Equally important, as these direct simulations, is the solution of inverse problem, through which one recovers the physical properties and the state of the simulated system based on observed data. The study of these inverse problems constitutes important research areas for all the aforementioned applications where Filtering Techniques, Theory of Control and Optimization are used. 2.5 Mathematical Economics Mathematical Economics has sprung from the outgrowth of Applied Mathematics in economic models and aims at the construction of a rigorous and unified Economic Theory. The Theory of General Equilibrium. Differential Equations and Dynamical Systems furnish mathematical economists with basic tools for process analysis or economic dynamics.
Probability is fundamental to the study of economic models where risk and uncertainly are present.
Allied to Mathematical Economics is Econometrics, which is the study of the properties of data generation processes, techniques of economic data analysis and methods of test evaluation of economic hypotheses. In this field the tools developed by Statistics are of central importance important. 2.6 Differential Geometry Differential Geometry deals with the application of the methods of local and global Analysis to geometric problems. The language and the models of Differential Geometry have found applications in related areas such as Relativity and Celestial Mechanics. Given its interdisciplinary nature, Differential Geometry has shown a great vitality and has extended in various directions which display a considerable amount of research nowadays.