Algorithmic Simplicity | A better way to think about Taylor series #SoMEpi @algorithmicsimplicity | Uploaded August 2024 | Updated October 2024, 1 hour ago.
#somepi #someπ
0:00 - Intro
1:06 - The Fundamental Theorem of Calculus
2:27 - Deriving Taylor's Polynomial
7:33 - Approximation Error Convergence Analysis
12:21 - Deriving the Generalized Taylor's Polynomial
Taylor's polynomial expansion is a core part of high-school level calculus. However, I was never satisfied with the way it was taught to me, as the motivation for it seemed to come out of nowhere. In this video, I show how Taylor's polynomial, and an explicit formula for the error of the polynomial approximation, and a generalized version of Taylor's polynomial with multiple centres, are all the result of just applying the fundamental theorem of calculus over and over again.
While I was working on this video, I was contacted by the team from GiveInternet, which is a charity organization that aims to provide internet access to students in under-developed countries. They offered to do a collaboration with me, but I didn't have time to look into their organization properly before this video went out, so I did not accept. Nevertheless, it seemed like a good organization, so if you want to donate money to their cause you can do so here: giveinternet.org/AlgorithmicSimplicity . To be clear, they have not sponsored this video in any way.
#somepi #someπ
0:00 - Intro
1:06 - The Fundamental Theorem of Calculus
2:27 - Deriving Taylor's Polynomial
7:33 - Approximation Error Convergence Analysis
12:21 - Deriving the Generalized Taylor's Polynomial
Taylor's polynomial expansion is a core part of high-school level calculus. However, I was never satisfied with the way it was taught to me, as the motivation for it seemed to come out of nowhere. In this video, I show how Taylor's polynomial, and an explicit formula for the error of the polynomial approximation, and a generalized version of Taylor's polynomial with multiple centres, are all the result of just applying the fundamental theorem of calculus over and over again.
While I was working on this video, I was contacted by the team from GiveInternet, which is a charity organization that aims to provide internet access to students in under-developed countries. They offered to do a collaboration with me, but I didn't have time to look into their organization properly before this video went out, so I did not accept. Nevertheless, it seemed like a good organization, so if you want to donate money to their cause you can do so here: giveinternet.org/AlgorithmicSimplicity . To be clear, they have not sponsored this video in any way.
