Why complex exponents matter | Laplace Transform Prelude

Description:

How dynamics explain Euler's formula, and vice versa. Early view of the Laplace Transform video: Instead of sponsored ad reads, these lessons are funded directly by viewers: An equally valuable form of support is to simply share the videos. Home page: Timestamps: 0:00 - Intro 1:51 - Euler's formula explained dynamically 9:27 - The harmonic oscillator 21:08 - General linear equations 22:47 - Motivating the Laplace Transform ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: Music by Vincent Rubinetti. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: Twitter: Bluesky: Instagram: Reddit: Facebook: Patreon: Website: