The course presents a series of mathematical models for industrial, biological and environmental applications. The course presents a grounding in the techniques of modeling, including approximation techniques and scaling, and exploring a range of continuum models arising from a variety of disciplines. All models are based on PDE and ODE, for which we look for analytical and numerical solutions.
The course aims at providing an overview on mathematical modeling of real-world problems. Looking at problems of practical interest it is shown how to build up a mathematical model that may furnish qualitative and quantitative informations on the phenomenon in object. In particular, it is shown hoe to formulate in mathematical terms a problem on the basis of constitutive laws and balance relations. The problems are formulated at macroscopic level based on classical continuum mechanics. Scaling techniques that allow for major simplifications are introduced and analytical and semi-analytical are sought. In some cases it is proven how to obtain quantitative informations by means of numerical simulations.
Prerequisites
Basic concepts of calculus and linear algebra. Vectorial and tensorial calculus. Basic notions on partial differential equations and ordinary differential equations. Basic knowledge of continuum mechanics.
Teaching Methods
Lessons with numerical examples (simulations) with the aid of mathematical software.
Further information
Attendance of lectures, practice and lab:
Not mandatory
Teaching tools:
None
Office hours:
Type of Assessment
Oral examination based on questions on the models presented in the course.
Course program
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.