A friend of mine recently explained to me a little bit about using Lie groups and symmetries to obtain solutions of PDEs. I was interested and wanted to learn a bit more about it. He's been using Olver's "Applications of Lie Groups to Differential Equations" but I found it a bit out of my reach.
I've taken a PDE course that followed Fritz John's "Partial Differential Equations" pretty closely, and a basic differential geometry course (curves and surfaces). I also have limited knowledge of group theory, but he said he didn't have any when he started learning the theory.
So my question is: should I study PDEs or group theory a bit more before attempting to tackle Olver's book, or should I try an easier text first?
Thanks for the help.
Best Answer
I found a solid background in PDE, together with some physics, to be a useful entry point to Olver's nice book. There's the 'Lectures on Partial Differential Equations' by V.I.Arnold which is fun to read alongside, if not before. Any solid book on mathematical methods in classical mechanics and quantum mechanics should prove useful as well. Finally, I agree with Deane- the most efficient path is to start reading the book, and learn the material you need as you proceed.