Note : For the sake of completeness, the lecture notes contain a great deal of detail, including full mathematical calculations and explanatory appendices. I realize this may be too much to digest, especially for those coming from a background other than physics. Here is a little guide/selection of required topics aimed at a better preparation of the oral exam, which applies to Geophysicists only (the requirements for Physicists are understandably stricter).

• Memories from thermodynamics
• A supposedly fun thing with tensors – Part 1
• A supposedly fun thing with tensors – Part 2
• Folio 1 – General notions on continuous media
• Folio 2 – Material derivative of integrals; Integral and local laws
• Folio 3 – Stresses; Fluid statics: Isotropy and continuity of pressure
• Folio 4 – Euler’s equation
• Folio 5 – Fluid statics: Mechanical equilibrium, equilibrium and stability of the atmosphere
• Folio 6 – Hydrostatics of incompressible fluids
• Folio 7 – Dynamics of ideal fluids; Momentum and energy flux
• Folio 8 – Steady flow: Bernoulli’s equation and applications
• Folio 9 – Incompressibility; Kelvin’s circulation theorem; Potential flow
• Folio 10 – Gravity waves
• Folio 11 – Energy transport in gravity waves; Appendices
• Folio 12 – Real (viscous) fluids: Velocity gradient and stress tensors; Navier-Stokes equation
• Folio 13 – Notes about the Navier-Stokes equation in non-Cartesian coordinate systems
• Folio 14 – Symmetry of the stress tensor; Mechanical pressure and local equilibrium; Momentum flux and viscous dissipation
• Folio 15 – Examples of viscous flow: Poiseuille, Couette and gravity flows
• Folio 16 – Similarity laws and dimensionless numbers
• Folio 17 – Stokes flow: Motion of a sphere in a viscous fluid
• Folio 18 – Oscillatory motions in viscous fluids
• Folio 19 – Damping of gravity waves; Surface currents: Ekman layer
• Folio 20 – Stability/Instability; Instability of tangential discontinuities, Kelvin-Helmholtz instability
• Folio 21 – Heat exchange: Heat transfer equation as an energy/entropy balance equation; Fourier’s law; Heat equation for incompressible flows
• Folio 22 – Heat exchange in the crust: Boundary conditions, steady-state and transient solutions
• Folio 23 – Green’s function for the heat problem; Similarity laws for heat transfer; Solid-fluid heat exchange, Nusselt number
• Folio 24 – Natural convection, Grashof and Rayleigh numbers
• Folio 25 – Rayleigh-Bénard instability
• Folio 26 – Elastic solids: Phenomenological laws of linear elasticity; Stress and strain tensors, constitutive equation
• Folio 27 – Statics: Lithostatic stress tensor; Dynamics: Continuity and Navier equations
• Folio 28 – Elastic waves; Beyond linear elasticity: Basic viscoleastic models