Week Nine – Tensor Properties III: The Eigenvalue Problem

In this last week of lectures before your second test, we shall be looking at the Eigenvalue problem you have encountered already in your Engineering Mathematics. There is an equipollency between the tensor eigenvalues and those of matrices. The issues here are therefore familiar. The tensor form has specific physical implications in our engineering courses especially as it relates to the Principal invariants of tensors and the spectral form using eigenbases.
We shall also have two tutorial classes on the worked examples to help prepare you for the test. Remember that the test is a paraphrase of the same problems that are solved for you in the Q&A at the end of each chapter. EVERYTHING in the Q&A is part of the questions populating the database from where your questions are drawn.

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Week Four – Vector Space

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There are a number of examples in the text that today’s lecture expects you to type in and practice. If in future, you do not know how to program, it will be because you were lazy in simply typing in code and running them. “The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings.” A word enough for the wise!
There is a test next week on Chapter One. Those who refuse to practise are going to have a cold shower on a harmattan morning!

Week Two – The Summation Convention

Here are the slides for the second week.

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I note that there have been no comments or questions from Systems Engineering students. There will be a test two weeks time on the first four weeks. Those who do not practice the Q&As as instructed will have themselves to blame.

Continuum Mechanics for Modeling, Simulation & Design

The site for the course is www.s2pAfrica.org the notes and other materials for the course are also there. Until further notice, reach me here for immediate answers to your questions. We are still organizing that site.
Here are the slides for the opening class:

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The following is the Course text.

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Required Preparation for Next week: Read Pages 23 to 50; Work Examples 1-25 in the Solved Problems Section.
Ask your questions online so that other students may benefit from your insight and the answers you get.

Computer Graphics & Design

You are welcome to today’s lecture. Here we are describing the scope and things that will be covered. I am excited to teach you. I hope you are excited to explore the possibilities that can come from our putting our hearts to work.
Note that these notes and ths page will continue to be active even if there is a strike. Those who want to learn cannot wait until all Nigeria’s problems are solved. Time waits for no one.
You can reach me on this site. It is my preferred choice of location to meet students as things we discuss openly here may be useful to others.
If there are things a sufficient number of you do not understand from the class lecture, let me know about it. I may prepare another set of notes of a video to cover the problem areas.

I have NO PATIENCE with lazy students. I am always willing to help you with the course material during the term. Post questions to this page and I will respond. If you want better grades, look for them now. At the end of the term, it is too late; This post on Quora may interest some as well as this other one on Nigeria
Here are the slides for today’s lecture.

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The recommended text is available in pdf from here:
Choose Lai, Rubin and Krempl, Introduction to Continuum Mechanics. I will give you a password in class.

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.