Partial Differential Equations I - Einzelansicht

May laws of nature can be cast in the form of an equation for the partial derivatives of an unknown function.
In this lecture we consider such equations in a systematic way. A large part of the lecture is devoted to studying the classical examples for the three main types of equations. The Poisson equation as an elliptic equation describing static configurations of the, the het equation which is a parabolic equation, and the wave equation as a hyperbolic equation.
The remaining part of the lecture considers the theory of existence and uniqueness of solutions to elliptic equations.

Literature on Partial Differential Equations:

• L. C. Evans: Partial Differential Equations, Second Edition, Graduate Studies in Mathematics, American Mathematical Society (2010).
• D. Gilbarg and N. Trudinger: Elliptic Partial Differential Equations of Second Order, Second Edition, Grundlehren der mathematiscehn Wissenschaften, Springer (1998). (Electronic Version.)
• Michael E. Taylor: Partial Differential Equations I, Basic Theory, Applied Mathematical Sciences, Springer (1996).

Interesting complements:

• J. Jost: Postmodern Analysis, Second Edition, Universitext, Springer (2003)

• Registration in the Course-Moodle is mandatory.
• The course starts with the lecture on tuesday, October 15th. There is no exercise on Monday.

Material from Courses Analysis 1-3 and Linear Algrbra 1 and 2.

Oral exam during the semester break in Spring. Appointments are managed in the Course-Moodle.