Derivatives in Flat, Euclidean Spacetime
4-derivatives: time and 3-space derivatives in a rank-1 tensor.
Signs of covariant and contravariant derivatives flip (arg!).
Covariant derivative.-
Contravariant derivative. -
The comma convention. -
The D'Alembertian operator.
The asymmetric rank-2 tensor that results from taking the 4-derivative of a 4-vector can be represented by the symmetric average amount of change tensor plus the antisymmetric deviation of change tensor.
Slide 26 stands for freedom constraints.