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## Elektromagnetische Feldsimulation (Seminar)

"Formalizations of Electromagnetic Field Theory
- A Guide to Self-study"

preliminary discussion:
Tuesday, 17th April 2018, 4:30 p.m., EN-610

instructors:

language:
english or german

target audience:
students (M.Sc., PhD)

• from electrical engineering, physical engineering, physics, mathematics, ...
• interested in electromagnetic field theory or computational electromagnetics

In the course, we focus on one main question:
Why are there various formalizations of electromagnetic field theory (e.g. by means of vector calculus, tensor calculus, differential forms etc.)?

The goal is to guide students during their self-study of the course's main question.

Selected subquestions are:

• What does "formalization" mean?
• How can electromagnetic field theory be "expressed"?
• Which significance does the course's main question have for the numerical simulation of electromagnetic fields?

We will discuss how to approach:

• Mathematical logic
• Set theory & category theory
• Modern Algebra
• Geometry
• (...).

• Participation (50 %)
• Presentation (50 %).

Selected references are:

• Video lectures

• Literature

• "Mathematical structures for dimensional reduction and equivalence classification of electromagnetic boundary value problems" by P. Raumonen (PhD Thesis, Tampere University of Technology, 2009)
• "Gauge fields, knots and gravity" by J. Baez, J. P. Muniain (World Scientific Publishing Company, 1994)
• "Type Classes and Filters for Mathematical Analysis in Isabelle/HOL" by J. Hölzl et al. (in Interactive theorem proving. Lecture Notes in Computer Science, Springer, pp. 279--294, 2013)
• "A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures" by J. Gratus (arXiv:1709.08492 [math.DG], 2017)
• "Discrete Differential Geometry: An applied introduction" by K. Crane (Carnegie Mellon University, 2016).

E-mail: