  In an abstract Hilbert space setting, we discuss many linear phenomena of
mathematical physics. The functional analytic framework presented is used to
address continuous dependence of the solution operators
$\mathcal{S}(\mathcal{M})$ of certain (linear partial differential) equations
on the coefficients $\mathcal{M}$. For this, we introduce a particular class of
coefficients $\mathcal{M}$ and study the (nonlinear) mapping
$\mathcal{M}\mapsto \mathcal{S}(\mathcal{M})$. We provide criteria that
guarantee the continuity of $\mathcal{S}(\cdot)$ under the norm, the strong,
and the weak operator topology. We exemplify our findings in non-autonomous
electro-magnetic theory, thermodynamics and acoustics.
