Phase Plane Plots

We discuss the use of Phase Plane Plots for understanding the qualitative behavior of systems of differential equations.

[DearMajesty]

Well done sir! Thank you very much. Very succinct. I played this at 1.5x speed to cram for a test instead of reading the book for an hour. YOU ARE THE MAN!

[patrickmoloney]

Jesus Christ you explained what my TA couldn't in less than 5 minutes. I've a pretty good sense of Linear algebra but you just explained it so elegantly.

[Ciukyexacta]

The part with the types of Critical Points at 7:40 was the illumination I was looking for. Thank you for the great explanation!

[dknuth]

Fantastic video. You don't baby your audience walking through how to do every basic step and get to the meat of the the topic which brings people to your video. Thanks much.

[krishanmanzano]

A very straightforward explanation without losing the listener by heavy calculations!

[ShAlAmAnAyA]

So concise and clear. Thanks so much, sir!

[theusualsuspect]

Thanks. I was looking for this topic. God bless u

[vanessa_annie_ikebudu]

thanks so much for this. It really brought a lot of concepts I've been learning at uni together :)

[mohancochin]

Thank you very much. This helped me for my exam preparation.

[stephenward]

Really great way to explain phase plane. I was struggling abit but this made it really simple

[shrutivashishth]

I have a test tomorrow and this was really helpful, Thanks!! :)

[ikramziane]

Thank you very much for the vid it's really well explained. But am I the only one who got different values for Landa ( equals -5) at 2:42 ?
I calculated | Landa*I _ A| . "A " stands for our matrix (4 -3, 6 -7) please correct if I'm wrong :)

[shahlayadollahi]

thanks so much dear Dr for this brief and at the same time comprehensive lecture. I'm new at this subject and studying on my own, so it was really cleared it out for me. Just a little question: critical points must be real or else it wouldn't be linear anymore. Am I right?

[اممحمد-قه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase diagram for a system of 3 differential equations And it has three parameters

[tentonk]

Can you elaborate on 6:12 ... i still dont understand how it tends to the right.

[merkelwave]

great video! but we just had an example where both lambdas are positive & real and still we got an saddle point.

y_1' = 2*y_1 - y_2
y_2' = -y_1 + 2*y_2

lambda_1 = 3
lambda_2 = 1

could u maybe explain that?

[FranCoVids]

I am still a little confused as to why the phase plane has a clockwise rotation at 6:20. Anybody have any further explanations?

[katlig]

THANK YOU SO MUCH I THINK YOU MAY HAVE SAVED MY LIFE

[اممحمد-قه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[wbushyeager]

Very well done and fast explanation thanks!