In this section, we consider the way calculus principles can be applied to objects that are larger than scalars. The objects of interest to us are Vectors and Tensors. More formally, we will try to give interpretations to the derivatives and integrals of tensor functions of orders 0,1,2,3 and 4. The arguments can also be tensors of all relevant orders.

Furthermore, we will look at tensor fields. These are tensors that are functions of the Euclidean Point Space that we will fully define. We will be free to refer the point space to Cartesian as well as general coordinates.

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We will show how to avoid direct computation of the resulting Christoffel Symbols by using symbolic computation available in Mathematica.