# Jacobian physical meaning [duplicate]

Possible Duplicate:
What is Jacobian Matrix?

Is there any physical intuition for the Jacobian?

I understand that it is the matrix of partial derivatives and how to construct it. What I want to know is

• what's the use of it? Application wise
• is there a nice intuitive explanation for it? I mean regarding its significance and otherwise

## marked as duplicate by Rahul, Sasha, user31373, Dylan Moreland, Zev ChonolesJul 6 '12 at 1:07

For $f:\mathbb R^n\to\mathbb R^m$, a fixed $x \in \mathbb R^n$, we have $$f(x+h) = f(x) + J(x)h + o(|h|) \qquad\text{for }h\in\mathbb R^m, h\to 0$$ provided that the various partial derivatives exist and behave sufficiently nicely.