MODELS OF PHYSICAL MATHEMATICS
Learning outcomes of the course unit
Aim of the course is to present some differential models in Applied Sciences together with the mathematical methods of investigation.
Course contents summary
Dynamical systems: definitions, properties. Stability. Liapunov’s methods for stability of equilibrium solutions of systems of ordinary differential equations.
Linear models: from harmonic oscillator to resonance phenomena.
Linear and non linear model in mechanics, chemistry, biology, economical sciences.
An introduction to bifurcations: stationary bifurcations, Hopf bifurcations and limit cycles.
Poincarè-Bendixson Theorem for planar systems.
Partial differential equations: equations of Mathematical Physics. Heat equation, Laplace’s equation, D'Alembert's equation.
R. RIGANTI, Biforcazioni e Caos nei modelli matematici delle Scienze applicate, LEVROTTO & BELLA TORINO, 2000;
M.W HIRSCH, S. SMALE, Differential Equations, Dynamical Systems and Linear Algebra, ACADEMIC PRESS, NEW YORK, 1974.