Method of characteristics and PDE

[@raultrigo]

Thanks a lot, as engineers in the industry we forget a lot of the mathematics underlying the solution of these PDEs, and we find a lot in the industry...this is a real push for science application...thank you

[@il2xbox]

This video was very useful. I was having trouble with a quasilinear PDE problem in my textbook, so I watched all of your videos covering the method of characteristics and quasilinear PDEs. The amazing thing is, the problem you did in this video is EXACTLY the same equation I was having trouble with! The Cauchy data was different but the equation itself was the same. So thank you very much for this video, now I should be able to solve more problems like this. And if I have trouble with other types of problems in the future I'll definitely watch your videos on those as well.

[@ankit87gupta123]

Thanks Chris for making my life easier. Your videos are really helpful. Really appreciate your efforts.

[@jameyatesmauriat6116]

Simple and beautiful explanation, I wish that all the videos like this so that even if I don't know how the equations come from, then at least I can memorize some small details

Thank for the lessons Chris! Much appreciated!!

[@tomlynd8836]

Your lectures are great but I am wondering how can I come up with factors that would simplify my problem. I mean is there a deterministic approach to this problem or I will have to go with heuristics?

[@yunsongliu8610]

im just getting confused about why C(1) is determined by C(2)? can we use the funtion of C(2) equals to some function of C(1)?

[@DrChrisTisdell]

Yes, you can write it that way if you prefer.

[@kkc60]

thank you very much, but i have one question.. shouldn't the 4th line ( when finding C1) be negative 1/u because we took it to the other side?

[@ianwong6534]

In the previous line, the RHS needed to be multiplied by -1 to get the denominators the same in order to cancel them out, thus taking 1/u to the other side would make it positive

[@loveislam9174]

Thank you, I pray that God gives you all the best

[@ciudadesoscuras]

how x(dx/dt) turns into 1/2 d/dt(x^2)?

[@DrChrisTisdell]

It's the chain rule or the product rule for differentiation applied to the 1/2 d/dt(x^2). 👍

[@DrChrisTisdell]

Hi - see if you can prove the identity that I work from in the top right hand corner of the screen at 04:12. Once you have that then you'll feel more comfortable with the method that I use.

[@jbergamp]

Id be nice if you can show how you verify that the solution is the correct one, its more challenging than solving it. Bytheway...what is suppose to be 'u' in the corfficient?thanks

[@ayeshasirkazi7345]

Can u give how to solve Lagrange's DE....and it's geometric interpretation....and what if denominator is zero in any of the ratio u r taking for finding the characteristics curve.....plz sir it's urgent

[@prakharshekharparthasarthi7741]

where is recording camera placed

[@ruchisaini4629]

Chup

[@rinchuimy1292]

It helps.. thank you

[@RakeshKumar-zw2ey]

Thanks sir

[@taniapq91]

thanks

[@ankurc]

awesome