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401-4782-25L 4 Credits DR , MSC D-PHYS , D-MATH
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Electromagnetics and Differential Forms

Lecturers & Examiners: Prof. Dr. Stefan Kurz
VVZ CR n/a

Last Updated: 2026-06-01 11:33:19

Objective

Students will acquire a detailed understanding of how to describe electromagnetics (EM) in terms of differential forms (DF). • How “space” (and “time”) can be modelled by differentiable manifolds; • How a class of physical fields can be represented by DF; • How Maxwell’s equations and constitutive relations translate into the language of DF; • How this continuous representation can be discretized.

Content

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. Maxwell‘s equations and the constitutive relations are expressed in terms of DF, and the main steps into discretization are outlined briefly.

Resources

Literature

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

General Information

Language
English (lecture with exercise), German (revision course / private study)
Levels
DR , MSC

Examination

Type
session examination
Mode
oral 30 minutes
The exam is only offered in the summer examination session 2025 and the subsequent winter session 2026.

Course Components

Type Title Time & Place Hours
lecture with exercise Electromagnetics and Differential Forms
This course is designed in a reading course/flipped classroom format. Meetings are planned 21.02.; 07.03.; 21.03.; 04.04.; 02.05.; 16.05.; 30.05.
  • Fri 14:15-16:00 (HG E 21)
  • 04.04 Date 12:15-14:00 (HG G 43)
1 h weekly
revision course / private study Electromagnetics and Differential Forms
Videogeführtes Selbststudium / Video guided self-study Video-Aufzeichnungen nur auf Deutsch verfügbar / Video recordings available in German only
No time listed 1 h weekly

Offered In