Linearization at Critical Points

[@NoOne-yw6pr]

In my experience success is always the result of team work: Professor Strang delivers a brilliant lecture, MIT uploads, we all benefit, the whole system benefits. Go team!

[@syedsheheryarbokhari2780]

Thank you Professor Strang and MIT OCW. Professor Strang is amazing and his method of building complicating structures from simplified versions is awesome.

[@georgesadler7830]

DR. Strang you are the grandfather of linear systems.

[@seamus9898]

Denoting the critical point as Y really confuses me... because whenever I see y or Y, I think of functions. But Y here is always a constant. Using a different letter helped me.

[@marverickbin]

y is a function, right? You tried to plot f(y), and got a curve. I am confused.

[@GammaSigma1234]

Yes, y should be interpreted as a function of time. For example, it could be y(t) = 2t - 1

[@germainguerin3063]

i surely miss something, i can't see a zero slope at the point Y in his graphs. Can someone help!

[@enderyu]

I think you mean at 3:00 ? f(y) is defined as dy/dt; so f(Y) = 0 [intersecting the y axis] and the slope of f(Y) is d²y/dt².

[@rakhimovv]

Worth mentioning that he draws phase plane (dy/dt y)

[@lalitsharma4233]

Wow

[@غديالحربي-س2ث]

G