Applied Systems of 1st order PDEs with many independant variables?

[jasonRF]

Does anyone know of any books or online resources that do a good job discussing systems of linear 1st order PDEs with several (more than 2) independent variables? I am not a mathematician, but can handle graduate level classical physics with the associated applied math. Analytical and numerical approaches are both of interest.

Thanks!

Jason

 

[Student100]

Chapter 7 of Mathematics of Classical and Quantum Physics from Byron and Fuller might interest you (Green's function method of solving differential and partial differential equations). It probably isn't exactly/enough of what you're looking for, however, but it's like 10 bucks on Amazon and worth the read.

 

[jasonRF]

Thanks for the suggestion, but I am already comfortable with Green's functions at that level; likewise, I am familiar with characteristics for wave-like PDEs . I believe Byron and Fuller mainly tackle typical second order linear PDEs like the wave equation, Schrödinger's equation, etc. Based on the table of contents, I don't think Byron and Fuller contain much (if any) discussion of systems of first order equations. I am also familiar with characteristics for solving a single first order linear and nonlinear PDEs, and have looked at a couple of treatments of systems with two independent variables. I am just not skilled or confident enough to try to derive the method for greater than two independent variables. I am interested in learning how to tackle problems that have, say, 6 equations, 6 dependent variables and 4 independent variables (x,y,z,t).

thanks,

jason