Topics for a 20 min talk (using the blackboard) in the exam.

1. Linear transport equations in one spatial dimension. Numerical methods entropies and uniqueness of solutions.

2. The Riemann problem for scalar conservation laws. Entropy conditions.

3. Front tracking for scalar conservation laws, including convergence.

4. Uniqueness of entropy solutions to scalar conservation laws.

5. Monotone numerical methods for scalar conservation laws, convergence to the entropy solution. 

6. Convergence rates for numerical schemes for scalar conservation laws.

7. The solution of the Riemann problem for systems of (hyperbolic) conservation laws.

8. Front tracking for systems of conservation laws (you don't have to go into much details...)