# Downloads

**Homework assignments**
**Class notes taken and slightly revised by Ibrahim Al Balushi**
- Lecture 1/2: Classical function spaces
- Lecture 3: Cauchy's method of majorants in the context of ODEs
- Lecture 4: Cauchy-Kovalevskaya theorem
- Lecture 5: Characteristic surfaces and well-posedness
- Lecture 6: Semilinear first order equations
- Lecture 7: Quasilinear first order equations
- Lecture 8: Conservation laws, Riemann problem, shocks, weak solutions
- Lecture 9: Fundamental solution of the Laplace operator, Green's identities
- Lecture 10: Green's formula, mean value property, maximum principles
- Lecture 11: Koebe's converse of the mean value property, derivative estimates for harmonic functions
- Lecture 12: Green's function, Poisson's formula
- Lecture 13: Removable singularity theorem, Harnack inequalities, Harnack convergence theorems
- Lecture 16-25: Newtonian potential, Schauder theory, heat propagator, nonlinear reaction-diffusion

**Lecture notes**
- Examples of PDE
- Cauchy-Kovalevskaya theorem