Elasticity:

1. The concept of continuum and continuous medium. Range of applicability of continuum theories.
2. Displacement field and strain tensor. Interpretation of the components of the deformation tensor. 
3. Stress and stress tensor. Cauchy construction (stress field vs. surface forces, also known as Cauchy's stress theorem).
4. The momentum balance in continuum media. Cauchy's equilibrium conditions. 
5. The angular momentum balance. Symmetry of stress tensor. 
6. Linear elastic media - relation between stress and strain. Elastic constants. Energy of deformation.
7. The Navier equations.
8. Twisting a shaft: Pure torsion. The Coulomb-Saint-Venant law.
9. Bending a beam: Pure bending. The Bernoulli-Euler law.
10. Deflections of slender rods. Force and torque balance. Buckling.

Hydrodynamics:

11. Dynamics of continuum media. Streaklines, Streamlines and particle trajectories. Eulerian and Lagrangian description. Material derivative. 
12. Ideal fluids. Mass and momentum balance. Euler equations. 
13. Invariants of motion of Euler equations. Cauchy-Lagrange integral. Bernoulli's law in different variants. Vorticity.
14. Velocity potential and stream function. 2D flows and complex potential. 
15. Potential flow around a cylinder: D'Alembert paradox, lift force, Magnus effect. Non-stationary effects, added mass. 
16. Rate of deformation tensor, viscous stress tensor and the relation between the two. 
17. The Navier-Stokes equations. Shear viscosity and bulk viscosity. 
18. Low Reynolds number flows and their basic characteristics. Stokes equations. Flow around a sphere at low Reynolds numbers. Stokes law. 
19. Time-dependent flows caused by oscillation or motion of the boundary. 
20. Thin film flows. Lubrication theory.