An Introduction to Tensor Calculus, Relativity and Cosmology

  • Special Principle of Relativity. Lorentz Transformations
  • Orthogonal Transformations. Cartesian Tensors
    • Special Relativity Mechanics
    • Special Relativity Electrodynamic
  • General Tensor Calculus. Riemannian Space
    • Generalized N-dimensional 􀁩paces
    • Contravariant and covariant tensors
    • The quotient theorem. Conjugate tensors
    • Covariant derivatives. Parallel displacement. Alline connection
    • Transformation of an allinity
    • Covariant derivatives or tensors
    • The Riemann Christoffel curvature tensor
    • Metrical connection. Raising and lowering indices
    • Scalar products. Magnitudes or vectors
  • General Theory of Relativity
    • Principle of equivalence
    • Metrn: in a gravitational field
    • Motion or a free particle in a gravitational field
    • Einstein’s law of gravitation
    • Acceleration of a particle in a weak gravitational l1cld
  • Cosmology