First cycle degree in MATHEMATICS

Campus: PADOVA

Language: English

Teaching period: First Semester


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.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.