Interesting Aspects of Calculus

In this lecture, Lee continues his explanation of the fundamental theorem of calculus. He believes that the understanding of this theorem has been declining and strongly feels that students should know exactly why they can find areas under the graph by the definite integral.

NOTE: A(x) is one of the antiderivatives f(x) and F(x) is any antiderivatives of f(x). There are a few mistakes towards the end of the video.

In this 3-part video, we follow Leibniz in his pursuit to find the area of a quater circle of unit radius via integration, trigonometry and series expansion.

We shall take a journey through the mind of English mathematician John Wallis and see how he in 1656 discovered an intrinsic formula known as Wallis's Product.

NOTE: Lee had to make this a 4-part video without sacrificing the mathematical rigour. Watch all of them for a complete proof.

In this video, Lee proves Kepler's First Law of planetary motion. This simple looking law actually turns out to be the hardest one to derive. The law states: A planet revolves in an elliptical orbit with the sun at one of its focus.