Phase Plane Pictures: Source, Sink, Saddle

[@samlaf92]

Anyone wondering why we use y' as an axis, it is because any second order ODE can be transformed into a system of 2 first order ODEs: d^2y/dt^2 + Bdy/dt + Cy = 0 becomes dy/dt = y' dy'/dt = -By' - Cy where here (y') is just treated as another variable. Phase plane diagrams are defined for system of equations (they relate how the 2 variables move with respect to t). Since in our transformed system y' is the second variable (and y is the other variable), this is why the axes on our phase planes are y and y'.

[@johnyeap7133]

Very helpful!! Cleared up some confusion!

[@akshayramachandran7857]

12:51 the statement is a bit misleading, the picture is not exactly the same, rather you would have eigenvectors as [1;-1] and [1;-2], hence it would be a reflection about y-axis. The rest is same as what he explained. Thank you for your teaching, love from India

[@georgesadler7830]

Thank you covering this part of differential equations. The graphing part of differential equations is very important.

[@tigerwuli2760]

I love the video. It will be better if the pictures can be shown by Matlab picture as well as shown on blackboard. With Matlab picture, we can zoom in and zoom out and see what happened right there.

[@wanomarfwanmahmudk891]

Thank you prof for the knowledge. Love from malaysia

[@marverickbin]

Wow, that was abstract. Is kind a velocity vs acceleration plane? Following a line I can see how the velocity and acceleration goes on when time pass? Edit: oh, I realized that I should change for position and velocity instead. Edit again: I realized that work both way, depends on interpretation.

[@jhjh1155]

great explanation

[@xsli2876]

I love Professor's teaching. However, the phase portrait on 11:58 is only correct for some part and is wrong for another 50% part: (0, 0) is the source node. Right after leaving the source node(t is a big negative value), e^t is dominant, which means following the 45 degree line both in 1st and 3rd quadrant. As t gets larger, now t is a big positive value, e^2t is dominant, now for the 1st quadrant, the line takes a down turn(a U turn), going down and parallel to the 60 degree line in the 3rd quadrant.

[@EliotMcLellan]

He is a recipient

[@fadifadi4573]

just for laugh dear prof. BIG BANG time began at 0 sec not at negatif unfinity

[@araafdr]

daccord