Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Tu/Th 10:00-11:00 in Research I, 107 |
Lectures: | Mo 9:45, We 8:15 in West Hall 4 |
Homework: | 20% |
Presentation: | 10% |
Midterm Exam: | 30% |
Final Exam: | 40% |
Mon, 2. Feb. 2015: | Introduction; linear transport equation |
Wed, 4. Feb. 2015: | Laplace equation, fundamental solution |
Mon, 9. Feb. 2015: | Poisson equation, mean value formulas |
Wed, 11. Feb. 2015: | Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, |
Mon, 16. Feb. 2015: | Harmonic functions: smoothness, estimates on derivatives, comment on analyticity, Liouville theorem with consequences |
Wed, 18. Feb. 2015: | Harnack inequality; Dirichlet problem, Green's functions |
Mon, 23. Feb. 2015: | Green's function for the half-space (ctd.); energy methods |
Wed, 25. Feb. 2015: | Heat equation: introduction, fundamental solution, solution formulas |
Mon, 2. Mar. 2015: | Initial value problem for the heat equation |
Wed, 4. Mar. 2015: | Maximum principle, uniqueness |
Mon, 9. Mar. 2015: | Energy methods for the heat equation |
Wed, 11. Mar. 2015: | Wave equation: introduction and d'Alembert's formula for the wave equation in one spatial dimension |
Mon, 16. Mar. 2015: | Wave equations in several dimensions; energy methods |
Wed, 18. Mar. 2015: | Review for midterm exam |
Mon, 23. Mar. 2015: | Midterm exam |
Wed, 25. Mar. 2015: | First order equations, generalized characteristics |
Wed, 8. Apr. 2015: | Scalar conservation laws, shock condition, entropy condition for piecewise smooth solutions |
Mon, 13. Apr. 2015: | Introduction to Hamilton-Jacobi equations, Legendre transform |
Wed, 15. Apr. 2015: | Discussion of Midterm exam |
Mon, 20. Apr. 2015: | No class |
Wed, 22. Apr. 2015: | Hopf-Lax formula, semiconcavity |
Mon, 27. Apr. 2015: | Lax-Oleinik formula for scalar conservation laws, entropy condition |
Wed, 29. Apr. 2015: | Riemann problem; Student presentation |
Mon, 4. May 2015: | Review for final exam |
Wed, 6. May 2015: | Final Exam, West Hall 1, 8:15-10:15 |
Mon, 11. May 2015: | Student presentations |
Wed, 13. May 2015: | Student presentations |
Wed, 20. May 2015: | Student presentations, West Hall 4, 15:00-19:00 |