An overview of several mathematical models (of differential type) used in various fields of applied science (biology, physiology, industrial technologies) will be presented. Where necessary, the suitable mathematical prerequisites will be introduced. The precise content of the course (i.e. the specific models to be presented) may vary from year to year.
Notes downloadable from Moodle website through student's credentials
Learning Objectives
Becoming aware of the possible use of mathematics to simulate natural/industrial processes
Prerequisites
Only curricular courses of the first three years.
Teaching Methods
Frontal lessons
Type of Assessment
Oral exam
Course program
Preliminaries about ODEs, stability of solutions and bifurcation theory. Mathematical evidence of John's hypotesis about the existence of cycles in Petrarca's Rerum Vulgarium Fragmenta. Climate and paleoclimate models. Models for thermal conduction and convection. Thermal boundary layers. Mechanical boundary layer theory. Prandtl's hypothesis. Blasius equation for the drag force exerted on an airfoil. Neutralization of acid waste waters. Evolution of the pH of a solution in contact with a reactant. Deposition and growth of wax deposits in the flow of waxy crude oils. Complex fluids of industrial nature. Bingham fluids. Model for the growth of a forest. River basins modeling. Mathematical models for seismic phenomena.