Thread: Transport Equation View Single Post
 P: 10 how do you use the change of variable: $\xi$ = x - ct on the PDE ut + c ux = 0 where u(t,x) = v(t,x-ct) = v(t,$\xi$) to get vt = 0 I am trying to follow the steps of Peter J. Olver in this document http://www.math.umn.edu/~olver/pd_/lnw.pdf starting on pg 4 but get stuck here...i think i am missing an important calculus concept but cannot figure out what. He says to use the chain rule but i cannot figure out how that helps. Any help GREATLY appreciated