James Ebhabha wrote on the scalar triple product of the base vectors. Here is my response:
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Please let me have a feedback on this post. Students who want to discuss details can send me their fully typeset comments using the Microsoft equations editor through my email address. I will paste their questions with my response on this page so to benefit other students.
Here are the slides on Tensor Calculus
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You can also try these and make your comments here.
Consider the following Mathematica code. Try it out and see what I am trying to do here by using the Cayley-Hamilton to get the inverse of a matrix without going through the usual co-factor route:
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Can you try it out.
Did you think I was taking you too far into mathematics when I taught the Cayley Hamilton theory in our last class. I think not! But you may not believe me. But what if I told you that secondary school pupils know this theorem? You better believe it because I have a proof! Just look at this web blog:
and tell me what you think about it.
You made a valiant effort to obtain the component representation of the third invariant of the second-order tensor. You are generally on the right track but you did not express the scalar product completely in the component form as you should have done. Since a scalar triple product is a scalar, you should be able to express it completely without any vector basis. I have decided to work it out fully for the class and my notes from now on will carry the explanation I am supplying below:
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This should provide a complete answer to what you were trying to do. If you have further questions, please comment below.
Home work 2 solutions are as follows:
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It is with a deep sense of loss that the Faculty of Engineering announces the passing of Mr Emmanuel Olanrewaju.
Until he passed on two days ago, Mr Olanrewaju was a 400 level student in the Department of Mechanical Engineering and was in fact writing his semester examinations at the time of the incident. Our hearts and condolences go to the parents and the entire family that are in deep mourning at this time. We also greet the fellow students, course mates and all other colleagues of the late Mr Olanrewaju.