First-Order Extrema in Classical Mechanics , Theoretical Minimum

[morangta]

First-Order Extrema in "Classical Mechanics", Theoretical Minimum

In the 3rd lecture of Classical Mechanics, 2011, by Dr. Susskind in his Theoretical Minimum series, he talks about calculating extrema, saddle points, etc. to "first order".

"if you move a little bit, the potential is zero, to first order"

What does he mean, first order? When I was in college in the 60's, if we wanted better accuracy, we just made Δx smaller, and eventually got the accuracy we wanted.

No one talked about "first order" in the 60's. I think I would have remembered. Maybe not. I've noticed he keeps saying that. Is there something new in math and physics that I am not aware of?

Thanks.

 

[Liquidxlax]

He is talking about expanding the equation in a taylor series around the minimum

example

y(x) = sqrt(a^2-x^2) ; for x<<1 y(x) = sqrt(1 -(x/a)^2) ~ 1- (1/2)*(x/a)^2 and this would be to first order

 

[morangta]

What does that have to do with the stationary points?