ON DETERMINING IMPORTANT ASPECTS OF MATHEMATICAL MODELS: APPLICATION TO PROBLEMS IN PHYSICS AND CHEMISTRY.

Mathematical modelling must always deal with two general problems. First, the form, parameters or distributed functions in a mathematical model are often imprecisely known and their impact on desired objectives or observables is an important issue. Second, even when the components in a model are 'known' there always remains the fundamental questions concerning the importance and interrelationship between the various components of the system. The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. These general tools are generic in nature, but this paper will emphasize their application to problems arising in selected areas of physics and chemistry.