Tutorial: Functional and Structured Tensor Analysis for Engineers

A step-by-step introduction to tensor analysis that assumes you know nothing but basic calculus. Considerable emphasis is placed on a notation style that works well for applications in materials modeling, but other notation styles are also reviewed to help you better decipher the literature. Topics include: matrix and vector analysis, properties of tensors (such as “orthogonal”, “diagonalizable”, etc.), dyads and outer products, axial vectors, axial tensors, scalar invariants and spectral analysis (eigenvalues/eigenvectors), geometry (e.g., the equations for planes, ellipsoids, etc.), material symmetry such as transverse isotropy, polar decomposition, and vector/tensor calculus theorems such as the divergence theorem and Stokes theorem. (A draft of this document was last released publically on Aug. 3, 2003. The non-public version is significantly expanded in anticipation of formal publication.)

You may download the rest of the document here.

8 thoughts on “Tutorial: Functional and Structured Tensor Analysis for Engineers

  1. Hello, again. I see that you have a new position since we last chatted a few years ago. I was searching to see if your book on tensors for engineers has since been published, but it seems that it’s “close”. I still think that this book (the Sep 03 version, at least) is by far the very best resource for the working engineer to get a handle on this important discipline. The clarity of your writing and the problems you illustrate resonate deeply with me.

    Please keep me posted when the formal book is available so I can get a “final” copy of this epic work for my study and reading enjoyment.

    Again, thank you for sharing your gift by spending so much of your life on our behalf on illuminating such a difficult, but incredibly useful and beautiful subject.

    –jim
    IEEE Senior Member

    • Thank you for the encouragement! This book has languished for so long being “nearly finished” that I have decided to submit a proposal to focus full time on completing it for my sabbatical, which I hope will be Fall of 2013. You’re on the list for getting a release notice!

  2. I would like to congratulate you for your excellent tutorials, thank you for your generosity in sharing them freely and, finally, ask you to include my name in the list to receive the book release notice.

    Luis Paulo

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