Marco Paggi (IMT Lucca)

Theory and Numerics of Ordinary and Partial Differential Equations

The first lesson of the course will provide a primer on complex variables. Using this mathematical formalism, the focus of the remaining first part of the course will be to introduce linear ordinary and linear partial differential equations, and the "cheap" methods to solve them using Fourier and Laplace transforms. The ordinary and partial differential equations will be placed into a context of applied mathematics (e.g. classic deterministic and stochastic systems) saving the theoretical approach for advanced lectures.

Funding and Management of Research and Intellectual Property (long seminar without exam)

This long seminar aims at providing an overview on the management of intellectual property rights (copyright transfer agreements; open access; patents, etc.). Funding opportunities for PhD students, post-docs, and researchers are also presented (scholarships by the Alexander von Humboldt Foundation; initiatives by the Deutscher Akademischer Austausch Dienst; scholarships offered by the Royal Society in UK; bilateral Italy-France exchange programmes; Fulbright scholarships; Marie Curie actions; grants for researchers provided by the European Research Council).

Numerical Methods for the Solution of Partial Differential Equations

The course introduces numerical methods for the approximate solution of initial and boundary value problems governed by linear partial differential equations (PDEs) ubiquitous in physics, engineering, and quantitative finance. The fundamentals of the finite difference method and of the finite element method are introduced step-by-step in reference to exemplary model problems related to heat conduction, linear elasticity, and pricing of stock options in finance. Notions on numerical differentiation, numerical integration, interpolation, and time integration schemes are provided.

Micromechanics

The course covers the fundamentals on modelling heterogeneous materials with periodic, quasi-periodic or non-ordered microstructures. Metamaterials, auxetic materials, chiral and anti-chiral microstructures belong to this class and their design and optimization requires a deep knowledge of their mechanical behaviour.

Computational Contact and Fracture Mechanics

This course provides an overview on the theories of contact and fracture mechanics relevant for a wide range of disciplines ranging from materials science to engineering. Introducing their theoretical foundations, the physical aspects of the resulting nonlinearities induced by such phenomena are emphasized. Numerical methods (FEM, BEM) for their approximate solution are also presented together with a series of applications to real case studies.

Advanced Topics of Computational Mechanics

The course is organized as a set of seminars and lectures delivered by IMT Professors and by invited recognized international experts. It covers advanced topics of computational mechanics.

Funding and Management of Research and Intellectual Property (long seminar without exam)

The long seminar aims at providing an overview on the management of intellectual property rights (copyright transfer agreements, open access, patents, etc.). Funding opportunities for PhD students, post-docs, and researchers are also presented (scholarships by the Alexander von Humboldt Foundation; initiatives by the Deutscher Akademischer Austausch Dienst; scholarships offered by the Royal Society in UK; bilateral Italy-France exchange programmes; Fulbright scholarships; Marie Curie actions; grants for researchers provided by the European Research Council).

Micromechanics

The course covers the fundamentals on modelling heterogeneous materials with periodic, quasi-periodic or non-ordered microstructures. Metamaterials, auxetic materials, chiral and anti-chiral microstructures belong to this class and their design and optimization requires a deep knowledge of their mechanical behaviour.

Computational Contact and Fracture Mechanics

This course provides an overview on the theories of contact and fracture mechanics relevant for a wide range of disciplines ranging from materials science to engineering. Introducing their theoretical foundations, the physical aspects of the resulting nonlinearities induced by such phenomena are emphasized. Numerical methods (FEM, BEM) for their approximate solution are also presented together with a series of applications to real case studies.

Advanced Topics of Computational Mechanics

The course is organized as a set of seminars and lectures delivered by IMT Professors and by invited recognized international experts. It covers advanced topics of computational mechanics.