Can someone explain to me what equilibrium points are when dealing with diff EQs and slope fields and such?

 

Nathan

Say you have a function [math]f(x)[/math]. Then the equilibrium points are those points x such that [math]f'(x) = 0[/math].

 

For example, [math]f(x) = x^2 + 3x + 2 \Rightarrow f'(x) = 2x + 3[/math]

 

So just the one equilibrium point at x = -3/2.

thanks, dude. that helped a lot.

 

Nathan

No problem

I am not sure about this. just following on from daves answer

 

If your working in fuctions of more variables [math]f(x_{1},x_{2},...,x_{n})[/math] then the eq point is the point [math](x_{1},x_{2},...,x_{n})[/math] where

 

[math]f_{x_1}=0,f_{x_2}=0,...,f_{x_n}=0[/math]

so u just get n simultaneous eq. for n variables.

A better way is to treat the variables x1 to xn as a column vector and get the derivative as a n cross 1 matrice then set it equal to the null matrice of same dimensions. Though in essence the same, it provides for a cleaner solution more appealing to the eye.

In practice, you're never going to be asked to do this. At most, you'll be asked for a 3D equilibrium point. For larger dimensions, it's better to use something like Mathematica to solve the equations for you.

In practice, you're never going to be asked to do this. At most, you'll be asked for a 3D equilibrium point. For larger dimensions, it's better to use something like Mathematica to solve the equations for you.

 

Speaking of Mathematica, I remember you praising it alot over SFN.

 

What's a better program overall: Mathematica or Matlab?

hey you fogot about MAPLE

Doesn't MATLAB use the Maple engine?

 

(Mathematica will pwn Matlab any day of the week )