|Re: HP 49G plus, DOMAIN and LIMITS|
Message #2 Posted by don wallace on 3 Oct 2005, 8:49 a.m.,
in response to message #1 by Slobodan Nikolic
It's 24 years ago for me since I dropped out of engineering (due to apathy and some stress, not "dumbness" ;-P) so forgive my being rusty. I am not saying I'm not dumb, just that I didn't drop out 'cause I am/was dumb ;-)
Valentin is the maths professor around here (literally,
I think...) so I am sure he will correct me where I am wrong.
His understanding of maths is really cool and he is really helpful.
I am not too worried about making a fool out of myself as the regulars here will know, , so I will say what little I remember
in general terms.
I'm not gonna tell you the nuts and bolts of it because I have forgotten, BUT:
You just need to do some BASIC READING ON "DOUBLE INTEGRATION".
It's quite involved maths, sort of.
I would google on that to start with. I think there are some equations of (very) different form which are f(x,y), being D.E.'s
That stuff is different, more involved, very useful to engineers, but really made my head spin (memory overload -> "fail" ME201).
Generally the function of one independent variable has a line or curve as a solution or a limit (they're different), but the function of TWO independent variables is a SURFACE in 3-space, so the limit could I think be a surface as well as a curve or line.
So your answer will be often be a non linear equation itself, not
neccessarily an easy solutin like a line or an axis.
There are simple cases, though:
Let's take Space and forget about the third dimension (z).
Say you have a (two dimensional) "gravity" function:
g = F(x,y) = SQRT(1/(x^2+y^2))
So we will make the third axis (z) plot our output or G force.
You would have as an example a black hole with an infinite gravity
force "at" the origin (0,0) with z (= g) = infinity. You can correctly say that the Z axis is a kind of limit, called a "pole".
That function also has a "ZERO" at infinity, the function decays to nearly zero at very large x and y. I visualize this as a circus tent.
Compare that with the simple hyperbolic function y = f(x) = 1/x, where the x and y axes are asymptotes, i.e. limits of the function.
I know I haven't explained much, but you could google on D.E.'s maybe (it's a bit o.t. given the functions you mentioned) and three dimensional calculus (?) Also google or Wiki on "mathematical poles and zeros".
The function DOMAIN is just the PLANE from x=minus infinity and y=minus infinity to x=plus infinity and y=plus infinity
(the "infinite plane")
I am sure Valentin will come to our rescue on this.
Edited: 3 Oct 2005, 8:56 a.m.