
Course unit
PHYSICALMATHEMATICAL MODELS
SC01111314, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2015/16
ECTS: details
Type 
ScientificDisciplinary 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 
Start of activities 
02/10/2017 
End of activities 
19/01/2018 
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.WorkEnergy Theorem. Constitutive
equations and the principle of material indifference.
6. Ideal elastic fluids. NavierStokes, Vorticity.
7. HagenPoiseuille flow, plane motion of NavierStokes fluids, Bernoulli Theorem.
8. Elementary Meteorology: Cyclones and Anticyclones.
9. Variational formulation of classical field theories: hyperelasticity 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 ClausiusDuhem
formulation. Balance laws and the second principle. Theorem of Clausius
Duhem. Thermoelastic materials.
11. Wave propagation. The method of characteristics: linear and quasilinear
theories. Singularities. Nonlinear theory and the HamiltonJacobi equation.
Wave propagation in systems of conservation laws. Weak discontinuities,
HugoniotHadamard. Sound speed. High frequency asymptotic waves. Shock
waves. RankineHugoniot.
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)


