ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables. Nature of problem: In many areas in the computational sciences first order partial derivatives for large and complex sets of equations are needed with machine precision accuracy. For example, any implicit or semi-implicit solver requires the computation of the Jacobian matrix, which contains the first derivatives with respect to the independent variables. ADF95 is a software module to facilitate the automatic computation of the first partial derivatives of any arbitrarily complex mathematical FORTRAN expression. The program exploits the sparsity inherited by many sets of equations thereby enabling faster computations compared to alternate differentiation tools. Solution method: A class is constructed which applies the chain rule of differentiation to any FORTRAN expression, to compute the first derivatives by forward differencing. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain when sparsity can be exploited. From a users point of view, only minimal changes to his/her original code are needed in order to compute the first derivatives of any expression in the code. (Source: