cod. 18975

Academic year 2011/12
3° year of course - Second semester
Academic discipline
Fisica matematica (MAT/07)
Formazione modellistico-applicativa
Type of training activity
72 hours
of face-to-face activities
9 credits
hub: PARMA
course unit
in - - -

Learning objectives

Introduction to mathematical modelling through differential equations


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Course unit content

Sturm Liouville problems. Eigenvalues and eigenfunctions.

Introduction to the Theory of Distributions.

Non-homogeneous boundary problems and Green's function.

Classification of linear second order PDE's. Cauchy problems.

First order quasi-linear PDEs. Method of characteristics.

Second order quasi-linear PDEs; Jacobi's method.
Weak solutions.

Dynamical Systems. Equilibria and Stability. Lyapunov Methods.

Linear and nonlinear models in Mechanics.

Mathematical models in population dynamics.

Van der Pol equation.

Bifurcation theory, Hopf theorem, limit cycles.

Poincarè-Bendixon theorem.

Lorenz model and chaos.

Discrete dynamical systems. Feigenbaum map.

Full programme

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G.Spiga, Problemi matematici della Fisica e dell'Ingegneria, PITAGORA,Bologna;

A.N.Tichonov, A.A.Samarskij, Equazioni della Fisica Matematica, MIR,Mosca;

F.G.Tricomi,Equazioni differenziali,EINAUDI, Torino;

F.G.Tricomi, Istituzioni di Analisi Superiore, CEDAM,Padova.

G.L. CARAFFINI, M. IORI, G. SPIGA, Proprietà elementari dei sistemi dinamici, Appunti per il corso di Meccanica Razionale, UNIVERSITA' DEGLI STUDI DI PARMA, a.a 1998-99;

G. BORGIOLI, Modelli Matematici di evoluzione ed equazioni differenziali, Quaderni di Matematica per le Scienze Applicate/2, CELID, TORINO, 1996;

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;

J.D. MURRAY, Mathematical Biology, SPRINGER-VERLAG, NEW YORK, 1989;

J. GUCKENHEIMER, P. HOLMES, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vectors Fields, SPRINGER-VERLAG, NEW YORK, 1983;

M. SQUASSINA, S. ZUCCHER, Introduzione all'analisi qualitativa delle equazioni differenziali ordinarie (ebook), APOGEO, 2008.

Teaching methods

Lectures and exercises

Assessment methods and criteria

Oral exam

Other information

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