First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MATHEMATICAL ENGINEERING
Course unit
DYNAMICAL SYSTEMS (MOD. B)
INP5070521, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2019/20
N0
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Degree course track MATHEMATICAL MODELLING FOR ENGINEERING AND SCIENCE [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination DYNAMICAL SYSTEMS (MOD. B)
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
Branch PADOVA

Lecturers
Teacher in charge MASSIMILIANO GUZZO MAT/07

Integrated course for this unit
Course unit code Course unit name Teacher in charge
INP5070520 MATHEMATICAL PHYSICS (C.I.) MASSIMILIANO GUZZO

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/07 Mathematical Physics 6.0

Course unit organization
Period Annual
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Practice 2.0 16 34.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 30/09/2019
End of activities 20/06/2020
Show course schedule 2019/20 Reg.2017 course timetable

Examination board
Examination board not defined

Syllabus

Common characteristics of the Integrated Course unit

Prerequisites: Basic courses in Mathematical Analysis, Linear Algebra, Geometry,
Analytic Mechanics (Newton's equation, conservative force fields, potential energy, Lagrangian Mechanics).
Target skills and knowledge: Objectives: Introduce the students to mathematical tools in continuum mechanics and dynamical systems.

Outcomes: a student who has met the objectives of the course will have a knowledge of :

• advanced topics in the mathematical description of continuous mechanics

• fundamentals of ODEs and dynamical systems, with special emphasis on applications
Examination methods: Final examination based on: Written and oral examinations
on both moduli CONTINUUM MECHANICS (MOD. A) and
DYNAMICAL SYSTEMS (MOD. B).

The final evaluation will be the weighted average of the evaluations obtained in the two moduli.
Assessment criteria: Critical knowledge of the course topics. Ability to present the studied material. Discussion of students' projects.

Specific characteristics of the Module

Course unit contents: 1) Ordinary differential equations: Cauchy theorem, phase-space flow, dependence on the initial conditions; linear equations; phase-portraits, first integrals; equilibrium points; linearizations, stable, center and unstable spaces.

2) Hamiltonian systems: Legendre transformation, Hamilton's equations, Poisson brackets, canonical transformations.

3) Integrable systems: elementary examples from population dynamics, from Mechanics and from Astronomy; integrability of Hamiltonian systems, Liouville-Arnold theorem, action-angle variables, examples.

4) Non-integrable Systems: discrete dynamical systems, Poincaré sections; bifurcations, elementary examples. Stable and Unstable manifols, homoclinic chaos; Lyapunov exponents, the forced pendulum and other examples; Center manifolds and partial hyperbolicity. The three body-problem, the Lagrange equilibria,
Lyapunov orbits, the tube manifolds.

5) Examples and Applications: analysis of three and four dimensional systems; the Lorenz equation, the three-body problem; examples from fluid dynamics, non autonomous dynamical systems, chaos indicators, Lagrangian Coherent Structures.
Planned learning activities and teaching methods: Classroom lectures and exercises. Lectures are given in English.
Additional notes about suggested reading: "Lecture notes in Dynamical Systems" by M. Guzzo available through the Moodle website of the course on the e-learning platform of the DICEA (https://elearning.unipd.it/dicea/).
Textbooks (and optional supplementary readings)
  • Massimiliano Guzzo, Lecture notes in Dynamical Systems. --: --, 2019. Available to regostered users through the Moodle website of the course on the e-learning platform of the DICEA (https://elearning.unipd.it/dicea/)

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex
  • Mathematica
  • Simulations in Fortran

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