Originally Posted by Scott N Denver

I though int{e^(x^2) ] was more usually evaluated by squaring it, converting variables via r^2=x^2+y^2,evaluating using complex variables, and then taking the square root. Something involving a square root of Pi. Int[-inf,inf]e^x^2; Int[-inf,inf]e^x^2*e^y^2=[r^2=x^2+y^2] Int[r=0,r=inf, theta=0 to 2Pi]e^r^2, evaluate in complex variables [gamma function connection maybe???] to get that 2Pi* other constant and then take a square root
I don't know if that is the "normal" way of doing it, but we did use it when learning about winding numbers, etc.

Also, the method doesn't really solve the indefinite integral, if I am not mistaken.

I thought the integration by parts was a lot more straight-forward.

Originally Posted by Scott N Denver
So how much do you know about PDE's? Non-linear PDE's? Solution methods to PDE's other than SoV's [ie integral transforms, greens functions, numerical, method of characteristics]?

How much do you know about, say, fluid dynamics or continuum mechanics?

How much math and physics background do you have? I remember you posting in a theoretical physics thread, I should comment on that if I can find it again.
I do have some background in PDE's, very little with non-linear PDE's, I am quite familiar with Fourier and Laplace transforms, but that is it.

I know what Green's functions are but have very little experience because I deal with linear dynamics for the most part.

I am not familiar with the numerical method of characteristics.

I have undergraduate degrees in Discrete Mathematics and Computer Engineering, and a Master's in Electrical Engineering where a significant portion of my classes were on feedback systems and controls.

I take it you are an Aeronautical Engineer, or otherwise focused on turbulence and fluid dynamics.
Nevermind, I looked you up. "laser reseach specialist" and now material science/electrical engineer, huh?
To be honest, the people who come on Ventrilo and other places generally have rather simple math related frustrations. I may try to tackle some of the questions you pose, but it is clear we specialized in different areas of mathematics.

I generally have a preference for the more abstract froms of math: Groups, Rings, Vector Spaces, etc. some amount of Topology, and the study of limits. Combinatorics, Graph Theory, and Algorithm Design are my bread-n-butter type of mathematics. Statistics and Control Theory, are close seconds. I let the computers deal with PDE's...not my favorite branch of math to be sure. I do really like Numerical Analysis (though I don't have much experience in designing algorithms for PDE solvers).