Method of Characteristics - Partial Differential Equations | Lecture 39

In this lecture we show that the wave equation can be decomposed into two first-order linear partial differential equations. We further solve these resulting first-order PDEs using the method of characteristics. It is shown that the solutions simply propagate the initial condition left or right in space as time goes on. We then generalize the method to nonlinear systems where now the speed of translation can be nonlinear and the initial profile can be expanded, contracted, or both in time and space.
Lectures series on differential equations: • Welcome - Ordinary Dif...
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[@jldai95]

Very succinct lecture!

[@uhigreuho]

What a nice video and clear way of explaining this topic. I'm looking forward to more of this series for sure

[@drneuropharmacology2496]

Jason you've clearly put so much into this, thank you for your efforts teaching. Would you consider doing an applied series on neuronal dynamics using "Dynamical systems in neuroscience" by izhikevich 2005?

[@shinyshih2000]

That book is a classic!

[@hrkalita159]

one of the best yt channel but yet very under rated .

[@jasonbramburger]

Thanks for your support!