Diff EQ help

[Treadstone]

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

 

Nathan

[Dave]

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.

[Treadstone]

thanks, dude. that helped a lot.

 

Nathan

[Dave]

No problem

[bloodhound]

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.

[pulkit]

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.

[Dave]

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.

[NSX]

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?

[bloodhound]

hey you fogot about MAPLE

[Dave]

Doesn't MATLAB use the Maple engine?

 

(Mathematica will pwn Matlab any day of the week )