Let $M$ and $N$ be smooth manifolds. There is a description of the strong Whitney topology on $\mathcal{C}^{\infty}(M,N)$ in terms of partial derivative in charts (using locally finite sets of charts in the domain and the codomain) and there is a description coming from the strong topology on $\mathcal{C}(M, J^\infty(M,N))$.

However, if $N=\mathbb{R}$ I think there must be an easier description of the topology of $\mathcal{C}^{\infty}(M,\mathbb{R})$ without using charts or jets, but just vector fields instead.

Does anyone know if such a description appears anywhere in the literature?