Lecture Notes

• Review Notes on Matrix Algebra.
  Notes for an undergraduate course on matrix algebra. Penn State 2025 (63 pages)

• Hyperbolic conservation laws: an illustrated tutorial.
  Notes for a summer course, Cetraro 2009 (81 pages).

• Viscosity solutions of Hamilton-Jacobi equations and optimal control problems. An illustrated tutorial. Original version: Trondheim, NTNU 2001. Revised: Shanghai Jiao Tong University, 2011 (64 pages).

• Noncooperative differential games.
  Notes for a summer course, Padova 2010 (81 pages).

• Lecture Notes on the Center Manifold Theorem
  S.I.S.S.A., 2003 (16 pages).

• Notes on the Boltzmann equation
  Lecture notes for a summer course, S.I.S.S.A. 2005 (28 pages).

• BV solutions to hyperbolic system by vanishing viscosity
  Lecture notes for a C.I.M.E. course, 2003 (77 pages).

• Symmetries and blow up patterns
  A short tutorial, S.I.S.S.A. 1999 (17 pages).

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Slides of tutorials

• Slides for an introductory course on control theory

  1 – Introduction

  2- Review of ODE Theory

  3 – Multifunctions, Selections, and Differential Inclusions

• A tutorial on hyperbolic systems of conservation laws in one space dimension

  I – Basic concepts

  II – The Cauchy problem

  III – Uniqueness, continuous dependence, and viscous approximations

• Conservation law models for traffic flow

• Dynamic blocking problems
  

• Controlling Lagrangian systems by active constraints

• An Introduction to Nonlinear Control Systems

• Control problems for traveling fronts and moving sets

  I – Optimal control of traveling profiles

  II – Control of moving sets – existence of optimal strategies

  III – Necessary conditions for optimality.

IV – Sufficient conditions for optimality. Problems with geographical constraints.