  Let $V$ be a finite set. Let $\mathcal{K}$ be a simplicial complex with its
vertices in $V$. In this paper, we discuss some differential calculus on $V$.
We construct some generalized homology groups of $\mathcal{K}$ by using the
differential calculus on $V$. Moreover, we define a co-simplicial complex to be
the complement of a simplicial complex in the complete hypergraph on $V$. Let
$\mathcal{L}$ be a co-simplicial complex with its vertices in $V$. We construct
some generalized cohomology groups of $\mathcal{L}$ by using the differential
calculus on $V$.
