First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SC01111314, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination PHYSICAL-MATHEMATICAL MODELS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge MARCO FAVRETTI MAT/07

Course unit code Course unit name Teacher in charge Degree course code

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

Course unit organization
Period First semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
8 Modelli Fisico-Matematici - a.a. 2019/2020 01/10/2019 30/09/2020 FAVRETTI MARCO (Presidente)
CARDIN FRANCO (Membro Effettivo)

Prerequisites: Pr.: Calculus, elementary algebra and geometry, and a first course in Mathematical Physics.
Target skills and knowledge: Critical knowledge of the course topics. Ability to present the studied material as a written dissertation. Ability to use different sources (books,lecture notes, handsout) to study.
Examination methods: Written exam
Assessment criteria: Assessment of the ability of the student to give a written exposition of the content of a couple of the course topics in a given time (1h30')
Course unit contents: 1. Kinematics of Continuous systems, spatial and material representation.
2. Mass conservation principle. Balance and Conservation laws
3. Cauchy tetrahedron theorem.
4. Principle of virtual works in continuum mechanics. Balance law and the first
cardinal equation.
5. Material description of the stress tensor.Work-Energy Theorem. Constitutive
equations and the principle of material indifference.
6. Ideal elastic fluids. Navier-Stokes, Vorticity.
7. Hagen-Poiseuille flow, plane motion of Navier-Stokes fluids, Bernoulli Theorem.
8. Elementary Meteorology: Cyclones and Anticyclones.
9. Variational formulation of classical field theories: hyper-elasticity and linear
10. Principles of thermodynamics. Legendre transformation and thermodynamic
potentials. First principle of thermodynamics for continuum systems. Balance
laws and the first principle. The second principle in the Clausius-Duhem
formulation. Balance laws and the second principle. Theorem of Clausius-
Duhem. Thermoelastic materials.
11. Wave propagation. The method of characteristics: linear and quasi-linear
theories. Singularities. Nonlinear theory and the Hamilton-Jacobi equation.
Wave propagation in systems of conservation laws. Weak discontinuities,
Hugoniot-Hadamard. Sound speed. High frequency asymptotic waves. Shock
waves. Rankine-Hugoniot.
12. Fourier series and applications.
Planned learning activities and teaching methods: lectures and tutorials.
use of Moodle and One Note software
Additional notes about suggested reading: See the book:
F. Cardin & M. Favretti, Modelli Fisico Matematici, CLEUP 2014 (2^ edizione)
Lecture notes of the course (in englishi) available on Moodle
Textbooks (and optional supplementary readings)

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

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Latex