As I've stated before I am logging topics/subjects I come across in classes and research. I am taking a vector calculus mainly for review, but I am also understanding the fundamentals much better and learning new stuff. On top of that, I am taking a mathematical methods for physicists and inviscid flow and both are giving added and large doses of vector analysis. I always have the point of view that the more you hear and see something the more you remember and take away from it. Thus, it becomes "easier" or almost second nature. I also encourage getting a wide range of views from various people as they have very different teaching techniques, experiences, and their own learning background. So, while I may have tortured myself by taking a couple of extra classes which are not necessarily "needed" for my degrees, I am gaining much valuable insight to the fundamentals and basics.
So, one of the first things (or eventual topics) in vector courses that comes about appears as matrices. Matrices are very important in physics and math and thus most sciences. Matrices appear in many math courses such as linear/matrix algebra and numerical linear/matrix algebra. Matrices are associated with linear algebra due to collecting systems of linear ordinary differential equations ODEs into sets which are easily converted into matrices. In fact, in Shores [1] book, Applied Linear Algebra and Matrix Analysis, he opens by remarking that
"The two central problems about which much of the theory of linear algebra revolves are the problem of finding all solutions to a linear system and that of finding an eigensystem for a square matrix."
In progress...
[1] T. S. Shores. Applied Linear Algebra and Matrix Analysis. Springer Science+Business Media, LLC., New York, NY. 2007
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