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: CauchyKovalevskaya theorem
 Lecture 5: Characteristic surfaces and wellposedness
 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 1625: Newtonian potential, Schauder theory, heat propagator, nonlinear reactiondiffusion
Lecture notes
 Examples of PDE
 CauchyKovalevskaya theorem
