Tensor Tricks: The "Illegal" Derivatives That Actually Work (Sometimes) скачать в хорошем качестве

Tensor Tricks: The "Illegal" Derivatives That Actually Work (Sometimes)

In GR and tensor calculus you’ll often see “illegal-looking” shortcuts like ∂xₚ/∂yᵅ = ∂yₐ/∂xᵖ (for example, I used it in the derivation of the Christoffel symbols in my course on General Relativity). They’re not proper notation, but they’re useful, especially when going from a local inertial frame to general coordinates. In the video, I justify these tensor tricks using the line element, Jacobians, and index raising/lowering with the metric. These are simple derivations in tensor calculus. #GeneralRelativity #TensorTricks #Tensors #ChristoffelSymbols #DifferentialGeometry #math #mathematics #mathlove