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| Preface | |
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| Introduction | |
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| Vector and tensor fields | |
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| Introduction | |
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| Coordinate systems in Euclidean space | |
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| Suffix notation | |
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| Tangents and gradients | |
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| Coordinate transformations in Euclidean space | |
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| Tensor fields in Euclidean space | |
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| Surfaces in Euclidean space | |
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| Manifolds | |
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| Tensor fields on manifolds | |
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| Metric properties | |
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| What and where are the bases? | |
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| The spacetime of general relativity and paths of particles | |
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| Introduction | |
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| Geodesics | |
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| Parallel vectors along a curve | |
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| Absolute and covariant differentiation | |
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| Geodesic coordinates | |
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| The spacetime of general relativity | |
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| Newton's laws of motion | |
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| Gravitational potential and the geodesic | |
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| Newton's law of universal gravitation | |
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| A rotating reference system | |
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| Field equations and curvature | |
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| Introduction | |
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| The stress tensor and fluid motion | |
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| The curvature tensor and related tensors | |
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| Curvature and parallel transport | |
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| Geodesic deviation | |
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| Einstein's field equations | |
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| Einstein's equation compared with Poisson's equation | |
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| The Schwarzschild solution | |
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| Physics in the vicinity of a massive object | |
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| Introduction | |
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| Length and time | |
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| Radar sounding | |
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| Spectralshift | |
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| General particle motion (including photons) | |
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| Perihelion advance | |
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| Bending of light | |
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| Geodesic effect | |
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| Blackholes | |
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| Other coordinate systems | |
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| Rotating objects; the Kerr solution | |
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| Gravitational radiation | |
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| Introduction | |
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| What wiggles? | |
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| Two polarizations | |
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| Simple generation and detection | |
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| Elements of cosmology | |
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| Introduction | |
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| Robertson-Walker line element | |
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| Field equations | |
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| The Friedmann models | |
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| Redshift, distance, and speed of recession | |
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| Objects with large redshifts | |
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| Comment on Einstein's models; inflation | |
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| Newtonian dust | |
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| Appendices | |
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| Special relativity review | |
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| Introduction | |
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| Lorentz transformations | |
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| Relativistic addition of velocities | |
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| Simultaneity | |
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| Time dilation, length contraction | |
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| Spacetime diagrams | |
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| Some standard 4-vectors | |
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| Doppler effect | |
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| Electromagnetism | |
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| The Chinese connection | |
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| Background | |
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| Lanchester'stransporteronaplane | |
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| Lanchester'stransporteronasurface | |
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| A trip at constant latitude | |
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| Tensors and Manifolds | |
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| Introduction | |
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| Vector spaces | |
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| Dualspaces | |
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| Tensor products | |
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| The space <$>T_s^r<$> | |
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| From tensors to tensor fields | |
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| Manifolds | |
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| The tangent space at each point of a manifold | |
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| Tensor fields on a manifold | |
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| Solutions | |
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| References | |
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| Index | |