Classification of PDEs into Elliptic, Hyperbolic and Parabolic

In this tutorial I will teach you how to classify Partial differential Equations (or PDE's for short) into the three categories. This is based on the number of real characteristics that the PDE has. The class of PDE has important consequences. We will also do two worked examples to ensure that you are following the theory. It's really very simple.
The technique is very simple and just involves applying the discriminant (think quadratic equation), B^2-4AC with the coefficients being determined by comparing with a reference equation.

[@AJ-et3vf]

Thank you very much for this comprehensive lecture. I learned a lot.

[@parvtrivedi2800]

Thanks a lot bro, Finally understood it. Idk if I am stupid or you are great teacher, but thanks anyways.

[@mohsenfazareh3384]

hello and thank you for this video the question I have is that what is the proof of such claim. how did we get the original rules of an elliptic or hyperbolic or ... equation?

[@mamtashakya4554]

classify the following PDEqs as elliptic, parabolic or hyperbolic -d^2/dx^2+d^2u/dy^2+d^2u/dz^2=1/c^2*d^2u/dt^2

[@thrivenipogu7521]

hyperbolic

[@strangeperson700]

If you use the form AC - (B^2) then a negative integer means that it's elliptic and not hyperbolic.

[@emo_nemo]

Does this (classification of pdes) come in handy if trying to solve numerical pde's through some automatic process ?

[@VaShthestampede2]

Yes. The handiness comes from the intuition about the expected behavior of the solution in case there are times when the automatic process(I'm assuming CFD software) doesn't return the solution that you expect.

[@dhruvinrathod69]

Hi educator, his helped me. Thank you.

[@이윤수-y1v]

Can the coefficient of delta y^2 be A and delta x^2 be B or does coefficient of x always has to be A? How about a pde with x and t which coefficient is which (A or B)?

[@timileyinaworinde48]

same reason why I'm here...lol.. did you get the answer?

[@cewinharhar7899]

Even after 7 years you saved me a lot of time reading badly writen scripts

[@puremaths2444]

Thnks sir and how do u solve it

[@VikingOlberg-NymoenOfNorway]

Great video man

[@nimrakhalid7211]

what about 3rd order and higher order pde??plzz reply

[@TheCompleteGuide1]

It is vastly more complex. If you search for The classification of third order PDE with respect to symmetry you will find one paper discussing it. 3rd order PDEs are not my area of expertise.

[@dphpl9973]

thank you!

[@Smartboy12]

Very very thanks sir

[@Rahulaakanksha]

Can anyone help me with this PDE U(x,x)+U(y,y) - U(z,z) =0 What is this type para/ecliptic/hyper?

[@gopalanjayashankar1125]

It's a hyperbolic PDE because the eigenvalues of the diffusion matrix are going to be 1, 1 and -1. So this means that this PDE has 1 -ve eigenvalue and n-1 +ve eigenvalue. Which makes this a 3D hyperbolic PDE. It's quite a different kind of classification technique but it's not so different if you look at it carefully. I hope I'm not wrong. If yes, please correct me :)

[@Aarti-ib8qq]

Thanks for the help really you explained it in a simple way

[@G7ALLWINDAVIDd]

Are yoU from TCE?

[@Aarti-ib8qq]

No

[@lobnasaeed]

thank you very much !!! that was really so helpful

[@DeepakYadav-ys7dg]

Thank you for the lecture, I lund a lot

[@samsunggadgets7340]

Thanks sir for your help❤❤❤❤

[@moatazmohamed2384]

Wow .. thx

[@joeyquiet4020]

thank you

[@antsnerd-8018]

you are amazing!!!!!!!

[@emenikecharles6235]

Thank you so much

[@nuhumusah795]

Really appreciated

[@SeppyDawg]

Thank you sir!

[@abinash.m]

Thanks alot

[@loisiamuge8977]

Thanks a lot

[@Nerroo09]

thx a lot :)

[@hymnmccoll4215]

this helped me, thanks a lot

[@SaadSaad-st1nk]

x is a real number so for x=0.75 hyperbolic not eliptic

[@starlight7499]

perfect thanks a lot .

[@anjud3433]

Tq sir

[@architsaini27]

Thanks!

[@adityasonker1504]

thank you