The Covariant Derivative (and Christoffel Terms)

In this video (GR - 07), the idea of the “Covariant Derivative” is introduced. As a means of trying to ‘justify’ it, a one-dimensional ‘proof’ (of sorts) is offered and worked through. This is then used to try and make the two dimensional version (and hence the multi-dimensional version) of the Covariant Derivative, with its associated Christoffel Symbols, acceptable. Inevitably, the final versions of these equations are in “Einstein Summation” form, and so for the benefit of those who are coming to this for the first time, the video ends with examples of how to expand such equations, and try to ‘see into them’ exactly what they mean. This video is part of a series of videos on General Relativity (GR-01 to GR-20), which has been created to help someone who knows a little bit about “Newtonian Gravity” and “Special Relativity” to appreciate both the need for “General Relativity”, and for the way in which the ‘modelling’ of General Relativity helps to satisfy that need – in the physics sense. The production of these videos has been very much a ‘one man band’ from start to finish (‘blank paper’ to ‘final videos’), and so there are bound to be a number of errors which have slipped through. It has not been possible, for example, to have them “proof-watched” by a second person. In that sense, I would be glad of any comments for corrections ……. though it may be some time before I get around to making any changes. By ‘corrections and changes’ I clearly do not mean changes of approach. The approach is fixed – though some mistakes in formulae may have been missed in my reviewing of the final videos, or indeed some ‘approximate explanations’ may have been made which were not given sufficient ‘qualification’. Such changes (in formulae, equations and ‘qualifying statements’) could be made at some later date if they were felt to be necessary. This video (and channel) is NOT monetised