Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | We 10:00-11:00 in Research I, 107 |
Grader: | Zymantas Darbenas |
Email: | z.darbenas@jacobs-university.de |
Lectures: | Tu 9:45, Th 8:15 in West Hall 8 |
Homework: | 20% |
Presentation: | 10% |
Midterm Exam: | 30% |
Final Exam: | 40% |
05/02/2013: | Introduction; linear transport equation |
07/02/2013: | Laplace equation, fundamental solution |
12/02/2013: | Poisson equation, mean value formulas |
14/02/2013: | Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity |
19/02/2013: | Harmonic functions: analyticity |
21/02/2013: | Harmonic functions: Liouville's theorem, Harnack's inequality |
26/02/2013: | Dirichlet problem, Green's functions |
28/02/2013: | Green's function for the half-space; energy methods |
05/03/2013: | Heat equation: fundamental solution, solution formulas |
07/03/2013: | Mean value formulas for the heat equation, maximum principle |
12/03/2013: | Maximum principle on unbounded domains |
14/03/2013: | Regularity |
19/03/2013: | Midterm review |
21/03/2013: | Midterm Exam |
02/04/2013: | Energy methods, backward uniqueness |
04/04/2013: | Wave equation: D'Alembert's formula, energy methods |
09/04/2013: | First order PDEs, method of characteristics |
11/04/2013: | Boundary conditions, local existence theory, examples |
16/04/2013: | Scalar conservation laws, Hamilton Jacobi equations, connections to Hamilton's equation of motion in classical mechanics and the Hamilton variational principle; Legendre transform |
18/04/2013: | Legendre transform, Hopf-Lax formula |
23/04/2013: | Weak solutions for Hamilton Jacobi equations, uniqueness, semiconcavity; uniqueness theorem without proof |
25/04/2013: | Integral solutions for conservation laws |
30/04/2013: | Shocks, rarefaction waves, entropy condition |
02/05/2013: | No class |
07/05/2013: | Lax-Oleinik solutions. Afternoon Presentations: 15:45-17:00 in Research I, 107 |
14/05/2013: | Presentations |
16/05/2013: | Review for final exam |
30/05/2013: | Final Exam, 9:00-11:00 in the Research II Lecture Hall |