Lecture 34 - Partial Differential Equations

[shaivalinikashyap]

no sound??????

[xBl00dBrothersX]

Great video. Everything was super easy and clear.

[sathishamrita]

This one is really good!!! Probably if the prof shares his codes in some websites, people can practise simultaneously!!!

[boredomtube]

Dear Prof. Sunil Kuma, in my corner shop you have helped me with your differential equations, i made record profit last quarter, I have no idea how as i don't really understand your videos.

[spodhore]

does anyone know what language he is programming in? 

[sathishamrita]

@spodhore C

[misium]

Excellent lecture. Helped me to understand PDEs a lot.

[hfcell]

Thanks to Prof. Sunil Kumar for your lucid explanation & thanks to NPTEL & MHRD, India for producing this video. I'm now subscribing to your channel.

[ura239]

COOL VIDEO ......I LEARNED PDE'S EXTENSIVELY ON MY OWN THOUGH!!!!.....I THINK THE BEST INSTRUCTOR YOU CAN HAVE IS YOURSELF....... MATHEMATICS IS ABSOLUTE BEAUTY!!!!.

[shaneymane15]

@ura239 what resources did you use to teach yourself?

[ura239]

@shaneymane15 :WELL THE MAIN SOURCES WERE GOOD BOOKS ON PDE'S .AT LEAST 2 OR 3 BOOKS AT A TIME AS WELL AS A PASSION FOR THE SUBJECT AND TIME.....ARE YOU AN ENGINEERING STUDENT?.

[shaneymane15]

@ura239 I'm a math major, actually.

[ura239]

@shaneymane15 ;THAT'S AWESOME!., I WISH MORE PEOPLE WERE INTERESTED IN MATHEMATICS INSTEAD OF TRYING TO GET IT OUT OF THE WAY.

[UnitedPebbles]

Oh yeah? the computer can solve it already. There are Maple and Mathematica to find the answer and it is cheaper than hiring a mathematician.

[tafwolf]

why did he add one when he turned it into the indices form?

Im just a high school senior trying to learn this as my passion

[guillermo9400]

You're a genius! thank you very much

[edisonlly19881105]

i will having my numerical method exam in two days time. from zero, u make me fully understanding PDE.. God bless you!! and thanks so much =)

[groundzerobuild]

why this video has to be hindhu based?

[hereinweymouth]

@groundzerobuild Did you not notice this was from Indian Institute of Technology? You can watch or not watch. It's your choice.

[dravidr007]

@groundzerobuild its for hindus only u dumb prick!! fuck of if u dont want to learn

[sehrglanzvoll]

@groundzerobuild Hindu is a religion not a race or language.

[AAAnkit100]

thank you sir..............

[cimoalpacino]

there is a mistake when time is around 28:00, for point (2,0)...the right equation should be:

u(3,0)+u(1,0)+u(2,1)+u(2,1)-4u­(2,0)=0

The mistake is at the second element: u(1,2) should be u(1,0)

[Eddyah]

Error at the 3 minute mark regarding the classification of PDEs...The discriminant formula is not the same as for solving a quadratic. I think this should be fixed as it's misleading :)

I hope i'm not the first to recognise this otherwise you all need to go back to class haha :P

[longjonsilver45]

@Eddyah I think you are forgetting the conditions on which those formula are defined. Some texts use A*Uxx + 2BUxy + C*Uyy, others forgo the 2B term as simply B; that is to say A*Uxx + BUxy + C*Uyy. In the first case b^2-AC is what classifies the equation. In the later it is b^2-4*AC. At 2:08 it clearly shows which style is being utilized.

[elizachen1]

i thought IIT stands for the technion so i ran into this

and i am glad i did good lecture

[thepoet82]

Longest intro evar!

[psur47]

@thepoet82 ever!

[jmchristian63]

Calm down you troll.

[GayaniDeepika]

Thank you very...very...much ..sir,

[amirtaaki]

this tutorial was fantastic explanation. thanks

[fraude13]

nice work

[fizXgirl314]

DAMN!!!! SHUT YOUR IGNORANT ASSES UP... this man is a genius!

[earthwormjim3D]

fuck you all, just listen to the fucking lecture and shut the fuck up

[whoopssinead]

what the hell are all the raciest coments about? this lecture really helped me understand p.d.e.s, and i thenk p.b.sunil kumar for putting it up. top man, thanks for the help

[Baalsaack]

What are all these comments about?!

[duck24x]

Joseph Stalin was a far better man than you, and he polluted the entire Asian continent.

You fucking subhuman shits know that you lost the GW debate (not that there ever was one) decades ago. You guys are a hoot to look at as you squirm and writhe.

You never even made it past the 1st grade.

[duck24x]

You fucking subhuman terrorist.

[duck24x]

You fucking asshole big-government-loving War-on-Drugs-loving anti-freedom capitalist shit. I long for the day you will eat my excrement and be honored for the privilege. Raising my taxes and destroying the United States.

[duck24x]

I cheer the day you will be locked away in prison for life and raped by a North Korean guard.

[duck24x]

Go join your lover boys, the Muslim theocrats, just like all you Reaganite-religionist-free-mar­keteers who dealt arms with Iran and Iraq back in the 1980s (when they were at war with each other, no less!)

[duck24x]

You're just another anti-drug anti-porn terrorist who wants to take away personal freedoms and raise our costs - through extremist court costs - because you vote only for Republicrats and Demopubs.

You're an unpatriotic America-hating coward who damages the United States by your resistance to fight for the War Against Global Warming.

[duck24x]

Yeah - right. Fighting against selfish tyrants - whether they are dictators or corporations - to give MORE money to the poor, to free people from prison over TRIVIAL things - such as THEIR right to put what drugs or porn into THEIR bodies, or to have abortions - and to put cowardly selfish subhuman trash like Reagan, Bush, Clinton in prison for raising OUR taxes and giving them to the rich and for MURDERING and TORTURING trillions of animals - yeah, that "really" "causes" holocausts.

[duck24x]

Anti-GW activists and environmentalists have the guts to stand up for what they believe and to fight for a truly hard cause. Not like you cowardly bitchy corporate crybabies, who whine and cry at merely some perceived, trivial tax increase that hasn't been passed yet.

Meanwhile, you extreme terrorist corporatists cost me and courageous environmentalists (Greenpeace, Peta) tax dollars with your trilions in corporate welfare. You owe us.

[duck24x]

And you Holocaust-denying GW-denying wacko rightwing religionists are the cause for all the starvation, murder, death, enslavement and imprisonment in the world.

[duck24x]

Ultraconservative religionist muslims (I am a proud patriotic atheist) have denied GW for years, just like they have bashed Darwin and the fact of Evolution.

Thanks to you and your kind, even braindead ultraconservative Bin Laden now knows GW is real and serious. Thanks to you and your ultra-conservative religion-kiss-ass friends, Bin Laden will make more attacks on the US.

[duck24x]

Polluting far more than your fair share of the environment and interfering with national and international security - yes, even the US's National Security Agency knows that GW is a serious threat - and those of us who do what we can do stop it - is not free speech. GW is not speech: it is a real physical action.

So much for your "math" and math-modelling (with PDEs) abilities.

I would love to wipe my ass with you.

[OkazakiMasamune]

haha, look at all these comments for a video about PDEs! havent been on youtube in a while, good to see all the usual suspects are here voicing their opinions that they're afraid to say away from the safety of the internet. i know half of ye are only doing it to stir up the rest of them but seriously, get a life!

[duck24x]

But Partial Differential Equations fully support the FACT that subhumans like you are polluting the world and raising the global average termperature and destroying OUR planet for the REST of us.

[duck24x]

And I'd make marxism the law in the United States. And I'd prevent you from voting and from any political power, just like the two rightwing conservative fascist Democrat and Republican parties do to ALL other parties - not just the Communist Party USA and Socialist.

I would laugh if somebody raped your kids. Oh wait. That couldn't happen. There's no way you could reproduce voluntarily!

There's nothing about Partial Differential Equations to support your twisted views.

[duck24x]

HA! Typical anti-environmentalist wacko. You admit it: you hate democracy. You would use criminal violent force to keep Socialists and Communists in America from having the same political rights as the Republicrats. One party dictatorship. So then YOU should die and be tortured for

YOUR stupid cause.

FYI: rightwing nationalist Stalin and China and North Korea - not true socialists - LOVE your anti-environmentalism. These so-called "communist" states OPPOSED all environmental laws.

[duck24x]

You preach a lot of hot air against North Korea. But what are you capitalists doing about it? Are you willing to risk your lives to blow up prisons in North Korea or China to free prisoners?

North Korea and China are not communist, no matter what they claim. They are anti-worker, because they suck up to overseas corporations.

You should go live in North Korea if you hate democracy so. Socialists and true communist parties in USA are illegally discriminated against, denied ballot access.

[duck24x]

That was merely a name to deceive DUMBFUCKS like YOU into believing Hitler was "liberal". Hitler MURDERED 20 million of the COMMUNIST RED ARMY, 9 million Socialist and Communist political prisoners in his own country.

Hitler outlawed WORKERS' UNIONS. Read a book. Get an education, you worthless shithead.

[duck24x]

Socialists and Marxists never hurt anyone. Get your facts straight. Only extreme nationalists hurt people with laws against private matters that are nobody else's business. Those who were arrested for disobeying Socialist economic laws were guilty of crimes. They deserved to be punished.

So you advocate blowing up and killing socialist governments just because you disagree with them?

You're a terrorist.

You're just an extreme historical revisionist: Hitler was the most anti-socialist.

[duck24x]

Yes, I did meet Freeman. At a bookstore lecture in Princeton, NJ in 1998. Just because he's one of MANY of hundreds of scientists who work in quantum mechanics means that he has personally worked on the calculations of GW, any more than he can perform heart surgery.

Freeman hasn't put all the variables together to work on systems. Sure, he can may be an expert on a few particles acting in isolation.

And you're a child molestor, because you wouldn' be ruining children's future like you are.

[duck24x]

About your BULLSHIT in the other post about who clogs up YouTube accounts: GW-denialists = evolution-denialists win the gold medal for clogging up forums with worthless posts that have nothing of value to say. I count 15 (fifteen, since you can't count) posts by you on this forum alone.

Go watch the movie 11Hour. Stephen Hawking (physicist) is one of the many interviewees who knows AGW is real.

[duck24x]

THAT is PRECIOUS! You admit that ODEs are not very lucid to you. YOU'RE not lucid at all. Someone who can't do simple ODEs thinks they are the world "expert" on anthropogenic GW? HBO - you are a world-class ass and laughingstock. I would LOVE to see you humiliate yourself in front of the UN with your so-called ideas on climate.

Name ONE REAL scientist who claims that "changing the heat capacity of the atomosphere" is the PRIMARY mechanism for GW.

[duck24x]

I've met Dyson in person. He is an armchair philosopher. He's not doing the HARD WORK that the Greens, Greenpeace, the IPCC and other environmentalists do.

You've obviously got some fucking easy do-nothing stress-free job that destroys society and justice. Probably cop or prison guard.

FYI: I've got a PhD & an MS in Mathematics and a BChE (Bachelor of Chemical Engineering) and an AS in Biotechnology. And I've published in peer-reviewed math journals.

[duck24x]

You are a fucking subhuman piece of fanatic shit that never did a day of work in your life.

If you want to attack anyone, attack the massive tax-wasting corporate welfarists who give infinite amounts of money to the industrial-military elite. You drink at the Kool-Aid that they do anything for me.

WTF do they do for me? Will they blow up courthouses and prison to secure my freedom? The ACLU and Greens & Socialists fight for YOUR and my freedom more than big government.

[duck24x]

NASA & IPCC have shown the math a thousand times over. They don't have to waste their time and money proving anything more to big-corporate-welfare supporters like you.

Only Greens and Socialists are real Americans.

[duck24x]

Alex Jones has completely discredited the AGW-denialist with his New World Order paranoia.

Until you SHOW US THE MATH - not just verablize bullshit philosophies - like NASA and IPCC have - stop wasting everyone's time here and clogging up. You and the AGW-denialists have no free speech rights on other people's YT forums (I don't either, yet I don't clog up their forums with the same tired old comments). AGW-denialists should be banned for clogging up forums.

[duck24x]

What a dumb thing to say. No, I never said that. Everything is politics: how big we allow corporations to grow, whether we outlaw murder - all laws are the result of politics. So, you're saying there's no science in forensics, because it's politics that determines who gets to kill and why (e.g. GW Bush going free for murder).

Consequences, such as GW, are determined by science.

You and the AGW nutjobs are just Holocaust deniers who believe the moon landings were faked.

[duck24x]

It's not about the CO2's heat capacity. It's about humans crossing the line from a stable system to an unstable one by increasing the level CO2, which lowers the ratio of heat which radiates back out to space over that which is absorbed.

The AGW deniers = Holocaust deniers = Alex Jones worshippers. At least Alex Jones is courageous on 911 Truth. But the AGW denialists distort his views on GW even more than Jones does the original facts on GW.

[duck24x]

You're the one who is brainwashed and full of rhetoric and parrot back only political agendas of the oil companies.

So, have YOU put ALL the variables that the IPCC and NASA have into computers and crunched all the numbers?

Only after you do that should you be given any right to talk.

FYI: you can tell morons instantly in the GW "debate" when they drag up Al Gore's name, as if that single name "disproves" the fact of AGW.

[duck24x]

To the poster who thinks the heat equation "disproves" anthropogenic global warming (AGW): not only are you dead wrong, but the heat equation and every other law of physics and science known to humans proves AGW is a serious threat to the world.

[Mattprole]

Very neat hand writing skills on the board. Impressive.

[cwxzeng]

are u actually learning anything? PDE requires some strong math foundations..

[lordivoll]

gracias men me salvo de un parcial tesisimo ke tenia too bn

[banlat18]

Excellent Explaination and Accent is acceptable.

[574r54i13r]

Fuckin Rubbish.

[hignia]

great explaination

[cmslewis]

it all makes so much sense now!

[alksprem]

BRILLIANT EXPLANATION.

[darkscv]

I speak french and I understood everything he said. Yes this guy has an accent but it is not that bad...

[blkscreen15]

if you can't understand his accent, it you with the problem buddy. how about you go learn fuckin' english. and plus, who has accent and who doesn't is all relative.

[dacianr]

@blkscreen15 lol

[morza05]

@blkscreen15 Well, i would say he has a pretty good accent. It is 100% understandable.

[jholdaw2]

90% of the people watching this video cant understand you beacuse of your accent. You should slow down and work on your english pronunciation before you try to teach this course in english.

[VerraStrngNUCF]

90 % of the people watching this video should go to class instead of trying to learn online. This lecture is a privaledge, also whether the people watching it dont understand it is irrelevant. It is posted for students from an Indian university, I doubt they are in youre 90 %. Its not like he's trying to give you a nice alternative to not attending youre class or looking at the topic a different way, this is a posted lecture for a different class. Its nice we get to see it right.

[redliquid33]

Verra, No one ever said that they were not going to class. I'm an engineering student here in the U.S. Does that mean that i should not watch these videos. Even if i were not a student, should i not watch these videos. Its called "freedom," you can do what ever you want within whats tolerable. Watching these videos is way better than just someone playing video games and getting into trouble.

[VerraStrngNUCF]

I agree, but actually my post was in response to someone who complained about how the lecturer cant speak english and '90% of the people watching this cant understand him', so as to those people who complain about posted lecturers I was suggesting that if he has a problem with watching video's from someone else's class that he should find some other way to learn the material as opposed to complaining about the accent of someone who took the time to make this available.

[cwxzeng]

im watching this cuz i didnt go to my class lol......

[Nanumir]

good job thanks

[illusion422]

If the boundary conditions in the Laplace Equation is homogeneous... why not just seek a solution of the form: U(x,y) = X(x)Y(y) and replacing that in the Laplace Equation instead of using the definition of partial derivatives like you did.

If the boundary conditions are not homogeneous, you can always use a substitution with chain rule to make it homogeneous and again seek a solution of the form : U(x,y) = X(x)Y(y)

[doctorpatil007]

You have explained it well, except In the first example (Heat transfer) before the end the step where you convert the equation to del format, you multiplied the equation by dx/dy which does get ride of dx or delta x before the = sign. Can you please explain

[hamsterpoop]

He divided both sides of the equation by: dx*dy

The first term loses the dy on the top and only has the dx at the bottom.

The second term loses the dx on the top and only keeps the dy at the bottom.

The right side stays 0.

Then he notices that the limit as dx tends to 0 makes the first term the definition of the first partial derivative with respect to x.

The same thing goes for the second term but with respect to y.

Was that what you were asking or did I totally miss the point?

[pollardrho06]

Unclear!