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# [Lecture] MIT-Multivariable Calculus: Vectors (1-8)

Updated: Apr 28, 2020

Hello all,

I've recently begun watching Multivariable calculus by MIT OpenCourseWare for many reasons, but biggest of them being the course's reputation for being very useful for STEM students. In fact, it was around last year summer that I first began listening to this lecture, but thanks to the master procrastinator in my head, I sacrificed the lecture for other extracurriculars. Honestly, the first part of the lecture wasn’t that fun, so I didn’t feel that much intrigue to the course either. It was just that I chose to take the course because I heard that it was useful.

Then, the coronavirus gave me lots of time at home, and I decided to add some productivity into my life by resuming this course. And after wathing 8 videos, I do not regret doing so at all. At first, I was honestly bored listening to an introduction to vectors. But later on, when the lecture continued on about how Kepler’s second law could be proven using simple vectors, I was literally flabbergasted and was watching the entire video with my jaws fully open. I am not even kidding about how beautiful and simple the proof was. I’ve attached a picture of my notes, and it will probably clearly show the proof. I am thinking of posting about it separately when I have some spare time. Anyways, the proof was one of the best applications of mathematics that I’ve ever seen, and I am thinking of teaching it to people in the math society.

Below are some of my notes. I could type them, but there were simply too many diagrams and equations that it would be a waste of time to digitally document them given the benefit of simply scanning them. The notes are a part of my project to create free notes for olympiad and undergraduate-level maths.

Multivariable Calculus_Lec 1-8
.pdf