I have self-studied physics, calculus, and a little bit of linear algebra, but the closest thing to “records” I have is my notebook with notes and problems I solved, which is all over the place. I thought it would be nice if I have a place where I can record my progress, which is why I’m writing this page right now.
My first topic to self-study is multivariable calculus. I figured it’s something I would have to learn anyway, and it could be useful for my research in the future.
To begin, I reviewed the basics that I had to know. Although I already knew a little about vectors and their operations from physics and linear algebra, I wanted to make sure I have a steady foundation. This category will be all about summarizing what I learned after each session.
A vector, in its most basic explanation, is something with a magnitude and direction. An easy way to understand this is through the position vector (introduced in physics as well).
For example, in 2 dimensions,
Would show the position of point P.
In 3 dimensions, it would be
In these cases, the magnitudes of the vectors can be found easily using the Pythagorean Theorem. For any dimension n where there are points
the vector between them would be
However, vectors can be more abstract. A vector is an element of a vector space, where a vector space is a set of objects where you can add, multiply by scalars, etc.
I will continue in the next part.