CompuServe Messages

Hi, Eric&Audrey! Thanks for the "SXP ineerworkings" file. But let me point out to some "weak" points you've made: 1. You are not 100% correct stating that (F(x+dx,y,z)-F(x,y,z))/dx is an estimate of partial derivative only at (x+dx/2,y,z). It IS a valid estimate of dF/dx at (x,y,z) and for that matter at any point from (x,y,z) to (x+dx,y,z). 2. Second and MORE IMPORTANT: you are critisizing YG for using (F(x+dx) – F(x))/dx instead of F(x+dx/2, x-dx/2). Yes, it would be better estimate of partial derivative, but you keep forgetting what it is used for. YG restores implicit surface by Euler method: they need all partial derivatives AND some STARTING point. Then they have to move from this point only in one direction: what I mean is: x-dx/2 is UNAVAILABLE at the starting point! And one more note: there is a notion of false precision: you may evaluate partial derivative better, but what the benefit if after that you will numerically integrate using trapezoids method – you will lose all gained precision right away. >>I mean, you probably had calc in grade school, right? 😉 >>OK, OK, so maybe middle school…. I had calc in the top mathematical boarding school = appr. 8th grade (because I jumped through couple of school years, it is even 6th grade, not 8th). But I still like it. 🙂 Alex, Video International