My school offers Matrix Calculus class next semester. I have never heard about this subject before and got intrigued. After a short chat with professor I found myself unable to get rid of suspicion that matrix calculus might just be simplified version or a special case of Tensor Calculus/Tensor Analysis. Moreover, the first sentence in Wikipedia article about Matrix Calculus says

In mathematics, matrix calculus is a specialized notation for doing multivariable calculus

I have been self-studying tensor analysis for a little and took multiple classes related multivariable calculus. Does it worth to take this class for someone focusing on applied math/mathematical physics, or is it pretty much going to be covered by multivariable calculus + topics from tensor analysis? To be more precise, let me reformulate the question.

If we were to draw an Euler-Venn diagram with three main circles corresponding to Multivariable Calculus, Matrix Calculus, and Tensor Analysis, then what would be the topics lying in the

  1. intersection of Multivariable Calculus circle and Matrix Calculus circle?
  2. intersection of Tensor Analysis circle and Matrix Calculus circle?
  3. Matrix Calculus circle, and not in any other circle?

Thank you for advice.

  • 1
    $\begingroup$ it might help to see the text book they're using. Honestly, course titles are hard to go by. I will say this, there are doubtless sneaky trick notations to take the thinking out of calculus with vector or matrix variables. I saw some of that in some engineering literature I ran into for some reason I forget. But, is it important enough to warrant it's own specialized reserved notation? Or, it is it just one chapter in a larger story of multivariate analysis of normed spaces? I don't know, but, the book would help. $\endgroup$ – James S. Cook May 28 '15 at 6:36
  • $\begingroup$ Unfortunately, the textbook is not listed in the course catalogue $\endgroup$ – Vlad May 28 '15 at 6:43

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