
PHYSICALMATHEMATICAL MODELS
First cycle degree in MATHEMATICS
Campus:
PADOVA
Language:
English
Teaching period:
First Semester
Lecturer:
FRANCO CARDIN
Number of ECTS credits allocated:
6
Prerequisites:

Pr.: Calculus, elementary algebra and geometry, and a first course in Mathematical Physics. 
Examination methods:

Written. 
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. 

