The increasing use of artificial neural networks and other connectionist systems in engineering, and the advantages obtained from that use, motivated the development of an approach wherein a single or multiple input feedforward artificial neural network with piecewise linear hard limit transfer functions could be directly "constructed." By viewing the network as a function approximator, algebraic constraint equations for the input and bias weights were derived which transformed the mathematical character of the net into one amenable to rigorous analysis without changing the architecture. Further application of the method of weighted residuals allowed direct solution for the output weights without any training. Ordinary and partial differential equations were solved using this method and the resulting accuracy and reliability verified. Further extension of this research will hopefully lead to the creation of adaptive engineering systems able to incorporate both governing equations and experimental data.