Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Numerical solution of PDEs

Room 128: 8/3, 14/3, 21/3, 5/4, 12/4, 19/4

Room 139: 15/3, 22/3

Room 133: 4/4, 11/4, 18/4, 25/4, 2/5, 9/5, 10/5, 16/5, 17/5

Room 134: 3/5

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Advanced analysis - A

Rooms:

Lectures from 26/09 to 24/10 are in room 005

Lectures from 26/10 to 19/12 are in room 133

Program of the course Advanced Analysis –A (2023-2024)

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Concentration problems for nonlocal energies

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Limit analysis of variational problems

The aim of this course is an introduction to the analysis of variational problems depending on a parameter. Such problems appear in different ways, and the parameter may be constitutive, a geometric inhomogeneity scale, or a coefficient of a perturbative term. It may have different effects favoring oscillations, concentration, topological singularities, dimension-reduction, etc., some times a combination of these.

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Topics in continuum mechanics

This is a 60-hours introductory course on continuum mechanics and its applications. The aim is to provide first year students with a solid understanding of the fundamental principles of the subject.

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Problems of Moving Sets

The course is divided into two parts, each related to the control of expanding sets either with a barrier or by removing a fixed amount of area per unit time.