The exercises will be solved on Wednesday from 14:30. They will be uploaded on the Friday, the week before they will be solved.
Exercise sheet 3
Subjects: spherical symmetric solutions of the poisson equation and the Green's function in the first quadrant.
Solution sheet 3
Correction: In exercise 4 it is not possible to get the uniqueness of the solution for the given assumptions. Therefore I changed the exercise and one now just has to show that u is a solution.
Exercise sheet 4
Subjects: Newtons theorem and an application, a part of the proof of Thm 1.17 and uniqueness of the boundary value problem for specific elliptic differential operators.
Solution sheet 4
Exercise sheet 6
Subjects: A property of spherical symmetric functions, the Heat equation with L^1 initial condition and the Heat equation on the half line with Neumann boundary conditions.
Correction: The integration domain in Exercise 3 was changed, now it makes sense.
Solution sheet 6
Remark: I may have said Dirichlet boundary conditions in the exercise session for Exercise 3, that was wrong.
Exercise sheet 8
Subjects: The damped string, the clamped plucked string and another problem that can be solved using seperation of variables
Solution sheet 8
Remark: I was made aware of a BIG mistake in Exercise 1, see Exercise sheet 14 for more details
Exercise sheet 9
Subjects: The solution formula for the transport equation and for the homogeneous and inhomogeneous wave equation
Solution sheet 9
Remark: Due to time constraints we did not discuss the solution of Exercise 4 and 5, this will be done next time.
Exercise sheet 10
Subjects: Inhomogeneous 1-dim and homogeneous 2-dim wave equation plus concrete calculations of solutions
Correction: There were some typos in the problem sheet.
Solution sheet 10
Remark: Disregard the incomplete solution for Exercise 3 from the exercise session. A complete and corrected solution is given here.