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 straightforward.
I do have some background in PDE's, very little with nonlinear 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 breadnbutter 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).
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05302009, 01:40 AM #11
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
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