Differential Equations in the Curriculum
P. Miidla (University of Tartu)
The model by general definition is an analog of the object under consideration which replaces this object in our cognition. Continuous modelling (CM) means applying a model to continuous object or data. The main tools of CM are differential equations (DE). For the curriculum of mathematics in industry the courses where the possibilities of using DE to construct models are teached, are in great importance. On these courses students will understand the essence and nature of DE models and outputs of modelling. Computer, the most modern tool, is a very good teacher of DE models bridgeing numerical and continuous solutions, because it is reasonable to offer e-courses in the education of industrial mathematicians. Web makes it possible to increase synergy and efficiency of corresponding resources.
Main modelling stages which might to be covered by a curriculum are: identification and formulation of problem; choice of mathematical methods for use in different stages; final elaboration of the model, included to make clear computer resource needed; application of model, simulations and numerical experiments; interpretation of results.
For real DE modelling the first and last stages are quite complicated and contains enough heuristics, also presence of other specialists. Success here can be supported by enough examples, case studies and training possibilities in education. Other stages are theoretical and in education these would be teached and trained. In my presentation this will be shown more precisely. Some realisations are discussed.