Lectures on Linear Systems Theory

Lectures on Algebraic System Theory: Linear Systems Over Rings

Lectures Notes on: Math 6410: Ordinary Differential Equations

2 Linear Equations 14 2.1 Matrix Exponentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Normal Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Non-Autonomous Linear Equations . . . . . . . . . . . . . . . . . . . . . 19 2.4 Inhomogeneous Linear Equations . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Stability and Boundedness . . . . . . ....

Notes on the Dynamics of Linear Operators

These are notes for a series of lectures that illustrate how continuous linear transformations of infinite dimensional topological vector spaces can have interesting dynamical properties, the study of which forges new links between the theories of dynamical systems, linear operators, and analytic functions.

Two Lectures on Max-plus Algebra

Exotic semirings such as the “(max,+) semiring” (R ∪ {−∞},max,+), or the “tropical semiring” (N ∪ {+∞},min,+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, Hamilton-Jacobi theory; asymptotic analysis...

Une introduction à l’analyse algébrique constructive et à ses applications

This text is an extension of lectures notes I prepared for les Journées Nationales de Calcul Formel held at the CIRM, Luminy (France) on May 3-7, 2010. The main purpose of these lectures was to introduce the French community of symbolic computation to the constructive approach to algebraic analysis and particularly to algebraic D-modules, its applications to mathematical systems theory and its ...