In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general. Taylor series can approximate many complicated functions by turning them into simple summations of polynomials. Even in the field of cymatics and the vibrations of drumheads can be modeled very accurately using Bessel functions.
Timestamps
- Introduction: Sequences are ordered lists of numbers, and series are summations of sequences: 0:00
- Many functions are defined as sums of series: 1:14
- Taylor series approximate functions: 1:50
- Bessel functions model vibrations of drumheads and cymbals: 2:31
Notes and playlists
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
- Notes: https://peakd.com/publish?edit=mes%2Finfinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more .
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