# Numerical Linear response

I have two lists: the first is {t,f[t]} and the second {t,l[t]}.

What i need is the first order expansion of f[t] in l[t]:

$f(t)\sim f(t)\vert_{l(0)}+\int_{0}^{t}d\tau\; l(\tau)\;\frac{\partial f(t)}{\partial l(\tau)}\big\vert_{l(0)}+\dots$

There is a way to do it?

• Have you considered replacing f[t] with f[InverseFunction[l][s]] and working from there? – Pillsy Apr 9 '17 at 18:20
• Might get better responses if actual lists are posted. – Daniel Lichtblau Apr 9 '17 at 20:04
• Daniel the lists are very long, how can i post them? – Kowalski Apr 9 '17 at 20:34
• Then try to find shorter lists, or come up with a representative subset of your actual lists. – J. M.'s discontentment Apr 9 '17 at 23:16