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.

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

Tensor Algebra

Defines what a tensor is and shows its attributes. Please note the submission dates of the homework assignments. No lateness in submission allowed.

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We will need to arrange one extra class in the next two weeks in order to complete the section. A class test is for the week of April 4.

Questions & Answers for First Test

The first test will be based on the questions answered here. They will likely come in the form of objective questions covering the same scope.

You are expected to practice these and let me know if there are things you still do  not understand by posting specific questions below.

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Please endeavour to discuss with others and make an effort before posting a question. After a good effort, all questions are welcomed.