Laplace Equation
ฝัง
- เผยแพร่เมื่อ 5 พ.ค. 2016
- 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-18-009F15
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
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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.
Oswald Chisala couldnt Agree more!
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.
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.
Couldn't agree more
God bless this man and whoever made this available.
0:18 When he said I don’t have time, I thought this video was going to be over.
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.
Indeed
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 TH-cam from MIT and Stanford open lectures. They are offering the greatest services to mankind.
same here
This man comes from another planet. You are the best teacher .
This is how teaching should be done! So clear for once!
I think teaching is done in this way everywhere
@@akhildhatterwal3785 Not really
Explaining concepts with such elegance.
Sir, Great Video. The illustration and example of the Laplace Equation were perfectly supported by your explanation. Thanks for uploading!
I have gained much better insight from these videos. Thanks, professor Strang and MIT. I am forever grateful.
If someone asked me to describe a mathematician, It'd be Gilbert for sure.
lovely teaching method, more power to you Prof. Strang
He is such a great professor!!!!! It makes so sense though his lecture.
Excellent video pro.Gilbert and very... thanks for this.
I love you prof. Strang! I needed this concept & no context could help me as much as you did!
He verifies the quality of his teaching! Fantastic!
Are you form sir
@@ankeshkumaryadav1056 no I am human
Dr. strang is the best math professor period. Excellent lecture.
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.
This is a superb lecture, thank you very much. - a pure maths major from Arizona
Congratulation Mr Gilbert Strand and thank you for your lesson.
Flawless explanation. Thank you professor.
Splendid! Keep up the fantastic work!
I love this man
Great teacher... 🙏🏻 Huge respect to you sir...
Thank you so much. I am so happy right now. Professor, you made this so EASY.
after listening to prof gilbert in my final year of bachelors I am feeling like mind=blown.
you are a life saver professor , thank you
Thanks to MIT, am capturing lectures across the continent in one of the world best universities . Thank you MIT. Thank you USA.
What a GREAT teacher!
Great teacher!
So accessible!! I wish my profs lectured like this!
Every video starts with 'OKAY!!' :D
Bringing back the cool to maths, one lecture at a time.
Absolutely lovely.
Love you oldie! God bless you!!
thank you, perfect and simple explanation
are you student?
Well done Professor.
Dr. Strang truly is the GOAT.
whoa never thought of it that way
Very nice lecture.
a great topic given by great a sir
thank you this this very useful
Thank you MIT
God bless you;Prof.
Utterly amazing
this is just great
Yes Sir , Your Videos was Really Helpful a Lot for 'Sky Wolves' students.... Thank You soooo Much❤❤❤❤
Thank you very much indeed.
wow this is beautiful ...
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.
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.
Beautiful
Love love love this one😂
Oh my! I didn't know this was Gilbert Strang.
All the college maths teachers should watch and learn from this video before teaching
Why not parametrize the boundary in a constrained optimization problem? Or are these things equivalent?
concept building thankyou
he's retired yet we're still learning from him
5x + 10y + 15z = x = y = z = zeros. factorization zeros equation. la place equation.
Sir Please make a vedio on E.T Whittakers 1903 Decomposition of scalar potentials, its much related to laplace equations.
This may give further information of repeated compression and expansion derivatives involved in Laplace equation assisting Fourier series seems to be more informative.
fantastic
Big fan of prof. Strang, from india
rip saar, I louve ur veedios
1:31 , why when u equal x, the second derivatives will be zero 0?
thanks in advance
Brilliant
Beautiful 😍
Can someone give me the links of all the courses taken by Gilbert Strang ?(without the linear algebra course)
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
The lunar boundary temperature value at the top bottom and inside seems to be surprising by applying Laplace Equation.
The null space of the Laplacian operator... Thank you!
Gilbert Strang is the original kungfu master of mathematics. He is not a common textbook reader like the majority.
hmm, since when theres videos specifically made for... well, online videos instead of lecture recordings?
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).
I was strugling with the laplacian and real valued functions. And now I suddenly know the basics up to fourier 😂
It was kind of satisfying when he changed the cordinate system form Cartesian to polar 😌
Wow!
Careful, he starts going all "Final Solution" at 6:25.
Does the infinite family of b's provide you with infinite amounts of honey?
I like the elegance in the (x+iy)^n solution, but the infinite sums with cos and sin seem to get messy.
how so?
please explain us about the mess, how you are going to clean it up???? LOL :)
I can’t believe what I watch!!! So shocked!!,
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?
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/
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.
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.
Would you say this concept is hard to grasp for a high school student?
Nope, if he or she already knows about partial derivatives, polar coordinates and eulers formula.
Gravitation3Beatles3
Nope. I'm on the same boat and I also looked into Complex Numbers.
The real or imaginary part of a holomorphic function is a solution to Laplace's Equation.
,infinite likes sir
I like u sir
미쳤따리 미쳤따 교수님의 명강에 balls를 탁 치고 갑니다!
انا أشاهد هذا فيدو من الجزائر
Studying in fisat mookanur.hope someone sees it in future
i like to see it as the groundwater level in a confined aquifer with steady flow
do this ,,,,,evalute the lablacian 7x^2/x^2+y^2+z^2
math is beautiful
The infinite me's is the solution to my consciousness.
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
9:16 dont look so closer .....😂😂
Everyone here smart as fuck, while I came looking for laplaces box from The Gundam series...
Gilbert strang is like Dr strange
RITA YULIANA FIGRID
he keeps winking at me
This professor has the exact same clothes as my professor in differential equations.
Coincidence? I think not.
Let's Start A Business I was thinking the same for one of my partial equation professors, identical outfit!
Excellent video pro.Gilbert and very... thanks for this.