The most efficient way to learn theory is to sit down and have another human being explain it to you, and then for you to go off and work out a problem yourself. Thanks for posting this, it's a great resource.
holy shit you might be on to something. we should come up with a name for that system. in medieval latin "lectura" meant a reading. we should call it that.
Great course. The professor put everything in perspective. The professor writes a lot on blackboard, so that one can follow his flow of thought closely. Unlike flipping through slides, one can get lost easily.
I am so glad this is here on the tube. I bought Prof. Strogatz book as a personal study. I have loved his book so far, and will likely use these lectures as a supplement.
I'm a physics undergrad and I'm annoyed at the way differential equations is being thought at my university we do these topics but obviously at undergrad level. I was skeptical to start watching storgatz lectures, I just said let me try it, and its perfect!!!!!!!. Very concise and makes it interesting
I love how the professor reminds the class that they can pirate his own textbook. Seems a little rash at first glance, but it shows that he's being selfless for the sake of the students' learning.
And exactly because of this, I believe more students tend not to pirate compared to the scenario in which the professor complain about it in a very serious tone
It’s kind of mind blowing that these universities pay professors that wrote textbooks that a company then turns around and sells to their students. Like why not just give to the students directly and not pay at all?
Bought his NLD book just for the shiggles (shits+giggles). The DVDs on Chaos from the Teaching Company featuring Dr. Strogatz were amazing as well. He really enjoys talking about math and as a result of this I really enjoy listening. Thanks for sharing this video, I appreciate it!
Steve, Steven, Professor, Professor Strogatzx, I think Jedi of Chaos is the appropriate title - in the best possible sense. Hey Don, do you agree? And also, Don, thanks for sending the link. This is delightful, amazing, so insightful... what better thing can be there than making sense of the apparent randomness in nature. (Well, OK, "that" is better, but let's leave that in our personal spheres.)
0:08:50 - Historical Overview the year 1666 0:11:18 - Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist," since he excelled in all fields of the discipline as it existed during his lifetime. Wikipedia
12:06 If I am not mistaken, Poincaré submitted his proof about the stability of the solar system to an announced prize award from the Swedish king (not the Nobel prize, yet). He submitted and won the prize, eventually. When one of the PhD student from the Russians, who checked the Russian printing and symbols and stuff had a feeling that one of the step is wrong. It wasn’t a big mistake, but it caused a small hole in the web of the proof. Poincaré tried to correct the mistake and cover the hole when he realised that actually he can’t prove the stability of the solar system in his original way. Correct me If I am wrong.
There's also a course on The Great Courses based on his book. I never saw that it was based on the book, but that has to be haha. Even the order matches ahaha. Of course the book goes deeper sometimes, sometimes gives another example and sometimes the VIDEO SERIES goes deeper, etc..., but the general scope is the same. I recommend it 100%. That's the best thing I found this year.
1:10:26 Why is x only asymptotically approaching pi instead of reaching pi and then staying there? What I mean is: how did the sinusoidal phase portait (which is to the right of the x(t) graph) tell us that x(t) only asymptotically approaches pi?
Excellent book with an excellent professor and lectures. But how come the video quality is so bad! Please fire the technician who recorded the lectures, would you!
Not only are there pirated copies of Non-linear Dynamics second edition (2014), but there are also pirated copies of the Solutions Manual (2nd Ed), and they only have solutions to every other problem.
He left out the work of Devaney in the early 80's, a simple and straightforward example being x^2 - 2, with seed 2*cos(k*Pi/N), N is odd. Abs values are 1.80193....-> 1.24697...._.-> .445041....-> back to 1.80193....(period 3 for N = 7.) A few periods: for N = 3, 5, 7, 9, 11, 13, 15, 17....; are respectively 1, 2, 3, 3, 5, 6, 4, 4....Devaney came up with the concept of "conjugates": Other formulas that give the same periods as with x^2 - 2, but iterates can be transformed into one another with simple (usually) arithmetic. Some other conjugates are (x^2 - 1) / (2*x), with seed cot(k*Pi/N), , the unit circle using x^2, and the iterative logistic map.. Another involves the Beraha constants.
Absolutely! Go on.. maybe the best start pointing. I would recommend some basis and tools in linear algebra, and Calculus book (1 and 2) for consulting
57:55 "There is no chaos in one and two dimensional nonlinear systems, you need three dimensions or more for topological reasons." I have comments on this. We need to have our systems described in ODE to satisfy the above statement. But if our system is described by difference equations, then the above statement is biased and may not be so correct.
Hey guys (Engineers to be specific) I’m looking for books/reference materials on * Nonlinear Dynamical Systems and Buckling Phenomena *Chaotic Motion of a Rigid Pendulum with external force *Chaos Control using OGY Method and application to Henon Map. Thanks Guys!
I know it is a variable course but numerical solutions for odes are quite satisfying what is your opinion is it worth taking the time and go through lectures with the book
54:02 Prof puts logistic growth as a 1st order system But is it not 2nd order as xn+1 = rx(1-x) which is 2nd order since its quadratic? OK perhaps the order is the order of the derivative? I don't quite get it please.
The order of the system is the highest order of derivative as you said. You can also transform a differential equation of order n into n coupled first order differential equations. In this case, the order of the system is the number of coupled differential equations.
Can someone help me - in the part where he draws the graph showing velocity vs. position (dx/dt on the y axis, x on the x axis) the prof says that the position tends to 1 as a limit (as t approaches infinity)- this confuses me, as the formula for velocity just describes an object that accelerates and then slows down and stops, at position x=1. seems like zeno's paradox, surely we don't believe that the object would never reach point x=1 because there are an infinite number of points between 0 and 1!
Yeah, that's true. Having that 0 at the origin is confusing, I would just see it as "small x" rather than 0. In that case: x' = rx(1 - (x/K)) (divide x on both side x'/x = r(1 - (x/K)) (assume x
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
He said that logistic difference equation doesn't have chaos ??? Some explanation is needed here ... If growth factor is changed then there is bifurcation more and more rapidly etc etc Isn't that chaos
I think that this type of changes that you said it isn't chaos, because if you now the initial condition (population as time=0), you exactly know the raises of population. If you do an analysis with a small perturbations on initial conditions you have the same result, in chaotic systems this not happend, a little variations of initial conditions diverge in a completly different solutions. Sorry for my english.
Is this lecture series taught with the current (2nd) edition of the book in mind? Or was this series published when the 1st edition was still the most recent?
Can anyone explain me why the growth rate tends to "K " when Time tends to infinite if actually with increasing the time, the growth rate decreases to negative values ( Not Zero) ?
Your second remark is wrong. It's not the with time that the growth rate decreases, it's with x. When you let time go to infinity, x will stabilize at the carrying capacity K, which 0 growth rate (fixed point).
He is talking about what website that student will connect with each other and thay post their question instead mailing me directly so they can get answer from other student on that website? Fayaz Khan from Charsadda, KPK Pakistan.
I'm just entering second year u/g math so maybe it's a dumb question, but how would you quantitatively analyse a DE that has no equilibrium points? Something like dx/dt = 1/sinx
Quantitatively it's kinda annoying, qualitatively when you look at the graph of 1/sinx we have x values where x dot explodes. If you use the same methods discussed in the video, the vertical asymptotes switch between stable and unstable the further we are from the origin.
Linearity in wave function (Psi) allows for addition of wave vectors thus accomodating the concept of interference and superposition. It's the same reason that a Psi is multiplied to the potential energy factor in the Hamiltonian, to account for linearity.
From the graph to the left, we can see that as x moves toward pi, the rate of change gets slower and slower. As x gets very close to pi, the rate of change is nearly zero. That's why it is asymptotic.
The most efficient way to learn theory is to sit down and have another human being explain it to you, and then for you to go off and work out a problem yourself. Thanks for posting this, it's a great resource.
holy shit you might be on to something. we should come up with a name for that system. in medieval latin "lectura" meant a reading. we should call it that.
8:12 is when he finishes talking about the syllabus and starts the lecture.
Thanks yr
Thank you, Cap'n
TY...
and the actual technical part starts at 36:46
I really like Professor Steven Strogatz style of teaching, clear, concise and easy to follow.
He shocked me from the beginning. What a great teacher!
Professor Strogatz, thank you for a fantastic introduction to Nonlinear Dynamics and Chaos. This is real mathematics that impact life in all forms.
Great course. The professor put everything in perspective. The professor writes a lot on blackboard, so that one can follow his flow of thought closely. Unlike flipping through slides, one can get lost easily.
I already have a better understanding of the topic than when my prof taught it. I am definitely using this as a guide for my Nonlinear course.
Hlo leche ..can you sent ur non linear dynamics notes
I am so glad this is here on the tube. I bought Prof. Strogatz book as a personal study. I have loved his book so far, and will likely use these lectures as a supplement.
Same
I'm a physics undergrad and I'm annoyed at the way differential equations is being thought at my university we do these topics but obviously at undergrad level. I was skeptical to start watching storgatz lectures, I just said let me try it, and its perfect!!!!!!!.
Very concise and makes it interesting
Such a wonderful wholesome professor. Thank you!
it's so cool to be able to watch this lecture series!
36:47 Logical structure of dynamics (Explains the notations)
59:11 The big chart of linear/nonlinear equations with order
I love how the professor reminds the class that they can pirate his own textbook. Seems a little rash at first glance, but it shows that he's being selfless for the sake of the students' learning.
And exactly because of this, I believe more students tend not to pirate compared to the scenario in which the professor complain about it in a very serious tone
it is his "helplessness" in stopping piracy that made him say that.
@@subramaniannk3364 Yeah but it makes me want to buy the book instead of pirating it tbh.
@Bryan Bernard hey did you mail him, yet ?.,
It’s kind of mind blowing that these universities pay professors that wrote textbooks that a company then turns around and sells to their students. Like why not just give to the students directly and not pay at all?
Thank you Prof Strogatz. Wonderful series of lectures and an excellent text.
Bought his NLD book just for the shiggles (shits+giggles). The DVDs on Chaos from the Teaching Company featuring Dr. Strogatz were amazing as well. He really enjoys talking about math and as a result of this I really enjoy listening. Thanks for sharing this video, I appreciate it!
Commenting so I can later find the series you describe.
Had to go through 175 videos of Khan academy's multivariate calculus to understand the introduction. Let see what the second lecture demands
Hahusahusahuashuashusahu, same here Bro ..
Why is this comment so accurate
I had to watch zero videos of the khan academy, because everything in this video is trivial
If you had the grit and determination to go through 175 Khan Academy videos, NOTHING!
@@Neilcourtwalker yes.
Historical part ends at 35:50
I should have read this before watching the video. xD
you saved my day :D thank you
thanks dude
He seems to be an excellent teacher and scientist.
Questions from the students are the fun part of these lectures!
great course!!!!!!!! Thank you for sharing it online.
Steve, Steven, Professor, Professor Strogatzx, I think Jedi of Chaos is the appropriate title - in the best possible sense. Hey Don, do you agree? And also, Don, thanks for sending the link. This is delightful, amazing, so insightful... what better thing can be there than making sense of the apparent randomness in nature. (Well, OK, "that" is better, but let's leave that in our personal spheres.)
You did a great job sharing it online
Great! I wish I had found those lectures before
alexvanwestwijk I am only discovering it now😁😁😁
I was gonna skip the history part, but its actually pretty interesting, he explains it very well, he even talks about Jurassic Park
0:08:50 - Historical Overview the year 1666
0:11:18 - Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist," since he excelled in all fields of the discipline as it existed during his lifetime. Wikipedia
HE IS A GREAT TEACHER!
This is truly an awesome course.
What an awesome lecture!
This guy is soooo good at explaining.
He's a Dronacharya to my Ekalavya. 🙏🏻
4:20 "do not hand in a photocopy of an answer manual. That would be ridiculous" I cannot stop laughing for the next 5 minutes. I just can't stop!
Very useful overview, appreciated work.
great teacher
Thanks for your sharing. We'll try our best to learn.
Can we call him agent of chaos?
12:06 If I am not mistaken, Poincaré submitted his proof about the stability of the solar system to an announced prize award from the Swedish king (not the Nobel prize, yet). He submitted and won the prize, eventually. When one of the PhD student from the Russians, who checked the Russian printing and symbols and stuff had a feeling that one of the step is wrong. It wasn’t a big mistake, but it caused a small hole in the web of the proof. Poincaré tried to correct the mistake and cover the hole when he realised that actually he can’t prove the stability of the solar system in his original way. Correct me If I am wrong.
Starts at 5:20
god i wish he were my professor. hes so chill 😭😭
Exciting topic, thank you.
Great! Exactly what I need!
There's also a course on The Great Courses based on his book. I never saw that it was based on the book, but that has to be haha.
Even the order matches ahaha. Of course the book goes deeper sometimes, sometimes gives another example and sometimes the VIDEO SERIES goes deeper, etc..., but the general scope is the same.
I recommend it 100%. That's the best thing I found this year.
What's the name of the course
@@SushantSingh-sl7vz Differential Equations
1:10:26 Why is x only asymptotically approaching pi instead of reaching pi and then staying there? What I mean is: how did the sinusoidal phase portait (which is to the right of the x(t) graph) tell us that x(t) only asymptotically approaches pi?
Great lecturer, recommend 2x speed to retain sanity though lmao :)
Very cool stuff
1:00:00 this is where it really begins
Excellent book with an excellent professor and lectures. But how come the video quality is so bad! Please fire the technician who recorded the lectures, would you!
STROGATZ!!!!!
Not only are there pirated copies of Non-linear Dynamics second edition (2014), but there are also pirated copies of the Solutions Manual (2nd Ed), and they only have solutions to every other problem.
He left out the work of Devaney in the early 80's, a simple and straightforward example being x^2 - 2, with seed 2*cos(k*Pi/N), N is odd. Abs values are 1.80193....-> 1.24697...._.-> .445041....-> back to 1.80193....(period 3 for N = 7.) A few periods: for N = 3, 5, 7, 9, 11, 13, 15, 17....; are respectively 1, 2, 3, 3, 5, 6, 4, 4....Devaney came up with the concept of "conjugates": Other formulas that give the same periods as with x^2 - 2, but iterates can be transformed into one another with simple (usually) arithmetic. Some other conjugates are (x^2 - 1) / (2*x), with seed cot(k*Pi/N), , the unit circle using x^2, and the iterative logistic map.. Another involves the Beraha constants.
Respect
thank you professor
Likes his humorous!
34:00 I believe he was talking about the Voyager II, right?
Thank you.
For those who have finished this course: I am a biology major is this series a good starting point for me? What prerequisites are required?
Absolutely! Go on.. maybe the best start pointing. I would recommend some basis and tools in linear algebra, and Calculus book (1 and 2) for consulting
Thanks for sharing.
i am probably asking this question too early, but what happens to the phase space if it is non-autonomous?
57:55 "There is no chaos in one and two dimensional nonlinear systems, you need three dimensions or more for topological reasons." I have comments on this. We need to have our systems described in ODE to satisfy the above statement. But if our system is described by difference equations, then the above statement is biased and may not be so correct.
Hey guys (Engineers to be specific)
I’m looking for books/reference materials on
* Nonlinear Dynamical Systems and Buckling Phenomena
*Chaotic Motion of a Rigid Pendulum with external force
*Chaos Control using OGY Method and application to Henon Map.
Thanks Guys!
This professor reminds me of Saul Goodman
I know it is a variable course but numerical solutions for odes are quite satisfying what is your opinion is it worth taking the time and go through lectures with the book
Gold!
54:02 Prof puts logistic growth as a 1st order system But is it not 2nd order as xn+1 = rx(1-x) which is 2nd order since its quadratic? OK perhaps the order is the order of the derivative? I don't quite get it please.
The order of the system is the highest order of derivative as you said. You can also transform a differential equation of order n into n coupled first order differential equations. In this case, the order of the system is the number of coupled differential equations.
Can someone help me - in the part where he draws the graph showing velocity vs. position (dx/dt on the y axis, x on the x axis) the prof says that the position tends to 1 as a limit (as t approaches infinity)- this confuses me, as the formula for velocity just describes an object that accelerates and then slows down and stops, at position x=1. seems like zeno's paradox, surely we don't believe that the object would never reach point x=1 because there are an infinite number of points between 0 and 1!
1:13:52 How can x'/x = r when x=0? When x=0, x'=0, so x'/x = 0/0...
Yeah, that's true. Having that 0 at the origin is confusing, I would just see it as "small x" rather than 0.
In that case:
x' = rx(1 - (x/K)) (divide x on both side
x'/x = r(1 - (x/K)) (assume x
14:00 sensitive dependence
I wonder if dissipative structure was part of the history ?
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
He said that logistic difference equation doesn't have chaos ??? Some explanation is needed here ... If growth factor is changed then there is bifurcation more and more rapidly etc etc
Isn't that chaos
I think that this type of changes that you said it isn't chaos, because if you now the initial condition (population as time=0), you exactly know the raises of population. If you do an analysis with a small perturbations on initial conditions you have the same result, in chaotic systems this not happend, a little variations of initial conditions diverge in a completly different solutions. Sorry for my english.
Is there a way to have access to the homework released?
Is this lecture series taught with the current (2nd) edition of the book in mind? Or was this series published when the 1st edition was still the most recent?
What are the Prerequisites for this course?
Is there any pre-requirement needed in this lecture?
Better if you know differential equations, Eigen values and eigen functions and basics of physics
youtube, and no spouse
Great lecture but it seems to me that what he calls a fixed point at 1:06:45 is rather an equilibrium point.
what if - just what if... those two words mean the same thing?
Can anyone explain me why the growth rate tends to "K " when Time tends to infinite if actually with increasing the time, the growth rate decreases to negative values ( Not Zero) ?
Your second remark is wrong. It's not the with time that the growth rate decreases, it's with x. When you let time go to infinity, x will stabilize at the carrying capacity K, which 0 growth rate (fixed point).
2-body problem or 2-bodies problem ?Is that a problem ?
He is talking about what website that student will connect with each other and thay post their question instead mailing me directly so they can get answer from other student on that website?
Fayaz Khan from Charsadda, KPK Pakistan.
Can someone please tell me the title of his book. Thank you
NONLINEAR
DYNAMICS AND
CHAOS.
I'm just entering second year u/g math so maybe it's a dumb question, but how would you quantitatively analyse a DE that has no equilibrium points? Something like dx/dt = 1/sinx
Quantitatively it's kinda annoying, qualitatively when you look at the graph of 1/sinx we have x values where x dot explodes. If you use the same methods discussed in the video, the vertical asymptotes switch between stable and unstable the further we are from the origin.
What head is sir talking about at the end of the video :)
Why Schrodinger equation is linear? I thing, It is nonlinear.
Linearity in wave function (Psi) allows for addition of wave vectors thus accomodating the concept of interference and superposition.
It's the same reason that a Psi is multiplied to the potential energy factor in the Hamiltonian, to account for linearity.
Dr. Chaos is that you?
How do we know from the drawn picture that the curve does not hit pi?
From the graph to the left, we can see that as x moves toward pi, the rate of change gets slower and slower. As x gets very close to pi, the rate of change is nearly zero. That's why it is asymptotic.
46:47 Use Simulink then.
00:46:00
🤔
I c u 😂
47:20
How long u been gift. Cool thanf about the ridiculous ability to lie l. Its more about the dsn-5 sosiopath😅
Side bar... 😅
“..“
Imagine wanting to learn chaos theory and cheat 😂
He a fraud .... nonlinear means a st8 lines then he goes x y
He is a fraud @!!
I can do them shits i over a beer.
Don't pay 4 this
Sad man trying to validate . Sad falling man😂
Ur a con man
40:51 (autonomous system)