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Introduction to Tensor Calculus, Relativity and Cosmology

Autor: Derek F. Lawden

Jazyk:

Vazba: Brožovaná

Vydavatel: Dover Publications Inc.

Dostupnost: Skladem u dodavatele

Odesíláme za 14-21 dnů

299 Kč

Preface List of Constants Chapter 1 Special Principle of Relativity. Lorentz Transformations 1. New...

Informace o knize

Autor

Derek F. Lawden

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2003

Stránek

224

EAN

9780486425405

ISBN

0486425401

Enbook ID

02565967

Vydavatel

Dover Publications Inc.

Hmotnost

340

Rozměry

235 x 159 x 15

Kompletní popis

Preface List of Constants Chapter 1 Special Principle of Relativity. Lorentz Transformations 1. Newton's laws of motion 2. Covariance of the laws of motion 3. Special principle of relativity 4. Lorentz transformations. Minkowski space-time 5. The special Lorentz transformation 6. Fitzgerald contraction. Time dilation 7. Spacelike and timelike intervals. Light cone Exercises 1 Chapter 2 Orthogonal Transformations. Cartesian Tensors 8. Orthogonal transformations 9. Repeated-index summation convention 10. Rectangular Cartesian tensors 11. Invariants. Gradients. Derivatives of tensors 12. Contraction. Scalar product. Divergence 13. Pseudotensors 14. Vector products. Curl Exercises 2 Chapter 3 Special Relativity Mechanics 15. The velocity vector 16. Mass and momentum 17. The force vector. Energy 18. Lorentz transformation equations for force 19. Fundamental particles. Photon and neutrino 20. Lagrange's and Hamilton's equations 21. Energy-momentum tensor 22. Energy-momentum tensor for a fluid 23. Angular momentum Exercises 3 Chapter 4 Special Relativity Electrodynamics 24. 4-Current density 25. 4-Vector potential 26. The field tensor 27. Lorentz transformations of electric and magnetic vectors 28. The Lorentz force 29. The engery-momentum tensor for an electromagnetic field Exercises 4 Chapter 5 General Tensor Calculus. Riemannian Space 30. Generalized N-dimensional spaces 31. Contravariant and covariant tensors 32. The quotient theorem. Conjugate tensors 33. Covariant derivatives. Parallel displacement. Affine connection 34. Transformation of an affinity 35. Covariant derivatives of tensors 36. The Riemann-Christoffel curvature tensor 37. Metrical connection. Raising and lowering indices 38. Scalar products. Magnitudes of vectors 39. Geodesic frame. Christoffel symbols 40. Bianchi identity 41. The covariant curvature tensor 42. Divergence. The Laplacian. Einstein's tensor 43. Geodesics Exercises 5 Chapter 6 General Theory of Relativity 44. Principle of equivalence 45. Metric in a gravitational field 46. Motion of a free particle in a gravitational field 47. Einstein's law of gravitation 48. Acceleration of a particle in a weak gravitational field 49. Newton's law of gravitation 50. Freely falling dust cloud 51. Metrics with spherical symmetry 52. Schwarzchild's solution 53. Planetary orbits 54. Gravitational deflection of a light ray 55. Gravitational displacement of spectral lines 56. Maxwell's equations in a gravitational field 57. Black holes 58. Gravitational waves Exercises 6 Chapter 7 Cosmology 59. Cosmological principle. Cosmical time 60. Spaces of constant curvature 61. The Robertson-Walker metric 62. Hubble's constant and the deceleration parameter 63. Red shifts of galaxies 64. Luminosity distance 65. Cosmic dynamics 66. Model universes of Einstein and de Sitter 67. Friedmann universes 68. Radiation model 69. Particle and event horizons Exercises 7 References Bibliography Index

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Introduction to Tensor Calculus, Relativity and Cosmology

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