Partial Differential Equations I
(Lecture course in Winter Term 2018/19)
Instructors: Thomas Schmidt (lecture, exercise class), Lars Poppe (exercise class).
Lecture (first on October 16th):
- Tue, 8-10, H6 and Thu, 12-14, H4
Exercise classes (first on October 24th/25th):
- Wed, 16-18, Room 432, Lars Poppe
- Thu, 14-16, Room 432, Thomas Schmidt
Relevance: The course is eligible as a part of the master in Mathematics, Mathematical Physics, Industrial Mathematics, or Economathematics and is recommended to everyone with interests in analysis. Alternatively, it is possible to take and follow the course already during the third year of a bachelor. Clearly, other interested participants are also very welcome.
Prerequisites: The lecture builds on basic knowledge in analysis (including the theory of Lebesgue integration) and linear algebra.
ECTS points: The module (consisting of the lecture and the exercise class) has a worth of 12 ECTS points.
Contents:
Partial differential equations are equations, which involve an unknown function of two or more variables and finitely many (partial) derivatives of this function. The theory of such equations is very rich, can approached in very different ways and interacts with many other areas of analysis, mathematics, and physics. In this introductory lecture the richness of the theory will be demonstrated on the basis of the following three model equations:
- Laplace equation (with harmonic functions as solutions), Poisson equation,
- heat equation,
- wave equation.
A continuative course "Partial Differential Equations II" takes place in summer 2019.
Lecture notes: Last version in PDF.
Literature: Common books (of different scope) are:
- S. Axler, P. Bourdon, W. Ramey, Harmonic Function Theory, Springer, 2001,
- L.C. Evans, Partial Differential Equations, American Mathematical Society, 1998,
- D. Gilbarg, N.E. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 2001,
- J. Jost, Partial Differential Equations, Springer, 2013,
- J. Rauch, Partial Differential Equations, Springer, 1991,
- F. Sauvigny, Partial Differential Equations (2 volumes), Springer, 2012,
- M.E. Taylor, Partial Differential Equations (3 volumes), Springer, 1996
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