Expanding the fluxes can be an important part of constructing numerical solvers, for example by exploiting (approximate) solutions to the Riemann problem. In regions where the state vector y varies smoothly, the equations in conservative form can be put in quasilinear form: ∂ ∂ y ∂ ∂ t + A i ∂ ∂ y ∂ ∂ r i = 0 . where A i are called the flux Jacobians defined as the matrices : A i ( y ) = ∂ ∂ f i ( y ) ∂ ∂ y .