How to solve PDE via directional derivatives

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  1. Dr Chris Tisdell
  2. pde
  3. directional derivative
  4. solution
  5. example
  6. math
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Комментарии
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Very clear, in fact all of your videos are! Thank you for the great content Chris!

andrewmcleod
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Thank you so much!

I have a question however - do the characteristic variables in the canonical form of a 2nd order PDE and the method of characteristics (seemingly mostly used for 1st order PDE?) both rely on using the dirrectional derrivative in a direction where the solution is constant? For 2nd order PDE i understand it so, that we use characteristic curves (because they arent lines anymore) and find the transformation of variables by this curves slope?

And secondly, how would we extend the method of characteristics for three variables? u(x, y, z)

SanderKivi
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Thank you so much for this video and all the help.

ndkhan
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What if the variables are mixed, and you get, for example, dt/dx = (x+t)/x² ? This is not a separable equation :/

bonbonpony
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Why can't the solution be f(x-2xt)?

akshayan