This is really well explained in lecture 5 of 18.03 for those who want a more expanded explanation. Thanks David and MIT for this and all the recitations, I love your work.
The series of videos are very helpful to gain deeper understanding of DE concepts. There's a minor error here - no effect on the final results. Any graph of x-dot = ax +1 must be a line through (0,1), so the first graph is inaccurate. (Unless you argue that the vertical line labeled x-dot is not necessarily the x=0 line).
this is a solid explanation. i think everyone is getting hung up on the fact that they assume the origin has to be (0,0). he never said that it was (0,0). for the comment below mine stating they dont see how the line crosses the x-axis. if you dont know that a straight line with a non-zero slope crosses the x-axis at a point when the function equals zero, then i dont know how you got to differential equations.
Also when he's drawing the accompanying graphs for the phase lines he's not making it clear that the critical points at x(t) = -1 and x(t) = 1 are points along the vertical axis, not the horizontal axis. The horizontal axis representing the independent variable t. Again you could argue that he's drawing the nullclines at x(t) = -1 and x(t) = 1, but at one point I thought he was going to mark the critical points on the t axis! :P
The idea that really matters is what is positive and what is negative over which intervals, so even though he drew the graphs and intercepts incorrectly he used the correct points and intervals. But yeah this should be revised
this is wrong, first you graph (dx/dt) in terms of x ,thing he did wrong in the first graph,then you graph x in terms of t,he didnt did that it seems he tought x was the independent variable when it was t in short words, the stable solution is a horizontal line above or below the t-axis ,watch the lecture and you will see
The comments were turned off by request of the instructor. As you suspected it was because of the number of inappropriate comments related to being female.
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This is really well explained in lecture 5 of 18.03 for those who want a more expanded explanation. Thanks David and MIT for this and all the recitations, I love your work.
Thanks a lot for pointing it out !
Professor Shirokoff thank you for a solid explanation of Autonomous Equations and Phase Lines in ordinary differential equations.
I was not getting this topic from past 2 months.
Thanks sir.
This is some solid explanation 🙌🙌
The series of videos are very helpful to gain deeper understanding of DE concepts. There's a minor error here - no effect on the final results. Any graph of x-dot = ax +1 must be a line through (0,1), so the first graph is inaccurate. (Unless you argue that the vertical line labeled x-dot is not necessarily the x=0 line).
this is a solid explanation. i think everyone is getting hung up on the fact that they assume the origin has to be (0,0). he never said that it was (0,0). for the comment below mine stating they dont see how the line crosses the x-axis. if you dont know that a straight line with a non-zero slope crosses the x-axis at a point when the function equals zero, then i dont know how you got to differential equations.
his explanation is right , but his first graph is wrong. He is also human.
Also when he's drawing the accompanying graphs for the phase lines he's not making it clear that the critical points at x(t) = -1 and x(t) = 1 are points along the vertical axis, not the horizontal axis. The horizontal axis representing the independent variable t.
Again you could argue that he's drawing the nullclines at x(t) = -1 and x(t) = 1, but at one point I thought he was going to mark the critical points on the t axis! :P
Very helpful sir
he is human .why this video isnt replaced with new corrected video?
Thank you so much!! This was very helpful.
The idea that really matters is what is positive and what is negative over which intervals, so even though he drew the graphs and intercepts incorrectly he used the correct points and intervals. But yeah this should be revised
this is wrong, first you graph (dx/dt) in terms of x ,thing he did wrong in the first graph,then you graph x in terms of t,he didnt did that it seems he tought x was the independent variable when it was t
in short words, the stable solution is a horizontal line above or below the t-axis ,watch the lecture and you will see
I have a question! Why are the comments on all the videos that the lady recorded shut down? Because she is colored, or because she is female?
The comments were turned off by request of the instructor. As you suspected it was because of the number of inappropriate comments related to being female.
@@mitocw It's a pity that such things happend. She is a good teacher and deserves our respect.
MIT btw.
genius btw.
prestigious University btw
So confusing!
very inaccurate, sloppy