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)
- Preface (September 1960)
- $1$. 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
Further Editions
- 1962: Derek F. Lawden: Tensor Calculus and Relativity
- 1968: Derek F. Lawden: Tensor Calculus and Relativity (2nd ed.)
Source work progress
- 1975: Derek F. Lawden: Tensor Calculus and Relativity (3rd ed.) ... (previous) ... (next): Chapter $1$ Special Principle of Relativity. Lorentz Transformations: $1$. Newton's laws of motion