Lehrinhalte
In the recent years, the amount of literature that deals with physical models in terms of differential forms (DF) has increased strongly. For instance, DF allow a clear and elegant representation of electromagnetics (EM). The operators grad, curl, and div of vector analysis are replaced by a single operator of the exterior derivative. Similarly, the integral theorems of Gauss and Stokes are replaced by a single integral theorem. Vector analysis is limited to three dimensions, while DF can be applied to any dimensions. This is useful for the relativistic formulations in four dimensions.
Since DF can be canonically integrated over appropriate domains they lend themselves naturally to discretizations of the finite integration type.
This lecture series provides an introduction into DF calculus, and its relation to vector analysis. Maxwells equations and the constitutive relations are expressed in terms of DF, and the main steps into discretization are outlined briefly.
Literatur
M. Fecko: Differential Geometry and Lie Groups for Physicists, Cambridge University Press, 2006
F. Hehl, Y. Obukhov: Foundations of Classical Electrodynamics, Birkhäuser, 2003
K. Jänich: Vector Analysis, Springer, 2001
Voraussetzungen
It is recommended that the students have basic knowledge about
Electromagnetics (Maxwells equations in differential and integral form; constitutive relations; EM potentials);
Vector analysis (scalar and vector fields; differential operators grad, curl, and div; integral theorems of Gauss and Stokes).
Online-Angebote
Moodle
In the recent years, the amount of literature that deals with physical models in terms of differential forms (DF) has increased strongly. For instance, DF allow a clear and elegant representation of electromagnetics (EM). The operators grad, curl, and div of vector analysis are replaced by a single operator of the exterior derivative. Similarly, the integral theorems of Gauss and Stokes are replaced by a single integral theorem. Vector analysis is limited to three dimensions, while DF can be applied to any dimensions. This is useful for the relativistic formulations in four dimensions.
Since DF can be canonically integrated over appropriate domains they lend themselves naturally to discretizations of the finite integration type.
This lecture series provides an introduction into DF calculus, and its relation to vector analysis. Maxwells equations and the constitutive relations are expressed in terms of DF, and the main steps into discretization are outlined briefly.
Literatur
M. Fecko: Differential Geometry and Lie Groups for Physicists, Cambridge University Press, 2006
F. Hehl, Y. Obukhov: Foundations of Classical Electrodynamics, Birkhäuser, 2003
K. Jänich: Vector Analysis, Springer, 2001
Voraussetzungen
It is recommended that the students have basic knowledge about
Electromagnetics (Maxwells equations in differential and integral form; constitutive relations; EM potentials);
Vector analysis (scalar and vector fields; differential operators grad, curl, and div; integral theorems of Gauss and Stokes).
Online-Angebote
Moodle
- Lehrende: Stefan Kurz
Semester: ST 2020