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

MODELS OF PHYSICAL MATHEMATICS
cod. 18975

Academic year 2009/10
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’s methods for stability of equilibrium solutions of systems of ordinary differential equations. <br />
Linear models: from harmonic oscillator to resonance phenomena. <br />
Linear and non linear model in mechanics, chemistry, biology, economical sciences. <br />
An introduction to bifurcations: stationary bifurcations, Hopf bifurcations and limit cycles. <br />
Poincarè-Bendixson Theorem for planar systems. <br />
Partial differential equations: equations of Mathematical Physics. Heat equation, Laplace’s equation, D'Alembert's equation. <br />

Full programme

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Bibliography

<p>R. RIGANTI, Biforcazioni e Caos nei modelli matematici delle Scienze applicate, LEVROTTO & BELLA TORINO, 2000; <br />
<br />
M.W HIRSCH, S. SMALE, Differential Equations, Dynamical Systems and Linear Algebra, ACADEMIC PRESS, NEW YORK, 1974. </p>
<p>E. PAGANI, S. SALSA, Analisi Matematica 2, Masson editore</p>

Teaching methods

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Assessment methods and criteria

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Other information

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