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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 analysismechanics of materialsmicromagneticsmodelling 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.

Introduction to numerical analysis and scientific computing with python

Syllabus 2023-2024

  • Basics on Scientific Computing
  • Vector spaces, vector norms, matrices, and matrix norms
  • Basic linear algebra: direct solution of linear systems
  • Not so basic linear algebra: iterative solution of linear systems
  • Polynomial interpolation
  • Interpolatory Quadrature rules
  • L2 projection / Least square approximation
  • Introduction to Finite Difference Methods
  • Introduction to Finite Element Methods

Python laboratories

Antonio Ambrosetti Medal Winners

Edition 2021

Fabio Pusateri (University of Toronto), for his contributions to the field of non linear partial differential equations;

Po-Lam Yung (Australian National University), for his work on the Sobolev spaces; 

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