## An introduction to tensor calculus and relativity |

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### Contents

Special Principle of Relativity Lorentz Transformations | 1 |

Covariance of the laws of motion | 4 |

Special principle of relativity | 5 |

Copyright | |

35 other sections not shown

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### Common terms and phrases

acceleration accordingly affinity arbitrary assumed charge classical clock components constant contravariant vector coordinate frame corresponding covariant derivative covariant tensor covariant vector covariant with respect curve Deduce defined denoted differentiation displacement vector Einstein's electromagnetic field energy energy-momentum tensor equivalent Euclidean expressed field tensor follows force function geodesic given by equation gravitational field hence identical indices inertial frame instant interval invariant density Lorentz transformation equations Maxwell's equations measured mechanics member of equation metric tensor mixed tensor moving neighbouring points observer obtain orthogonal transformations parallel displacement particle particle's physical plane proper mass prove quantities rectangular Cartesian axes rectangular Cartesian coordinates reference frame relative tensor result Ricci tensor right-hand member rocket rotation scalar second rank Show skew-symmetric space-time special Lorentz transformation spherical polar coordinates stationary Suppose symmetric tensor density tensor equation theory transformation equations transformation law valid velocity world-line zero