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in video 30 of tensor calculus well continue our in-depth analysis of the chrostophal symbol in particular well derive a formula that lets us evaluate the christophel symbols for any coordinate system for the last few videos weve been analyzing the christoffel symbol well today we want to answer the question how do you evaluate these things for any given coordinate system well one way to do that is simply to appeal to the basic definitions as you see them here so lets see how that would work for example if we wanted to find the christophel symbol of the first kind for indexes 2 2 1 wed simply plug these indexes into our definition were going to need the dot product of covariant basis vector z2 with its partial derivative with respect to z1 so were just substituting the values of i j and k into the formula okay so to do this were going to need the basis vector z2 and its partial derivative well if you go back to video number 12 youll see that this was the expression for the ba