I'm still amazed that I get to sit in, for free, on this interesting class taught by someone who obviously knows the stuff cold AND is a good teacher. For this opportunity you used to have to apply and get admitted to college somewhere, and when you got there, maybe you would get a good teacher, and maybe not. Now, instead of all that hassle, I can just choose the best courses from anywhere in the world, without even having to get out of bed. That is stunning. Of course if I were a young person, it would be better all around for me to go to an actual college, and meet lots of students and teachers and make friends there. But I am not a young person anymore, and this is pretty much the best way for me to learn almost anything

@vaultvon2126

8 жыл бұрын

Happy for you. Wish you luck. It's nice to see people like you. Many people don't wanna learn anymore especially at your age. Keep it up.

@MrPoutsesMple

8 жыл бұрын

+Ralph Dratman Dear Ralph, since you're a lifelong learner (which is super cool) you can also check out websites as Coursera, EdX, Udacity for free courses given by universities around the world. All the best !

@jimkeller3868

8 жыл бұрын

+Vault Von Wow. Are you sure that many people his age don't wanna learn any more? Are you sure that many people your age do?

@IronCharioteer

8 жыл бұрын

+Ralph Dratman Just so you know; this video was recommended by my Mathematical Methods professor for homework. So you chose a good vid to watch and learn from.

@0530628416

8 жыл бұрын

i really feal the same and i am young , this is one of the few reasons i love modern world and technology

1:24 This man is eating a fine course meal

@austinfelker2156

4 жыл бұрын

Wtf

@HeyEveryoneHi

3 жыл бұрын

lol wtf

@aidanwiggins7857

3 жыл бұрын

what he doin ????

@ashishkumarsharma1323

3 жыл бұрын

bro? xd just noticed

@oliwakulla3341

2 жыл бұрын

That's just not the thing you do in the middle of a lecture. So many people want to stand out in so many ways, but this is plain unethical. I wouldn't want to sit next to him.

I now have to add Carl Bender to my list of Best Teachers Ever. The all have in common the obvious stuff -- totally grokking the subject, being able to explain it very clearly, completely understanding where a student's question is coming from and how to answer it, etc. But they also have something really special -- a great sense of humor. And I don't just mean telling jokes, which they all do with more or less success (sometimes less). I mean being greatly amused by, and making the students be greatly amused by, *the actual subject itself*! A sense of "Isn't this wonderful? Doesn't this make you practically laugh out loud by how wonderful it is?" P.S. I'm 73.

I keep coming back to this lecture series in awe. There is simply nothing like it. I am binge watching it as if it were a netflix series, this is not a joke!

THIS is what KZread was made for. Just looking at this fills my soul with joy and happiness, while it covertly fills my mind with knowledge and understanding.

Fine. Hope you like them. And please let me know if you happen to find the same series with better resolution or quality. Cheers.

@zada4a

4 жыл бұрын

Fine what? Who are you responding to?

@howardlam6181

4 жыл бұрын

@@zada4a 8 years ago, youtube comment section worked differently.

For everyone complaining about the guy eating, it's super common to eat during lectures in grad school. Between going to lab, teaching, and your own coursework, you don't have much time especially if you work in a wet lab where it is a safety violation to eat while in lab. I have had days where I was doing an experiment from 7 am to 1 pm and had to go to class immediately after that without a break for lunch. Also, departments frequently hold seminars where they bring in high profile speakers from around the world, and to encourage attendance, they actually provide free lunch/dinner (typically pizza) or drinks (beer, wine, etc...). I have gone to lectures for the explicit reason of eating a free lunch that was provided there. It's so common that they some times call these "Lunch and Learns" or "Brown Bag Seminars". As long as you're being quiet and not eating some obnoxiously smelly food, literally no one cares.

@matteogirelli1023

Жыл бұрын

Still rubbish behaviour. Very disrespectful

@hawkeye5626

Ай бұрын

@@matteogirelli1023 you know nothing

Prof. Bender is a star lecturer. A sheer pleasure listening to his way of teaching. Another excellent lecturer that I happened to come across while looking for some material for someone in my family is Denis Auroux when he was at MIT (MIT 18.02 Multivariable Calculus, Fall 2007).

Wow, a really gifted teacher, for the first time I really understand perturbation theory. Right on Professor!

DUDE.. is that a guy eating with a KNIFE and FORK in the front row? WHAT?

@drbonesshow1

9 жыл бұрын

MoTheDeliciousPeach Communist with knife and fork meets capitalist with steak and kidney pudding.

@ozgurkuzu2202

7 жыл бұрын

ahahhahahahahahahhahhahahahhahhahahaahahaahahahahha )))

@bettygoodbody

6 жыл бұрын

MoTheDeliciousPeach he was eating the lesson. an easier way to get the material inside

@bettygoodbody

6 жыл бұрын

eating the lesson is absorption of the information is what I mean

@lucasm4299

6 жыл бұрын

MoTheDeliciousPeach I think this is in Canada.

Having watched this lecture four or five times over the past few years (not always all the way through), I now enjoy watching it even more each successive time. Prof Bender has a pleasant impish quality that I like, and each time through I understand more of what he is doing. That is the kind of activity I call fun, but which most of the world would run away from, fast.

@ToriKo_

Жыл бұрын

It’s cool to see you coming back to it, after ur initial comment u left 6 years ago!

I like this guy's teaching approach. It is a very natural and reveals a free thinking attitude. This is contagious !

I love this man, he makes everyone be addicted to the subject, can't stop watching these lectures!

Excellent lecture focusing on Perturbation Theory and Asymptotic Methods. Much of the lecture may be supported with his now classic 1978 text Advanced Mathematical Methods for Scientists and Engineers. Prof. Bender is a master lecturer and explainer.

I remember finding this in 2018 and just being awestruck. I'm glad to see this is gaining appreciation, if I remember correctly there were only 30k views or so in 2018.

I love his sense of humour. It makes the lecture much easier to digest.

"But nevermind. That's just words." - ...and an attempt to draw parallels to something some students might recognize. For others it's something they need to hear. Beautifully done! :)

@Gruuvin1

Жыл бұрын

Thanks for pointing that out. I often read comments before I get far into a video, so I came back to this comment when I heard him say it.... Yes .. he's anchoring the concept for them. Outside of that, it's fairly meaningless, but within the scope of the classroom, it's powerful. He's a great teacher. I miss being in classrooms like this.

Wonderful lecture series; high quality stuff, unhurried, with deep insights and perspective. Watching these videos is probably better than sitting in the classroom since the professor's writing turns into microfiche at times.

mathematician: enter the video mathematician two seconds later: leaves immediately

@_Nibi

4 жыл бұрын

@Call me Joe It was actually a great lecture

@puppetsock

4 жыл бұрын

The sad part of the intro was that power expansions *are* a numerical technique.

@armycin

4 жыл бұрын

@@Wtahc no, because Mathematician aren't interested in non rigourous theories

@_Nibi

4 жыл бұрын

@@armycin aka, ya'll nerds

@armycin

4 жыл бұрын

@@Wtahc I would add that at least physicists comprehend what they study

Ahh, the man himself! When I was young, the "Bender and Orszag" book gave me many hours of both pleasure and frustration.

@liftingisfun2350

4 жыл бұрын

K Dub a sexual ideal

@9WEAVER9

3 жыл бұрын

(One of) his is grad student(s), William Paulsen, also went on to write a fantabulous book on Asymptotic and Perturbative Analysis.

LOL the hockey stick for pointing on the slides board.

Thank you for posting these. They're amazing lectures.

It's been about 10 years since the last time I saw someone explain such a deep concept with such simplicity and elegance.

@passerby4507

3 жыл бұрын

Because he didn't explain anything perhaps? He taught you how to compute and some bs about math that actively harms your notion of mathematical concepts. Funny thing, the computation methods he teaches is derived from "less powerful" rigorous math.

@Peter_1986

Жыл бұрын

​@@passerby4507 This video made it much easier for me to understand stuff about Perturbation Theory that I am currently studying in my own course. And I would say that "the ability to clarify a topic and make it easier to understand" is pretty much the definition of "explaining" something. By the way, are you very bitter about something? Because your post comes off as overly bitter, even if we take into account that you criticise this video.

@passerby4507

Жыл бұрын

@@Peter_1986 I have no idea, it's been two years. I do have a pet peeve against people teaching things that are so wrong that students get screwed over.

amazing professor....loved the way he teaches and makes us understand the whole in a very simple way....truly awesome

Amazing. Thank you Professor Bender. You are an incredibly awesome teacher.

Carl Bender is a good lecturer, and explains the concepts and methodology of perturbation theory exceedingly well.

1:22 is that guy eating dinner from a plate with a fork and a knife? What a legend.

Thank you. This is an awesome series of lectures. I’m just jotting down a few notes here that I think are helpful. 17:43 The 𝜀^3 term should have an extra 10 a^3 from the 10 S^3 term. 23:17 The terms do not form a geometric progression. If they did, the solution would be rational - in this case, ⅘. He explains this later. 50:29 The symbol ≅ means “is isomorphic to” and is very precise. It does not mean “is approximately”.

@ShakespearHD

3 жыл бұрын

"It does not mean “is approximately”." I have been in courses where the lecturer used it to mean the above.

What i like about this lesson is that he explained very well how You start from what you know about the solutions to how the unperturbated problem can be solved..............., but making small corrections that approximate the effects of the perturbation under consideration......OMG>.i found this course truly inspiring...

This guy made the subject matter very palatable.

what a good teacher to make it easy to understand for a lay person!

Here I am a college dropout who lost the passion for learning in middle school watching advanced mathematics at 2:00 a.m. because I can't sleep and I do find this type of stuff generally interesting but I don't have the passion or the drive to really get into it

Wow, wish I had found this guy's lectures years ago.

brilliant lecturer explaining perturbation theory as simple as teaching high school algebra

27:52 The exact answer is calculated by the computer using Numerical Methods: Sausage.

Thankyou Mr bender a great series of lectures.

Words fail me to express how wonderful this is. Thank you Carl Bender!

This is so cool! Easy to follow, and very powerful techniques!

I am in covid19 quarantine, it's midnight, I was not looking for this topic and now I am enjoying this introduction to perturbation methods, and moreover, my mother tongue is Spanish.

When I first watched this video, I thought this guy's name sounded familiar. It took me a bit to realize that he wrote a paper that I cited for my undergrad honors thesis. Small world.

Awesome, I've been looking for a lecture like this on youtube for awhile now.

I also had a mathematical physics teacher who used the word trivial a lot. What he meant was that the solution was already known, and could be looked up.

A small mathematical quibble. It's true from number theory that the general quintic can't be solved exactly by radicals. However, the particular example used in this lecture, X^5+X=1, _can_ be solved exactly. I can't figure out how to enter the exact solution here, but you can see it by going over to Wolfram Alpha and entering X^5+X=1.

You need the 10s^3 term as well in the expansion of (1+S)^5 in order to get 10a^3e^3

H bar is not negligible as you and I know that h bar is equal to 1. Pure gold, one of the best jokes I have ever heard. Now to find someone to tell it too :(

Superb series! I wish I'd had him as my lecturer!

This is a gem of a course..thanks a ton for making it available!

1:23 my man having his breakfast in the class wtf

@chelskaf

3 жыл бұрын

LOOOOOOOOOOOL

@involvedobserver4984

3 жыл бұрын

OMG, that kinda cracked me up tho but wtf

@vikraal6974

3 жыл бұрын

WTF

@sajateacher

3 жыл бұрын

He's "digesting" the knowledge...

Thank you for uploading this -- I think the lecturer is brilliant!

Ok, I studied with this video. Now I am going to watch best Benteke's goals...

Amazing teacher!

I am amazed, I just ran into this video by pure chance, I can’t believe Prof. Bender is still teaching at Wash U . I graduated as undergrad in 1985 and I was in his class! He looks good!What a brilliant mind....

@iroulis

4 жыл бұрын

This lecture is at the Perimeter Institute in Canada, not at your almamater Washington U. Bender used slides made for his courses at Washington U. pitp.ca/training/perimeter-scholars-international/lectures/2011/2012-psi-lectures I'm still not sure what Perimeter is about except that it's funded by Blackberry's founder. There's usually a -point- to privately funded research.

@sharatpandey8067

Жыл бұрын

@@iroulis first of all thankyou so much for informing us about the name of the institute. can you please tell me how to find other parts of this series or other lectures by prof bender. I went to the site through the link provided by you but it showed page missing. Is there any other place where i can find these lectures??? THANKYOU SO MUCH IN ADVANCE.

@iroulis

Жыл бұрын

@@sharatpandey8067 This video is part of a Series: kzread.info/head/PLOFVFbzrQ49TNlDOxxCAjC7kbnorAR1MU

@sharatpandey8067

Жыл бұрын

@@iroulis thankyou so much again for the reply. Can I find other lectures by prof bender anywhere??

@iroulis

Жыл бұрын

@@sharatpandey8067 Wow. You're done with that 25 hr lecture series already?

he got me so pumped with that pade summation! can't wait to get there

For me this is a good class.. The basic concept of this idea is that, to make a complicated statements ("hard problems") in which it can exist in a "true" or "false" statements (i.e one or zero) isn't going to be easy. Its like, imagine on your right hand is the language spoken in between human beings in which we can understand each other well and execute the task given accordingly. For example, if you are reading this comment, and you have the consciousness and awareness that if i told you to get some drink you are able to take some drink that you like before asking me what drink that I like. On the other hand (which is in your left hand), lies the "hard problems" which is converting what is inside in your right hand (the language that human can understand) into only "one and zero information". Then, you move your left hand a bit to the right then, you get a statement like "yes or no" or "true or false". If then, you can think if true= 1; so 0 must be equals to false. Then you work your way from your left hand to the right hand until it maps. At least this is from my perception only.

@footballCartoon91

4 жыл бұрын

Its like trying to teach a computer to do certain task in the form of "1 and 0s informations". For example, take the first example that i mentioned before , that if you want to teach the computer to take a drink, it wouldnt know how to execute it or do it. It will constantly ask you questions until it gets into one and zero information. This is called definition. Imagine if a computer exist as a human being , with eyes, hands and legs, but with the brain of a computer. So when you tell him to take the drink. Then you need to define to him what is "take" and what is "drink". Then you tell him take means move your hands towards something on the table which has a cylinder shape (presumably the drink is in the form of canned soda and it is the only drink that are available on the table). Then, the computer will keep asking questions, what is "hand" ? Then you can define it the way you want until you define it into numbers for example the coordinate of hand is (-5,4,0) based on (x,y,z) axis, in relative from your navel position. Then you define fingers, coordinates of it, etc,etc. Then, finally hopefully, when you want it to execute the action of taking the drink can on the table you can say something like your thumb x+3 , the other fingers x-5, or something like that. Every small definitions in the end will execute as a function the finger function and so on.

Add up the series, make your calculation. Simple. Thanks for the upload, Zicheng!

his remarks re: divergent series are reminiscent of Oliver Heaviside's comments"aha! the series diverges! now we can do something useful with it!

I don’t think the part around 1:02 when he moved from f(x)+g(x)=h(x) (1) to analyzing the asymptotic behavior of ex^5+x=1 as e ->0 is very rigorous. If we take e -> 0 then we have to assume that ex^5 and x are functions of e. Thus, it seems that we need to fix x as constant so that ex^5 is only a function of e. But with each e in the real number, there’re only 5 x’s (precisely the roots of the eqn) that satisfying that ex^5+x=1. But a function must uniquely maps each e to one y=ex^5, so how do we choose the mapping between 5 possible choices for x’s?

I downloaded them directly from the PSI webpage. To be honest, the resolution of these videos are far from being HD, which technically refer to no less than 720p, and which perhaps they could have provided. However, it would then take me too much time to upload them onto KZread, since each HD would be too large in size. So I guess these 360p lectures are just proper for web use.

@sharatpandey8067

Жыл бұрын

can you please provide the link to the site or at least some other lead??? thank you so much

i could hang with 80% of this, but was completely lost for the first 5 minutes of the 2nd lecture. What mathematics should I study in order to get up to speed for this?

For full syllabus of cbse chemistry, may be referred below for value addition:- World of chemistry class 11 and 12.

I have had a long fascination with & personal mathematical struggle with the Lagrange Inversion Formula (LIF) and its numerous incarnations, combinatorial interpretations, generalizations to multiple variables & equations, since 1988. For one thing, the LIF gives one only ONE root of inverting y=g(x), where g(0)=0 and g'(0)!=0 to x=f(y) where f(0)=0. But, I want to find ALL the roots, which, in general, is countably infinitely many.

I'm not that interested in math (never have been), but I found this lecture fascinating, i couldn't stop watching it hah.

@kingfrozen4257

4 жыл бұрын

Cuz its not math its bullshit

@imbicyl6667

4 жыл бұрын

@@kingfrozen4257 true, hate all this like comments

@socialprod4605

3 жыл бұрын

Cool do something with it

@flamingaish

2 жыл бұрын

@@kingfrozen4257 how so?

@achyuththouta6957

2 жыл бұрын

@@kingfrozen4257 They aren't working on string theory noob. Quantum mechanics is as real as it can get. Unless of course you want to say that physical evidence is bullshit. But yeah string theory and such are just fantasies of the physicists.

This is good to learn... I want to learn more.. I like it..

17:49 the ε cubed term is not complete (correct). It lacks 10*s^3 part, which turns out to be 10a^3ε^3, thus: ...+ε^3(5c+20ab+10a^3)+...

@docu73

4 жыл бұрын

Without the 10a^3, c wouldn't be -1/125. The prof probably already knew the answer

18:58 “You can do this in Jr. High School, this is not hard.” _takes one look at board in deep confusion_

Being rigorous is not about being powerful or not, it’s about being right. Hand waving is useful for starting out but won’t get you far.

Each coefficient of epsilon goes to zero because epsilon, epsilon^2... are linearly independent.

@vsdktbkm5012

8 жыл бұрын

+AnkhArcRod This is more important a point than was made in the lecture. Good catch.

awesome! And proffesor is really good! love it

Very successful. I felt like appluading several times.

Wish I had a teacher like him!!

he explained that at 14:20, the solution for the inperturbed problem is the first term of the series. That's the whole idea of the theory, you start with the unperturbed term a0 and add to it the infinite perturbations. did you understand?

So whenever you have a variable you add a epsilon?

Absolutely outstanding lecture.

What's the formula for the coefficents of the perturbation series for x^5+epsilon x =1?

Great video. Thanks for the upload.

Nice idea with the unsolvable quintic, but that polynomial is not irreducible...the solution can be written as a combination of radicals - no need for perturbation, I can write down the exact solution.

i loved when he said, its like sausage you never trust until you know what they go through lol

@nylehaywood2471

4 жыл бұрын

Ya

Can anyone tell me why he is substituting 0 as first term in Taylor series when all other terms of this series are power of epsilon, and therfore epsilon to power 0 should be one, not 0.

What an excellent teacher.

He did the 0.755 = 1 engineering thing

In the expansion of the ANS(epsilon), he uses a0=1, and says it's trivial, but doesn't give any reason why he does so. Is anyone here aware of why it is so? Or maybe someone could give me a link where I could read the concerned theory. Thanks in advance!

I really did a good job teaching math. If the students have learned with the teacher, they will understand the offer.

I remember math. Just for a while while I’m trying on break.

34:56 actually, I do not know what happens when you raise x to the 5th power. Can anyone explain it to e please?

@grandpaobvious

4 жыл бұрын

If you raise (a + ib) to the fifth power you get a polynomial whose coefficients obey the binomial expansion theorem and correspond to entries in Pascal's Triangle. The roots of that polynomial are the fifth roots of 1.

brilliant lecturer, thanks for uploading

How did you download videos from the perimeter institute website? I'd like to know so I can watch them on a tablet computer. Thanks for the upload though m8

@dp121273

10 жыл бұрын

You can maybe use keepvid.com to download the videos.

Does anyone know a good textbook to pair with these lectures? Or if he's following a particular book?

Im so lucky to have found this wow!

@squarerootof2

3 жыл бұрын

Well, Hi there!

this is a great lecture , but i have a question , the prof said that we can neglect 1 , but if we did then we have cx^5 ~ -x (c ---> 0 ) but this contradict the definition of f(x)~g(x) (x-->x_o) , so , Can any one clarify this please ? , i use c for epislon

first term in the series is for epsilon=0 but, does not it correspond a0*0^0 where 0^0 is undefined?

@Pdjwvdugowqnxbgze

10 ай бұрын

0^0 is 1

Very knowledgeable lecture for me👍🏻👍🏻🙏🏻🙏🏻🙏🏻

This guy is fantastic!!

Great teacher....and notice, no notes in his hands. Wow...

Operators are at the heart of mathematical physics. Understand the actions and the inherent meanings of the operators and you’ll understand mathematical physics.

what would be the prerequisites of this course?

Did I miss sth or why does he neglect the 10*S^3 term which then also makes sense with the given answer -1/125... Otherwise I get +1/125 for the epsilon^3?

@sumsar01

7 жыл бұрын

It's an approximation. The larger the terms the less they add. Therefore larger terms don't really matter.

@whyka2116

6 жыл бұрын

You are right, he did miss a term for the 3rd order in epsilon.

@elitacilan891

5 жыл бұрын

even if he hadn't missed it, it would still be a mistake

How he got the graph for x^5+x=1

Thank you for sharing these :)

Doesnt it have to be ε^3(5c+20ab+10a^3) at 17:55?

@darlzchriz1320

5 жыл бұрын

Exactly!! otherwise, you don't get c=-1/125

I can't believe that they still teach it like this. I watched a documentary online about this. Totally disproves it all. So crazy!!!

@pedramshirdel6865

5 жыл бұрын

please name that documentary.