Tensor Calculus

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.

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

1. Joshua Zelibe says:

Good day Sir. Please Sir, i’m completely at a loss as to how the tensor product symbol on the last expression on page 17 was contracted. Kindly assist me Sir.

2. Joshua Zelibe says:

Good day Sir, please Sir I am trying to understand Ricci’s theorem as applied in question 97 of the calculus q & a. In differentiating the metric tensor,we obtained the derivative of the metric tensor again on the right hand of the equation.Please help me Sir.Thank you Sir.

3. Aristobulus Tauna says:

Greetings Sir,

Is there a date for SSG 805 Exams?

Best Regards,

Aristobulus