Sir. I am a big fan of your teaching. your book " Nonlinear Dynamics & Chaos" is simply the best. I taught many times in my university. Love from Pakistan.

Thank you so much for these lectures again, Professor Strogatz! I will be following your contents and I look forward for the next ones!

Glad to see these available online. Thanks.

im so grateful that these lectures are available online, they are so valuable. thank you sir!

Thank you for this wonderful lecture and the entire series Prof. Strogatz.

My mentor recommended this course to me, and it's amazing! Now my life goal is to become as great a teacher as Steven:)

just wonderful, simple, direct and elegant lecture

This lecture is amazing. Thanks for this content.

Fascinating! cannot wait for the next lecture!

Awesome lecture! Looking forward to the next one

thank you!!! this is wonderful....

Thank you for posting it. Very interesting lecture. Looking forward to more.

Best instructor. Thank you so much Prof. Strogatz for sharing knowledge with us

Wow..Thanks million dear sir...

Very interesting. Thanks for sharing! I am also sharing my lecture online, but they are in Portuguese :-)

for F(10)...how are we can evaluate it numerically where it's has infinite interval..

Thank you.

Can someone tell me what are the prerequisites for this course.

Is there a chance to get your notes of this course ?

what is a closed form ? can anyone explain in comment section please!!

Why are there so many ads?

On a side note, the wallpaper on your desktop is gorgeous!

i wich that u have an course in complex analysis

kindly sir, make a video on ''Ritz method & its applications'' also.

Hello, Professor S. Strogatz I didn't know how to contact you sir, so I just wrote it here. Sir, would it be possible for you to explain HPM methods(Homotopy Perturbation Methods) ?

If g(x) = 0 for some x then we have a problem with the definition of ~. It is better to say that f ~ g at x0 iff there exists function h such that [h(x) -> 1 as x -> x0] & [f = h • g]. Here we assume that D(f) = D(g) = D(h). Thanks a lot! I'm not familiar with English but nevertheless I couldn't stop listening until the end of the lecture.

What software is used here to write out the lecture material?

@kritisehgal9840

3 жыл бұрын

It seems Notability app on iPad.

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Are these lecture notes available somewhere? It'd be great to have them.

I've been frustrated for ~5 years that in this context, "formal" literally means "informal."

@ilovethesmellofdbranesinth7945

2 жыл бұрын

Actually there's a formal meaning of formal which I think Prof. Strogatz was informally using :)

@dhawkins1234

Жыл бұрын

There are two different definitions-one is formal as in, manipulating the form without regard to the underlying meaning, and the other is what we typically think of as formal in math, i.e. obeying rigorous standards of proofs etc.

@dhawkins1234

Жыл бұрын

The 3rd sense from the Oxford dictionary is: "of or concerned with outward form or appearance, especially as distinct from content or matter." Which is closer to how the Prof was using it.

Great lecture! Tiny trivial typo around t=t=8:45, in the equation at the bottom, in the square brackets, there are sign errors in the last two terms, so it should be: [...] = 1 - t + t^2 - t^3 + ... This typo was fixed in intermediate steps and so does not propagate to later equations.

I see that this isn't the first time the lecture is being taught, is it the first time his lectures on this subject being recorded?

this lecture

In his definition of the asymptotic expansion, Strogatz seems to have neglected or failed to discuss the properties of the sequence of coefficients a_i. If his description is accurate, I am very surprised that the coefficients are in a sense determined by the phi functions. (Update: wikipedia confirms this).

@nickpreetic4670

3 жыл бұрын

in my understanding there is no constraint on the coefficients, they are completely determined by the asymptotic scale (the phi's) and the function whose asymptotic expansion you are determining

@nickpreetic4670

3 жыл бұрын

in fact, there's a theorem Borel Ritt theorem which says given any sequence of complex numbers, there is an analytic function with an asymptotic series with those coefficients. This was always very surprising to me

@maxwellsdaemon7

3 жыл бұрын

@@nickpreetic4670 That is an interesting theorem. What was also counterintuitive is that in that example Prof. Strogatz gave, the improper integral of exp(-xt)/(1+t), the coefficients in its asymptotic function increases with n (n!).

@nickpreetic4670

3 жыл бұрын

@@maxwellsdaemon7 There's a whole theory of divergent series out there, my research (the field is called resurgence theory) is very related to this (PhD student here). They occur naturally in the form of asymptotic series for ODEs and you can actually sum them! If you're interested, the beginnings go back to Euler, Hardy and Borel and the method of Borel Summation (more modern method is Borel_Ecalle Summation) allows you to handle some divergent series but not all

@maxwellsdaemon7

3 жыл бұрын

@@nickpreetic4670 I wasn't previously aware of the term or field "resurgence theory", but after I googled, I see it has applications to QFT, which makes sense.

well, well,well, ELO 3000 as GM Chess master

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