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Vector

Submitted by Zhigang Suo on

These notes are a part of the notes on linear algebra.  I compare spacetime and appleorange.

Attachment Size
vector 2016 10 10.pdf 3.8 MB
Xiaogai Li

Dear Prof. Suo,

Thanks for the note and I found many of your notes are very illumininating.

Now I wonder if you have some notes on Constitutive Modleing? As I wrote in my blog question, 

http://imechanica.org/node/20420

"I wonder if there is any good  material on constitutive modeling that explains how to develop a new constitutive model from scratch... These questions perhaps are addressed in many continuum mechanics text books. but I am looking for materials that explain in a concise (short) and easy to understand way. Perhaps some good constitutive  modeling papers, or some lecture notes? ..."

Would be greatly appreciated if you can recommend some or if you have some notes on this topic?

Thank you very much.

 

Sat, 10/08/2016 - 20:53 Permalink
Xiaogai Li

The best note I've seen on Vectors, Thank you very much!

I particurly like the concrete examples showing how change of basis changes a vector's components. The note provide a clear "why" to the vector transformation rules. I assume tensor is similar, because of the change of basis, a tensor's components also change, and the change of the components obeys the rules of tensor transformation rules. I have found Your note on "tensor" as well, looking forward to reading that, hope I will be able find (appreciate) a clear "why" for tensor as well (which is not usually explained in the text books or classes, and we are often taught to memorize these rules as a student). Thanks!

 

Sat, 10/08/2016 - 22:21 Permalink
Zhigang Suo

Thank you very much for your kind words.  I have just updated the notes on vector.  

In these notes, wish to show rules of calculation.  I also wish to show where vectors come from.  I show several methods to create new vectors:

  • Cartesian product of scalar sets
  • Subspaces and their intersections and sums
  • Maps from an arbitrary set to a vector space
Mon, 10/10/2016 - 16:08 Permalink