2006-12-19 23:51:15 · 6 answers · asked by leigh w 1 in Science & Mathematics ➔ Mathematics
If you have an autonomous equation dx/dy = f(x), where f is nonlinear, then you linearize by expanding f as a Taylor series but truncating after the linear term. So yes, it's about differentiating f (not integrating, which is what you'd like to do to solve the equation to get the solution x as a function of y).
As with a Taylor series, you linearize about a particular value of x, call it p. This is crucial! You linearize ***about a particular point***. Typically you linearize about a fixed point (a.k.a. steady state or equilibrium point) of the system, i.e. where f(p) = 0 for some value(s) x=p.
i.e. f(p+x) = f(p) + f'(p)*x + higher order terms
so you get dy/dx = f(p) + f'(p) * x as your linearized system. In classes and textbooks you're often given that the equilibrium has been moved to p=0 for extra simplicity (it can always be translated to be at the origin without loss of generality) so that f(p)=0, and so you might see dy/dx = f'(p) * x written instead.
To be a little more general, if x is in R^n (i.e. is a vector), then you take the Jacobian of f: R^n -> R^n instead of the usual 1D derivative.
It's not as simple as just ignoring the nonlinear terms, especially if there are only nonlinear terms in your differential equation to begin with!
2006-12-21 18:26:43 · answer #1 · answered by Ippus Dippus 2 · 0⤊ 0⤋
Linearize Differential Equation
2016-11-16 20:36:33 · answer #2 · answered by Anonymous · 0⤊ 0⤋
This Site Might Help You.
RE:
How do you linearize a non linear differential equation?
2015-08-11 21:54:52 · answer #3 · answered by Rhea 1 · 0⤊ 0⤋
Ignore the non-linear terms and make an approximation. Or reduce it to several 'piecewise approximations', each of which can be treated as a linear equation.
Doug
2006-12-19 23:55:25 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋
In some cases introducing a parameter will help, solve for the parameter and hopefully get it down to a linear equation.
2006-12-20 01:14:00 · answer #5 · answered by yasiru89 6 · 0⤊ 0⤋
You could call that business statistics for economic purposes. Another name is Econometrics. An example would be analyzing sales per department, like at Wal-mart, and determining if a particular department should remain open or be consumed by another department that has a higher average rate of return. If you're interested in an economics MA or PhD i'd take math/econ but otherwise i'd skip it.
2016-03-14 10:32:12 · answer #6 · answered by Anonymous · 0⤊ 0⤋
u gotta integrate it not differntiate.
2006-12-19 23:53:59 · answer #7 · answered by tonima 4 · 0⤊ 1⤋