Autonomous Equations, Equilibrium Solutions, and Stability

Autonomous Differential Equations are ones of the form y'=f(y), that is only the dependent variable shows up on the right side. This means the slope fields aka direction fields look the same for all values of the independent variable t. While these are examples of separable differential equations, they allow for a lot of new analysis. We can talk about equilibrium solutions that don't change in time, and we can talk about stability. That is, as time goes to infinity do solution approach or go away from the equilibrium solutions? This is referred to as asymptotic stability.

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[jamesstevens]

This video legit explained in 10 minutes what my lecturer couldn’t explain in an hour.

[pkkp]

After 8-9 years of youtube studying, this might be in my top 10 list in terms of quality

[xoxoxoxoxoxoxo]

You helped me in calc 3 and now you're here to save me in diff eqs. Thank you

[MrSoccerwin]

Dr. Bazett, thank you for explaining this concept in such an easy and concise way

[muneerahmad]

Great lecture. Sir I have taken calculus 3 and calculus 4 course from your chanel. Your videos are amazing.

[allysonperez]

Wow great job Dr. Bazett!! I like that you seem generally interested in teaching, really helps to keep engaged, thank you thank you!! And explaining it in such a small amount of time! :)

[calebloayza]

I can't imagine a world without you teacher!

[tevinabeysekera]

No way did you explain this better than my professor in a quarter of the time! Thanks so much

[owending]

Brilliant Explanations. Help me quickly understand the stable and unstable equilibrium solutions. THX!

[dsizov]

Great video, thank you! We need MORE stability analysis! XD

[kktech]

That was a rock star explanation! Thank you !

[georgesadler]

Professor Bazett, thank you for the video/lecture on Autonomous Equations, Equilibrium Solutions and Stability. These are powerful tools in Ordinary Differential Equations.

[speedbird]

very nice and short explanation, thanks

[dennisd]

"then you wouldn't change and so forth" that was the final piece that made everything click in my head

[zenithb]

Thank you Sir for this explanation. It was so much clearer than anything my professor taught.

[walterpu]

My crazy econ prof tried to teach this whole course within 3 weeks. last week we were talking about phase diagrams, now we are finishing calculus variation and optimal control theory? How can he expect us to learn so many things in so little time? I don't even fully understand how to solve systems of linear equations!
But I do find your textbook helps, Laplace transformation seems to be able to solve some special optimal control problems quite effectively.

[jasonthomas]

Have you ever noticed that these videos invariably have the comment: "You explained in 10 minutes what my lecturer couldn't explain in an hour"?

It's kind of unremarkable since your lecturer is just who you've got to teach you at uni. This bloke here is a fantastic communicator. It's hardly surprising that your lecturer isn't able to communicate like the best from the internet.

[tomasescobargallardo]

Great Explanation! It helped me so much. You're amazing.

[akif]

Very fundamental explanation Sir thanks a lot!

[j.o.]

Looking fabulous with sparkling hair (2:10)