Book:Derek F. Lawden/Tensor Calculus and Relativity/Third Edition

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Derek F. Lawden: Tensor Calculus and Relativity (3rd Edition)

Published $\text {1975}$, Chapman and Hall

ISBN 0 412 20370 7.


Subject Matter


Contents

Preface (September 1960)
Preface to the Second Edition (September 1966)
Note on the 1975 Impression (February 1975)
$1$. 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 $1$
$2$. 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. Tensor densities
14. Vector products. Curl
Exercises $2$
$3$. Special Relativity Mechanics
15. The velocity vector
16. Mass and momentum
17. The force vector. Energy
18. Lorentz transformation equations for force
19. Motion with variable proper mass
20. Lagrange's and Hamilton's equations
Exercises $3$
$4$. Special Relativity Electrodynamics
21. $4$-Current Density
22. $4$-Vector potential
23. The field tensor
24. Lorentz transformations of electric and magnetic intensities
25. The Lorentz force
26. Force density
27. The energy-momentum tensor for an electromagnetic field
28. Equations of motion of a charge flow
Exercises $4$
$5$. General Tensor Calculus. Riemannian Space
29. Generalized $N$-dimensional spaces
30. Contravariant and covariant tensors
31. The quotient theorem. Conjugate tensors
32. Relative tensors and tensor densities
33. Covariant derivatives. Parallel displacement. Affine connection
34. Transformation of an affinity
35. Covariant derivatives of tensors
36. Covariant differentiation of relative tensors
37. The Riemann-Christoffel curvature tensor
38. Geodesic coordinates. The Bianchi identities
39. Metrical connection. Raising and lowering of indices
40. Scalar products. Magnitudes of vectors
41. The Christoffel symbols. Metric affinity
42. The covariant curvature tensor
43. Divergence. The Laplacian. Einstein's tensor
44. Geodesics
Exercises $5$
$6$. General Theory of Relativity
45. Principle of equivalence
46. Metric in a gravitational field
47. Motion of a free particle in a gravitational field
48. Einstein's law of gravitation
49. Acceleration of a particle in a weak gravitational field
50. Newton's law of gravitation
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
Exercises $6$
Miscellaneous Problems
Appendix Bibliography
Index


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