Suppose I have some function $f(t) = f(a(t),b(t),c(t))$ which I want to evaluate at all times $t$.
Now, I know that in general function $c(t)$ varies very quickly ($\dot{c}(t)$ is large) whilst the functions $a(t), b(t)$ vary slowly.
If we say the timescale of the variation in $c$ is $T_c$ and analogously for $a, b$,timescale $T_{ab}$ then,
$$ \epsilon = \frac{T_c}{T_{ab}} << 1$$
How can I approximate/expand $f(t)$ in terms of $\epsilon$, accounting for the different timescales over which the variations occur? Since $a(t), b(t)$ are approximately constant for a $\delta t$ it seems there should be a way to approximate for this. I have been reading about methods of multiple scales but this seems more geared towards solving ODEs?
Thanks