Covariant Derivatives and Christoffel Symbols

This lecture covers the relation between accelerated coordinate systems and inertial coordinate systems, non-linear transformation of coordinates, Jacobian, one-to-one correspondence, volume elements, basis vectors, covariant derivatives, parallel transport, Christoffel symbols, Lorentz case, scalar functions, covariant and contravariant vectors, metric tensor, Kronecker symbol, tensors, and rules for covariant derivatives. It also discusses the properties of covariant derivatives, the metric tensor, and Christoffel symbols, emphasizing the importance of the symmetric property of the metric tensor. The lecture concludes with the concept of covariant derivatives of tensors and the relationship between the metric tensor and Christoffel symbols.