Symplectic geometry & classical mechanics, Lecture 3

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry.

Here in the 3rd lecture, I introduce the tangent bundle and introduce differential forms.

[mavaable]

I've studied symplectic geometry before but at my uni it was given solely from a mathematical point of view. As a physics student, this series has been extremely useful! Thank you Tobias!

[enriquemacias]

Thank you for the video, I finally understood why differential forms act on vectors

[mihaifrancu]

In some references I found sometimes that the pairing between the basis of the tangent and contagent spaces is not Kronecker delta, but rather the metric tensor. Can you point me to when this would be true?

[andreemcaldas]

At 57:20. Calling it a "volume" is a little dangerous, because the manifold is embedded, and the surface is curvy. So, "volume" is NOT base times height. I guess it is better to think of area and density.

[alejandropacheco]

Actually the definition F_x/F_x^2 is the dual of the tangente space. Anyway, good video.