Laplace Equation

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES...
Instructor: Gilbert Strang
Laplace's partial differential equation describes temperature distribution inside a circle or a square or any plane region.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@OswaldChisala]

Without imputing disrespect on other schools, I can tell quite easily from this video that MIT has incredible professors. Thank you for open-sourcing your content, it is going a long way to educate the interested among us. My regards, Oswald.

[@markus-sagen]

Oswald Chisala couldnt Agree more!

[@videofountain]

I enjoy listening to Mr. Strang. I wish he would make a statement about the excellent teachers he has experienced. Perhaps he already has. I would venture to guess he has experienced excellent learning inside and outside of MIT. He and others are great inspiration.

[@1mol831]

I'm just watching because the professors in my university has forgotten to do lectures about these, they are still coming up on the test, gotta do them anyways.

[@owen7185]

Couldn't agree more

[@adoniasyoseph3290]

This man comes from another planet. You are the best teacher .

[@SnydeX9]

God bless this man and whoever made this available.

[@manugupta1958]

Today in 13min:16 second I learned something about Laplace equation, fourier series and it's application to PDE that I couldn't learn in a whole semester. Thank you MIT.

[@wl4131]

Indeed

[@QrioverseOfficial]

You are absolutely right Manu. Our Indian education system is fallible, I got the same experience, my college lecturers never taught me that I am learning here on KZbin from MIT and Stanford open lectures. They are offering the greatest services to mankind.

[@linranwu4940]

same here

[@sjn7220]

0:18 When he said I don’t have time, I thought this video was going to be over.

[@chargeeverywhere]

This is how teaching should be done! So clear for once!

[@akhildhatterwal3785]

I think teaching is done in this way everywhere

[@zakmatew]

@@akhildhatterwal3785 Not really

[@dangakong6304]

Thanks to MIT, am capturing lectures across the continent in one of the world best universities . Thank you MIT. Thank you USA.

[@tariqandrea398]

This absolutely floored me. It is dazzling in its clarity and simplicity. Unbelievable.

[@shakennotstired8392]

I have gained much better insight from these videos. Thanks, professor Strang and MIT. I am forever grateful.

[@michaelangaloe]

If someone asked me to describe a mathematician, It'd be Gilbert for sure.

[@shubhgupta6110]

Explaining concepts with such elegance.

[@georgesadler7830]

This video helps with the introduction to partial differential equations. Laplace equation is well known in partial differential equations. Dr. Strang explains the subject very well.

[@taewoonglee4894]

He verifies the quality of his teaching! Fantastic!

[@ankeshkumaryadav1056]

Are you form sir

[@taufeeqkhan2629]

@@ankeshkumaryadav1056 no I am human

[@juniorcyans2988]

I watched this video last semester and I couldn't really understand. Now I watched, I could follow completely! Thank Dr. Strang and MIT!

[@mohammedkhan4990]

Dr. strang is the best math professor period. Excellent lecture.

[@Prophetic_heirs]

after listening to prof gilbert in my final year of bachelors I am feeling like mind=blown.

[@MechanicalEI]

Sir, Great Video. The illustration and example of the Laplace Equation were perfectly supported by your explanation. Thanks for uploading!

[@turokg1578]

he's retired yet we're still learning from him

[@maudentable]

Gilbert Strang is the original kungfu master of mathematics. He is not a common textbook reader like the majority.

[@parianhatami]

I love you prof. Strang! I needed this concept & no context could help me as much as you did!

[@Keeper.AFOL5]

Thank you for making this available. It is a big help in understanding and explaining this section.

[@MaxvonHippel]

This is a superb lecture, thank you very much. - a pure maths major from Arizona

[@amberliu3154]

He is such a great professor!!!!! It makes so sense though his lecture.

[@brocktj4]

Dr. Strang truly is the GOAT.

[@gangadharjha1406]

All the college maths teachers should watch and learn from this video before teaching

[@DJ-yj1vg]

Bringing back the cool to maths, one lecture at a time.

[@saptarshipaul1928]

Every video starts with 'OKAY!!' :D

[@backlash67]

I love this man

[@Overlander2022]

Best professor indeed!

[@vaibhavshukla6926]

Thank you so much. I am so happy right now. Professor, you made this so EASY.

[@quantummath]

lovely teaching method, more power to you Prof. Strang

[@nicomcmahon2491]

So accessible!! I wish my profs lectured like this!

[@udehhappiness2574]

This is mind blowing Thank you Prof..

[@hsheng3577]

Thanks, Professor Gilbert Strang♥

[@selfi23]

Yes Sir , Your Videos was Really Helpful a Lot for 'Sky Wolves' students.... Thank You soooo Much❤❤❤❤

[@rudhisundar]

Love you oldie! God bless you!!

[@nandakumarcheiro]

Combined effect of the Laplace equation and applying boundary conditions of wave theory reflects in energy amplification of crazy polynomials of real part and imaginary becomes an exponential function from logarithmic incrementa forming an exponential jump and collapse between a cos theta wave and sine theta waves promoting unimaginable amplification promoting a Psunami effect as boundary condition by merging by symmetry Fourier series.

[@axelmeramas976]

you are a life saver professor , thank you

[@allandavis6116]

Great video - but ... it would be helpful to have a discussion of when a solution exists, e.g. for 2-d circles, and when it doesn't, e.g. irregular boundaries. Also, what if time is a variable? What real world problems have solutions, which don't,, etc.

[@coder1124]

Thank you MIT

[@atriagotler]

I was strugling with the laplacian and real valued functions. And now I suddenly know the basics up to fourier 😂

[@jupiter7795]

Careful, he starts going all "Final Solution" at 6:25.

[@hikmatullahpakhtoon3694]

Flawless explanation. Thank you professor.

[@vidushitripathi2671]

Great teacher... 🙏🏻 Huge respect to you sir...

[@musicislife665]

Congratulation Mr Gilbert Strand and thank you for your lesson.

[@CatsBirds2010]

What a GREAT teacher!

[@nandakumarcheiro]

This may give further information of repeated compression and expansion derivatives involved in Laplace equation assisting Fourier series seems to be more informative.

[@iam_sketch]

It was kind of satisfying when he changed the cordinate system form Cartesian to polar 😌

[@AbuSayed-er9vs]

Excellent video pro.Gilbert and very... thanks for this.

[@deday6525]

1:31 , why when u equal x, the second derivatives will be zero 0? thanks in advance

[@wrox2757]

Oh my! I didn't know this was Gilbert Strang.

[@Matchless_gift]

Big fan of prof. Strang, from india

[@nandakumarcheiro]

The lunar boundary temperature value at the top bottom and inside seems to be surprising by applying Laplace Equation.

[@WadBex]

Splendid! Keep up the fantastic work!

[@KanalDerGutenSache]

Does the infinite family of b's provide you with infinite amounts of honey?

[@Yume-x9v]

5x + 10y + 15z = x = y = z = zeros. factorization zeros equation. la place equation.

[@vaibhavshukla6926]

Sorry professor but did you mean to say 'steady-state' at 11:37. I think it won't be equilibrium but the temperature along that line will be zero.

[@robertmines5577]

Yes, steady state is the correct terminology here. Systems can exist at a thermodynamically non-equilibrium steady state. E.G. We can fix the boundary temperatures such that there is a permanent heat flux from one boundary to the other, but after infinitely long time, the entire domain asymptotically approaches a fixed temperature gradient. In short, Laplace's Equation can be viewed as the steady state of the equation dU/dt = d^2 U/dx^2 + d^2 U/dy^2 since the time derivative is set to 0.

[@gauthampracharya9592]

rip saar, I louve ur veedios

[@saurabhmyblogging]

Very nice lecture.

[@qas168888]

Love love love this one😂

[@omega7377]

Great teacher!

[@Crossfire9211]

Utterly amazing

[@PATHMINDER]

God bless you;Prof.

[@dominicj7977]

Psychologically, people generally find handsome young men talking about mathematics more attractive than fragile old professors. Had this video been done by Zach star or grand Sanderson, it would have won way more likes

[@pappk.962]

thank you, perfect and simple explanation

[@sehrishsaqlain4682]

are you student?

[@jaeimp]

The null space of the Laplacian operator... Thank you!

[@chrispinchirhulwire4923]

a great topic given by great a sir

[@اجملاغانيلاطفال]

انا أشاهد هذا فيدو من الجزائر

[@alimohammadigheidari2614]

Well done Professor.

[@not_amanullah]

This is helpful ❤️🤍

[@flaxenkj]

Thank you very much indeed.

[@therealrictuar]

whoa never thought of it that way

[@erick.gudino]

thank you this this very useful

[@not_amanullah]

Thanks ❤️🤍

[@iam_sketch]

Beautiful

[@finaltheorygames1781]

I like the elegance in the (x+iy)^n solution, but the infinite sums with cos and sin seem to get messy.

[@galas062]

how so?

[@galas062]

please explain us about the mess, how you are going to clean it up???? LOL :)

[@nandha0150]

Absolutely lovely.

[@algebra5766]

wow this is beautiful ...

[@truthtutorials2312]

The infinite me's is the solution to my consciousness.

[@davidkwon1872]

I can’t believe what I watch!!! So shocked!!,

[@dhanraaj]

concept building thankyou

[@devotionalhymns845]

Beautiful 😍

[@robertwilsoniii2048]

Why not parametrize the boundary in a constrained optimization problem? Or are these things equivalent?

[@jaihind3693]

Sir Please make a vedio on E.T Whittakers 1903 Decomposition of scalar potentials, its much related to laplace equations.

[@wagsman9999]

math is beautiful

[@lucasm4299]

The real or imaginary part of a holomorphic function is a solution to Laplace's Equation.

[@mushtaqdass7421]

,infinite likes sir

[@_chip]

this is just great

[@ahmedbaig7279]

I also want to know the name of this professor.But my question is that at what level he teaches this peculiar subject of applied mathematics?

[@mitocw]

The instructor is Gilbert Strang. He teaches at both the undergraduate and graduate levels (he's even made a special series for high school students). For more info on Gil, here is his bio page: www-math.mit.edu/~gs/

[@libinbabu288]

Studying in fisat mookanur.hope someone sees it in future

[@XiaosChannel]

hmm, since when theres videos specifically made for... well, online videos instead of lecture recordings?

[@ghostzart]

They've made these sorts of videos since the early 1970s. Search for "OCW Herb Gross" and prepare to be amazed by the intimacy (and weird, black chalk).

[@Gravitation3Beatles3]

Would you say this concept is hard to grasp for a high school student?

[@omega7377]

Nope, if he or she already knows about partial derivatives, polar coordinates and eulers formula.

[@lucasm4299]

Gravitation3Beatles3 Nope. I'm on the same boat and I also looked into Complex Numbers.

[@lazykid2677]

Can someone give me the links of all the courses taken by Gilbert Strang ?(without the linear algebra course)

[@mitocw]

A quick search on our site (ocw.mit.edu) shows these courses and materials (not including linear algebra): 2.087, 18.085, 18.086, RES.18-001, RES.18-005, RES.18-009

[@hollywoodundead1010]

Everyone here smart as fuck, while I came looking for laplaces box from The Gundam series...

[@vitthalpatil1974]

9:16 dont look so closer .....😂😂

[@leophysics]

Gilbert strang is like Dr strange

[@terryhuang6464]

fantastic

[@Griffatron3000]

he keeps winking at me

[@MohamedEmad-bq8hs]

Brilliant

[@RajanNarasimhan]

Wow!