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
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.
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
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?
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
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
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.
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