Classification of PDEs into Elliptic, Hyperbolic and Parabolic

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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.

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

AJ-etvf

Hi educator, his helped me. Thank you.

dhruvinrathod

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

parvtrivedi

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

strangeperson

classify the following PDEqs as elliptic, parabolic or hyperbolic

mamtashakya

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)?

이윤수-yv

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

cewinharhar

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

emo_nemo

Thank you for the lecture, I lund a lot

DeepakYadav-ysdg

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?

mohsenfazareh

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

Aarti-ibqq

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

lobnasaeed

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

nimrakhalid

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

Rahulaakanksha

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

SaadSaad-stnk

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