This feels like a magician teaching forbidden spells to apprentices

These are just about the coolest mathematical methods lectures in existence, for several reasons. 1. Despite the rather "high powered" subject matter, Bender's presentation is remarkably clear, organized, accessible, encouraging, and un-intimidating. This combination is almost unheard of in these kinds of subjects. 2. The subject itself is unique, practical, original, and beautiful. How sick are we of the usual linear-only exactly solvable problems like in Jackson with tons of work but little insight to show for it? 3. As a bonus, we learn much more deeply what we were trying to do in the standard approximation methods in quantum mechanics, and look inside the black box. I could go on, but suffice it to say that I don't even do physics anymore (I was never smart enough), but I still watch and work through these lectures because they are just so cool.

@MDevincenzis

9 жыл бұрын

Keith Wald I agree. This is mindblowing.

@NotthatRossKemp

8 жыл бұрын

I agree, a wonderful set of lectures on an invaluable topic.

@godsadog

7 жыл бұрын

Nothing but agreement.

@ShakespearHD

Жыл бұрын

Watching Prof. Bender makes me realized how cheated I was having some of the math instructors while at UW-Madison. The ones I'm thinking of were simply time-card punchers as compared to Prof. Bender who cares enough to make sure things are clear to his students. He is a rare jewel in that World.

I have a pretty strong math background, but the Shanks transform officially blew my mind. Toast to the creativity of Mr. Shank, so elegant but yet so simple.

Best explanation of branch cuts I’ve seen

thank you very much for these lectures. I don't see in my life any teacher as like him. He is explaining a very complicated thing in a very interesting and easy way. Thank you again.

epsilon in the exponent is a measure of the non linearity of the equation. Think about that for a few moments and you'll see how true that is. Brilliant!!!!

This is really good stuff! Look forward to the rest.

The fact that the -x^4 potential gives bound states picked my curiosity, does he explain it later or does anyone know a reference where to look this up?

“Absolutely fascinating” it’s so true!!

'the dangers of drinking and deriving'

@jaydencallan1010

3 жыл бұрын

I know it is pretty off topic but does anyone know of a good website to stream new movies online?

@russellduke7959

3 жыл бұрын

@Jayden Callan I would suggest FlixZone. You can find it on google :)

@landyndonovan9958

3 жыл бұрын

@Russell Duke Yup, have been watching on flixzone for months myself =)

@jaydencallan1010

3 жыл бұрын

@Russell Duke thanks, I signed up and it seems like a nice service =) I really appreciate it!

@russellduke7959

3 жыл бұрын

@Jayden Callan No problem :)

I think the Möbius strip illustration at 42:10 is more illustrative than the real Möbius strip!

In case anyone is curious, I beleive the paper referenced at 0:48:50 is titled 'Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation'. Please correct me if I am wrong.

@gigijbijbj

8 жыл бұрын

Thank you

@praveenjanantha

7 жыл бұрын

Thank you

@JohnVKaravitis

4 жыл бұрын

Confused, the date on this paper is Sept 2018, yet these lectures are from 2011.

@aaavvv2862

10 ай бұрын

I think this is the correct reference: arxiv.org/pdf/1105.1137.pdf For he mentioned measurement and interference in lecture.

This guy is an awesome lecturer! I

In electrical circuits (and microwave cavities) complex power, is composed of two parts. 1. The average power that flows from a source to a load (Watts), 2. the rate of energy sloshing back and forth between circuit elements (magnetic and electric fields) during a cycle (Vars).

Thanks for sharing. Loved the first three lectures.

Would anybody know the exact reference for the (Richter?) microwavre cavity experiment mentioned from 48:46 to 50:35 in the video?

Direct sum the first 10^8 terms of the series gives a relative error 10^-8, I just tried.

"I wanna fill some holes" - Bender, Carl

The class is not lacking knowledge, but is lacking vitamins and protein. All the coughing and sneezing. Don't forget your immune system while doing maths :)

Brilliant!

42:00 made me spill coffee on my sofa.

@johannespanagiotopoulos4917

9 жыл бұрын

Kevin Falls Worse: I hurt my shoulder joint!

@danlurny4129

9 жыл бұрын

Johannes Panagiotopoulos AAHHAHHH)

@BartAlder

8 жыл бұрын

+Kevin Falls First done by Feynman so far as I know, in his Dirac memorial lecture to show what spin half looks like as a geometric proposition.

Anyone know which article he refers to at 52:00?

With the last part of the video, I had done something similar, but my new series just contained values that were the average of two values in the previous series, then the next series contains averages of consecutive values of the last series. It did a decent job, but not as fast as his method

wonderful

Two questions: At 7:20 does he use 1+epsilon? Its hard to see but it won't work for just Epsilon as he says. Also, at 14:18 shouldn't he use Epsilon/2 ? I'm thinking it may work both ways but I haven't worked it out yet...

@ivanphi

8 жыл бұрын

+Even Prime he uses 1+epsilon

36:40 the reason why square roots have plus and minus solutions

@jehehe76tcixi

4 жыл бұрын

No it’s because a negative squared is positive bruh

wondering waht the guy at 56:04 wanted to ask

The hockey stick though

at minute 13:38 how did he come up with the unperturbed problem ? It's seems very random to me and he could've picked another solvable differential equation .

@mudkip_btw

4 жыл бұрын

The thing that makes the equation hard to solve is the y√y term. It's natural to then raise √y to epsilon, and to make y_0 as simple as possible, why not include 1/√x in the perturbation.

But how does the system know where I drew the line between the two roots? And I think it must know because if I start the system at some energy level and vary the parameters, of say the microwave cabinet, then if I cross the branch line between the two roots and enter the second Riemann surface and then continue back to the place where I started I will be on the next higher or lower energy level (depending on the Riemann surface I started at). And if the branch line is placed in such a way that I don't cross it on my path then I won't reach the next higher or lower energy level. So how does the system know where the branch line is? Greetings Nick

@nicklasmunksgaardlarsen2436

4 жыл бұрын

Exactly, I was wondering the same. It seems like the students present were hinting at that particular question but no satisfying answer ever came of it. Drawing the line mathematically might be political but the physics sure isn't.

@gman91106

4 жыл бұрын

It's because what matters are the branch points, not the cuts. You can show that for any smooth, closed curve, what determines the final location on the Riemann surface is whether that curve wraps around a branch point, and how many times (this is called the winding number) - the exact location of the cut doesn't matter. And since the branch points are the same for any choice of branch cut, the final energy level of the curve will also be the same. You can try this yourself for, say, f(z) = z^(1/2). The branch point is z=0. Draw any arbitrary branch cut from 0 out to infinity, pick any nonzero starting point, then try to draw a closed curve that doesn't contain z=0 but still ends up on the other sheet of the Riemann surface. You won't be able to do it. Even if you cross the branch cut once, you'll have to cross back again to get to the original point.

@nickjung1199

4 жыл бұрын

@@gman91106 Awesome explanation and example. Thanks!

I'd call most of these methods meta-mathematical.

prof bender is much better lecturer than feynman, much clearer...ive heard feynman lecture i lost sometimes feeling confuse

why did the shanks transform work we choose Sn = L + AB^n which might be and might not be true so why did it work ??

@LeconsdAnalyse

9 жыл бұрын

+ln murthy Take Sn = L + AB^n (n=0,1,2,...) For eample, take S₀= L + A, S₁= L + AB, and S₂= L + AB². Then, L ≐ (S₂S₀ - S₁²)/(S₂ - 2S₁ + S₀) = LA(B² - 2B +1)/A(B² - 2B +1) = L ! In general, for *any three* consecutive partial sums in {S₀, S₁,...,Sᵧ₋₁, Sᵧ, Sᵧ₊₁,...}: L ≐ (Sᵧ₊₁Sᵧ₋₁ - Sᵧ²)/(Sᵧ₊₁ - 2Sᵧ + Sᵧ₋₁).

@BartAlder

8 жыл бұрын

+ln murthy because it is a series which has convergence from above and then below which is intrinsically self-correcting. All errors in the transformed series, *S*(S(n)), come from reducing errors in the original series. It was possible to find a scheme which no longer depended on A or B which involved ANY B AT ALL and so you could work with just L (the exact solution) and S(n-1), Sn and S(n+1) (increasingly accurate estimates of L guaranteed to be more accurate for larger n) and now the errors iteratively vanish.

what is this math for?? if im studying physic should i see this course even if im not a math pro

@alicewyan

5 жыл бұрын

Most physics courses will include a couple of these techniques within the specific fields of study, these techniques are all we have to study quantum systems (QM and QFT), statistical field theory, solid state physics...

What's up with those tiny people on the bottom left of the screen?!!

I tried 1/2 as the solution of : x^5 + x = 1 and I got 33/32 that I think the closest result.

Intro ends at 23:40

@welcomeblack

4 жыл бұрын

More like 58:15

Wow.

Perturbation methods need to be nerfed

Someone is being rude. He is making sharp annoying noises while the professor is trying to speak!

@22:03, the cutie in the lower left corner starts picking her nose.

The camera man is very poor, he must focus the writings of the board always and zoom them but the camera is focused totally which is not important.

Very complicated way to explain simple concepts. This guy should read Feynman and Landau and Lipshits to learn the proper way to explain this.

accept the Lord Jesus Christ who has not accepted yet because He is coming back ... sanctify more and more inside and outside ... doing works worthy of repentance and leaving worldliness ... leaving the vanities the tinctures, earrings, makeup, enamels , the fashions of hair and clothes, the short and tight clothes because the Lord is Holy and we must be holy in all our way of living "1 Peter 1: 15,16"