Mathematical Modelling with Partial Differential Equations
Many phenomena taking place in physical and engineering systems can be described by means of systems of partial differential equations (PDEs). This is, e.g., the case of heat transfer phenomena, contaminant transport, fluid dynamics, mechanics of complex media (inhomogeneous materials, metamaterials, …), and wave propagation, just to name a few.
The module of “Mathematical Modelling with PDEs” aims to provide a first introduction to the mathematical tools to model physical phenomena and rigorously set the governing equations describing the systems under analysis.
By the end of the module, students are expected to be able to:
- describe basic physical phenomena using PDEs;
- provide intuitive interpretation of the mathematical operators appearing in a PDE;
- predict the physical behaviour of an engineering system in view of its mathematical description using PDEs.
A tentative list of topics include:
- Diffusion phenomena and heat transfer
- Convection-diffusion-reaction problems, pure convection, conservation laws
- Homogeneous and inhomogeneous materials, Darcy’s flow
- Continuum mechanics, elasticity, viscoelasticity
Fluid dynamics, viscous flows, inviscid flows, potential flous
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