• Basic concepts regarding Cartesian tensors, Lagrangian and Eulererian coordinates
• Strain tensor, deformation, conservation laws, constitutive equations
• Linear elasticity, Navier equations
• Newtonian fluid mechanics, Navier-Stokes equations, ideal fluids, vorticity
• Viscous fluids, laminar flow, turbulent flow, boundary layer, aerodynamics
• Thermodynamics of continua
• Applications of the Euler equations: solar wind, stellar stability, Newtonian cosmology
• Waves and solitons (Korteweg-de Vries)
• Electromagnetic continuum in plasmas, magnetohydrodynamics (MHD), plasma waves
• Concepts from modern differential geometry: vector fields and differential forms, tensor
• analysis, Riemannian geometry
• Nonlinear continua
• Structural elements: beams, plates and shells
• Geometry and gauge theory in fluid mechanics
• Relativistic continuum, energy-momentum tensor, Einstein field equations, cosmology.
Final competences:
1 The student has gained insight in the foundations of the mechanics of continuous media.
2 The student has gained appreciation for the interdisciplinary character of the domain of
continuum mechanics and of the common applicability of the underlying physical principles
and the mathematical formalism in the multiple specialties wherein applications were
provided.
3 The student is able to use the acquired expertise to translate physical problems into
mathematical models and, conversely, to interpret mathematical conclusions in a physical context.
4 The student has acquired arithmetic skills, both analytical and by computer, allowing him/herto solve new problems in continuum mechanics, starting from the insight gained.
5 The student has acquired the necessary skills to commence a more specialized study in each of the subdisciplines discussed.
