Laplace Equation
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- čas přidán 5. 05. 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
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
0:18 When he said I don’t have time, I thought this video was going to be over.
God bless this man and whoever made this available.
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 CZcams 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 .
If someone asked me to describe a mathematician, It'd be Gilbert for sure.
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.
I have gained much better insight from these videos. Thanks, professor Strang and MIT. I am forever grateful.
I love you prof. Strang! I needed this concept & no context could help me as much as you did!
Sir, Great Video. The illustration and example of the Laplace Equation were perfectly supported by your explanation. Thanks for uploading!
I love this man
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.
Thanks to MIT, am capturing lectures across the continent in one of the world best universities . Thank you MIT. Thank you USA.
He is such a great professor!!!!! It makes so sense though his lecture.
lovely teaching method, more power to you Prof. Strang
Every video starts with 'OKAY!!' :D
after listening to prof gilbert in my final year of bachelors I am feeling like mind=blown.
Dr. strang is the best math professor period. Excellent lecture.
This is a superb lecture, thank you very much. - a pure maths major from Arizona
Excellent video pro.Gilbert and very... thanks for this.
Congratulation Mr Gilbert Strand and thank you for your lesson.
Thank you so much. I am so happy right now. Professor, you made this so EASY.
Splendid! Keep up the fantastic work!
Flawless explanation. Thank you professor.
Love you oldie! God bless you!!
He verifies the quality of his teaching! Fantastic!
Are you form sir
@@ankeshkumaryadav1056 no I am human
Dr. Strang truly is the GOAT.
Great teacher... 🙏🏻 Huge respect to you sir...
you are a life saver professor , thank you
What a GREAT teacher!
So accessible!! I wish my profs lectured like this!
Thank you MIT
Bringing back the cool to maths, one lecture at a time.
Great teacher!
he's retired yet we're still learning from him
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.
Absolutely lovely.
whoa never thought of it that way
God bless you;Prof.
Well done Professor.
All the college maths teachers should watch and learn from this video before teaching
Utterly amazing
Oh my! I didn't know this was Gilbert Strang.
Very nice lecture.
Gilbert Strang is the original kungfu master of mathematics. He is not a common textbook reader like the majority.
this is just great
Beautiful
Yes Sir , Your Videos was Really Helpful a Lot for 'Sky Wolves' students.... Thank You soooo Much❤❤❤❤
Thank you very much indeed.
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.
Why not parametrize the boundary in a constrained optimization problem? Or are these things equivalent?
thank you, perfect and simple explanation
are you student?
a great topic given by great a sir
This may give further information of repeated compression and expansion derivatives involved in Laplace equation assisting Fourier series seems to be more informative.
thank you this this very useful
Love love love this one😂
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 this is beautiful ...
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!
1:31 , why when u equal x, the second derivatives will be zero 0?
thanks in advance
5x + 10y + 15z = x = y = z = zeros. factorization zeros equation. la place equation.
concept building thankyou
Careful, he starts going all "Final Solution" at 6:25.
fantastic
Sir Please make a vedio on E.T Whittakers 1903 Decomposition of scalar potentials, its much related to laplace equations.
Big fan of prof. Strang, from india
rip saar, I louve ur veedios
Beautiful 😍
Brilliant
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
Does the infinite family of b's provide you with infinite amounts of honey?
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).
Wow!
I can’t believe what I watch!!! So shocked!!,
The real or imaginary part of a holomorphic function is a solution to Laplace's Equation.
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 :)
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.
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/
미쳤따리 미쳤따 교수님의 명강에 balls를 탁 치고 갑니다!
Studying in fisat mookanur.hope someone sees it in future
I like u sir
,infinite likes sir
math is beautiful
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 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
i like to see it as the groundwater level in a confined aquifer with steady flow
Everyone here smart as fuck, while I came looking for laplaces box from The Gundam series...
انا أشاهد هذا فيدو من الجزائر
Gilbert strang is like Dr strange
he keeps winking at me
do this ,,,,,evalute the lablacian 7x^2/x^2+y^2+z^2
9:16 dont look so closer .....😂😂
RITA YULIANA FIGRID
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.