401-0243-00L Analysis III
|Dozierende||M. Akka Ginosar|
|Periodizität||jährlich wiederkehrende Veranstaltung|
|Kurzbeschreibung||We will model and solve scientific problems with partial differential equations. Differential equations which are important in applications will be classified and solved. Elliptic, parabolic and hyperbolic differential equations will be treated. The following mathematical tools will be introduced: Laplace and Fourier transforms, Fourier series, separation of variables, methods of characteristics.|
|Lernziel||Learning to model scientific problems using partial differential equations and developing a good command of the mathematical methods that can be applied to them. Knowing the formulation of important problems in science and engineering with a view toward civil engineering (when possible). Understanding the properties of the different types of partial differential equations arising in science and in engineering.|
|Inhalt||Classification of partial differential equations|
Study of the Heat equation general diffusion/parabolic problems using the following tools:
* Separation of variables
* Fourier series
* Fourier transform
* Laplace transform
Study of the wave equation and general hyperbolic problems using similar tools and the method of characteristics.
Study of the Laplace equation and general elliptic problems using similar tools and generalizations of Fourier series.
Application of Laplace transform for beam theory will be discussed.
|Skript||Lecture notes will be provided.|
|Literatur||The course material is taken from the following sources:|
Stanley J. Farlow - Partial Differential Equations for Scientists and Engineers
G. Felder: Partielle Differenzialgleichungen.
|Voraussetzungen / Besonderes||Analysis I and II. In particular, knowing how to solve ordinary differential equations is an important prerequisite.|