First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
PHYSICAL-MATHEMATICAL MODELS
SC01111314, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2017/18
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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 http://matematica.scienze.unipd.it/2017/laurea
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
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

Lecturers
Teacher in charge FRANCO CARDIN MAT/07

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
INP5070522 CONTINUUM MECHANICS (MOD. A) FRANCO CARDIN IN2191

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

Mode of delivery (when and how)
Period First semester
Year 3rd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Syllabus
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. Discussion of the student project.
Examination methods: Written.
Assessment criteria: Assessment of learning theoretical and practical notions on the course.
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
elasticity.
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
Additional notes about suggested reading: See the book:
F. Cardin & M. Favretti, Modelli Fisico Matematici, CLEUP 2014 (2^ edizione)
Textbooks (and optional supplementary readings)
  • F. Cardin & M. Favretti, Modelli Fisico Matematici. --: CLEUP, 2014. (2^ edizione) Cerca nel catalogo