Mod-01 Lec-05 Autonomous dynamical systems (Part 1)

[@FarFromEquilibrium]

This guy is awesome professor. These classes are only 1 hr but take about 3 to digest. Amazing NPTEL, THANKS!!

[@Adityakashyap9022]

Absolutely India is proud of you Mr. Professor. 🤗

[@busygin]

@28:00 a very useful digression about exponentiating a 2x2 matrix analytically by using the Pauli matrix basis.

[@madier1000]

Dear Prof. Balakrishnan. Thank you so ever for such lecture which has been of great help.

[@naimulhaq9626]

Prof. Balakrishnan is the best teacher.

[@wagsman9999]

These are just brilliant.

[@just_kidding-j2e]

@9:55 He explains a second reason why global integrability might fail. But it's editing out. Any one knows what it is?

[@ashwin2112]

This is the definition of Rectification theorem in Wikipedia: The rectification theorem says that away from singular points the dynamics of a point in a small patch is a straight line. The patch can sometimes be enlarged by stitching several patches together, and when this works out in the whole phase space M the dynamical system is integrable. - In most cases, the patch cannot be extended to the entire phase space. There may be singular points in the vector field (where v(x) = 0), or the patches may become smaller and smaller as some point is approached. - The more subtle reason is a global constraint, where the trajectory starts out in a patch, and after visiting a series of other patches comes back to the original one. If the next time the orbit loops around phase space in a different way, then it is impossible to rectify the vector field in the whole series of patches. Maybe he is talking about a patch looping towards the starting point again. But not sure though.

[@HarishNarayanan]

We were all such babies in a class like this one day

[@beeflavre9748]

Great professor!

[@stepsvideos]

Thank you for sharing this treasure.

[@danijelmarkovic6470]

Where can I find Lecture notes from this Course.Thanks in advance

[@hansalogic]

This is very good

[@kaustavbhattacharjee224]

Excellent sir.

[@maxdelbruck]

Nice!

[@bhuvanjhamb2728]

How come these guys (the students) never change their positions 😅

[@ardra1905]

Everyone has their preferred seats, that was the case even when I went to this college; but I think this is just universal.