Tutorial Three

We hereby present tutorial three as a correction rearrangement, in slides of most of the Q&A in chapter 3 of Continuum Mechanics for Modeling Simulation and Design.

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Obviously, these cannot be covered in a single tutorial class. We will select a number of these if a tutorial is needed before you semester exams.

Week 12: Integral Field Theorems

Finally,…, in place of our Programming Clinic, we conclude this first set of lectures with a quick, largely computational approach to the Field theorems of Continua. This, combined with our earlier treatment of differential calculus, completes the application of the results of calculus to tensor objects.

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Time did not permit us to look too deeply into some of these matters. Take this as a way to whet your appetite to a fruitful understanding of Continuum Mechanics. We can avoid further theoretical work and the covariant formulation by using Mathematica for our computations. We shall more of such in the next chapter where we shall begin to look at the geometric formulations of continua.

Week Ten: Tensor Analysis

We proceed to Differential and Integral Calculus wit tensor valued functions and tensor arguments. In the first set of slides, we extend out knowledge of scalar differentiation to larger objects. The examples we begin with are simple and easy to understand. The lecture concludes with the Gateaux extension to our elementary knowledge of differentials

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In one more week, we shall cover the book up to the point of Integral Theorems.

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Week Eight – Tensor Properties II: Decompositions & Orthogonal Tensors

This week we continue our study of tensor properties with additive and spectral decompositions of tensors. We shall also look at orthogonal tensors. The slides are presented in the video

Here are the actual slides we will use in class. It begins with a repeat of some of last week’s outstanding issues that you ought to have gone through on your own. These are: Products of determinants, trace of compositions and scalar product of tensors. You must be current on these in order to understand this weeks menu.
The five topics covered here include:
1. The tensor set as a Euclidean Vector Space,
2. Additive Decompositions
3. The Cofactor Tensor, its geometric interpretation
4. Orthogonal Tensors
5. The Axial Vector
These are vocalized in the above Vimeo video and the downloadable slides are here

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Week Six – Chapter Two: Tensor Algebra

Chapter two of the course text is posted here for your use. It is our hope that you will make use of this material given to you this time. Most students ignored the materials, turned deaf ears to all warnings and reaped the expected results in the test! The second chapter will be no different. Here, as before, there are 100 solved problems that are being turned into Multiple-Choice Questions. You will be examined on them within four weeks of today. We are working on the Web server that will allow you to also self test.

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We will cover some outstanding materials, hopefully, during the Programming class. We also include some guidance on the Q&A problems that are relevant to the week’s slides. If you work through them weekly, it will make the rush to cover the 100 questions unnecessary when the time for testing is near. Remember, these are mere guides. They are not to constrain you.

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The same set of slides can be seen in the following video:

As in the past, we urge you to make your comments on these notes. Include information on your department and Matric number because we will grade your participation on the website as part of your Continuous assessment. The full details for the course grading are as follows:

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