Using the chain rule.
Hi Folks,
I am new to the method of characteristics for solving 1st order diff eqns. I am looking at an example in the book, which i do not quite follow..here goes
which is of the form
The characteristic equation is
which becomes
The bit I dont understand is making the transformation with
to the partial differential eqn as above with
How is this calculated?
Let me see if I can help here.
You have the PDE
If you introduce a change of coordinates (I'm using these instead of and )
then using the chain rule stated by HallsofIvy
then your PDE, after regrouping terms becomes
.
The idea is to choose and such that one of the two terms vanish. The method of characteristics gives you this. If you choose
Then substituting these into your original PDE gives an ODE (since there's no , the is treated as constant).