Incredible lecturer, such a breath of fresh air. Strogatz' book is a work of art, on-par with Griffiths, Feynman, and other great writers. I am so frustrated with my professor. Handwritten, unreadable course notes and completely jargon-filled bad verbal communication and horrendous lecture style.
50:30 - Hmmm. Well, cos(theta) has a line of symmetry, so the orbit will have to have similar symmetry, right? That still leaves a lot of possibilities, but it is *some* information. That tells us that the orbit has to cross that line of symmetry along a normal trajectory. The radius has to have inner and outer turning points, too (rdot == 0). These will occur where cos(theta) == (r^2-1)/u. It seems to me that these would have to be at theta=pi/2 and 3*pi/2, where cos(theta) is zero.
Then you can't prove a trapping region exists using the first-order approximation near the fixed point. You would need another method to show the inner annulus is still trapping I think.
Hi I would appreciate the help of someone who took the course or has the material to provide me with the assignments or problem sets in this course which are typically chosen from the textbook just problem numbers from the textbook for each assignment. Kind regards
Because IF g exists, then a closed orbit exist. This is simply true by the prrof of the theorem. The fact that g is hard to find, and guessing is needed to find it have nothing to do with the prior fact, it just makes the theorem on constructive.(And by many more application oriented people thought of as somewhat weaker than a constructive one. But hey, sometimes a nonconstructive one like this is the best we can to.)
Roshan Thomas Eapen probably not because you can turn a 2 dimensional non autonomous system. So then the theorem would also work for 3 dimensional non autonomous system.
0:00 - Testing for close orbits (dulac's criterion)
7:40 - 7.2.4 example
17:10 - Proof Dulac’s Criterion
28:30 - 7.3 Poincare Bendixson Theorem.
42:33 - 7.3.1 example
51:12 - 7.3.2 example
Thanks man
Cheers
Incredible lecturer, such a breath of fresh air. Strogatz' book is a work of art, on-par with Griffiths, Feynman, and other great writers. I am so frustrated with my professor. Handwritten, unreadable course notes and completely jargon-filled bad verbal communication and horrendous lecture style.
Professor Strogatz, thank you for an excellent lecture on Testing for closed orbits. This is real world mathematics.
Very good lecturer!
camera guy got sleepy by the end of the lecture
50:30 - Hmmm. Well, cos(theta) has a line of symmetry, so the orbit will have to have similar symmetry, right? That still leaves a lot of possibilities, but it is *some* information. That tells us that the orbit has to cross that line of symmetry along a normal trajectory. The radius has to have inner and outer turning points, too (rdot == 0). These will occur where cos(theta) == (r^2-1)/u. It seems to me that these would have to be at theta=pi/2 and 3*pi/2, where cos(theta) is zero.
in glycolysis, what if (a,b) lies on the borderline?
Then you can't prove a trapping region exists using the first-order approximation near the fixed point. You would need another method to show the inner annulus is still trapping I think.
I was just wondering why doesn't he use the third board.. 😅😅
He answered that towards the end XD.
Hi
I would appreciate the help of someone who took the course
or has the material to provide me with the assignments or problem sets in this
course which are typically chosen from the textbook just problem numbers from
the textbook for each assignment.
Kind regards
16:13 When function g is totally based on guess, then how can we affirm there is close orbit or not?
Because IF g exists, then a closed orbit exist. This is simply true by the prrof of the theorem. The fact that g is hard to find, and guessing is needed to find it have nothing to do with the prior fact, it just makes the theorem on constructive.(And by many more application oriented people thought of as somewhat weaker than a constructive one. But hey, sometimes a nonconstructive one like this is the best we can to.)
Is the Poincare-Bendixson theorem valid for 2 dimensional non-autonomous systems?
Roshan Thomas Eapen probably not because you can turn a 2 dimensional non autonomous system. So then the theorem would also work for 3 dimensional non autonomous system.
Thankyou
I have a feeling he does not like questions 😁 great teacher though!
thank you :)
The questions make me cringe.
Aviv Albeg why