LINEAR VECTOR SPACES MATRICES 1 Coordinate Systems | 1 |

The Geometric Concept of a Vector | 3 |

Linear Vector Spaces Dimensionality of Space | 6 |

Copyright | |

117 other sections not shown

### Common terms and phrases

angle arbitrary assume base vectors calculation called Christoffel symbols class C2 components consider constant coordinate system corresponding covariant derivative curvature curve curvilinear coordinate deduce defined definition denote derivatives determined differential equations displacement dynamical elastic element of arc Euclidean Euler's equations follows force formula Gaussian curvature geodesic geodesic curvature geometry given gravitational hence independent integral invariant Kronecker deltas Lagrangean equations length linear transformation linearly manifold mass matrix mechanics metric tensor mixed tensor motion n-dimensional normal obtain orthogonal cartesian parallel parameter particle plane problem properties quadratic form real numbers reference frame region relation relative tensor result right-hand member scalar set of functions solution space sphere spherical suppose symmetric tensor of rank theorem theory trajectory transformation of coordinates unit vector values vanish variables vector field velocity write Y-system yields zero