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Università degli Studi di Parma Università degli Studi di Parma
University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

MODELS OF PHYSICAL MATHEMATICS
cod. 18975

Academic year 2010/11
1° year of course - Second semester
Professor
Academic discipline
Fisica matematica (MAT/07)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
48 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

Aim of the course is to present some differential models in Applied Sciences together with the mathematical methods of investigation.

Prerequisites

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Course unit content

Dynamical systems: definitions, properties. Stability. Liapunov 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 equation, D'Alembert equation.

Full programme

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Bibliography

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.
E. PAGANI, S. SALSA, Analisi Matematica 2, Masson editore

Teaching methods

Lectures and computer simulations

Assessment methods and criteria

Oral examination

Other information

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