1.0 A better way to understand Differential Equations | Nonlinear Dynamics | 1D Linear Diff Eqns

Part 1: https://youtu.be/ySfs8YVMY7Q
Part 2: https://youtu.be/I9UEBRya4X0
Part 3: https://youtu.be/6mLCFyEv3Z0

Here we show another way to graphically interpret first order ordinary differential equations (ODE's) in the form dx/dt = f(x). Rather than solve the differential equation by integrating, which is often impractical, it's useful to graph them to get a qualitative understanding of the dynamics. As we'll see in future videos, there are many other advantages to this approach as well!

Chapters:
0:00 Intro
0:30 Practical Applications
0:46 The 'Normal Approach'
1:19 Plot dx/dt vs x
2:05 Initial Conditions
2:38 Stability of Fixed Points
3:42 Linearization Proof
3:56 Summary
4:10 Part 2
4:27 Outro

Music:
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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Видео 1.0 A better way to understand Differential Equations | Nonlinear Dynamics | 1D Linear Diff Eqns канала Virtually Passed