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Session 1532

Enhancing the teaching of electromagnetics using differential forms

Richard H. Selfridge, Karl F. Warnick, and David V. Arnold Brigham Young University

Introduction: During the past three years we have introduced our electromagnetics students to differential forms. We teach a sequence of 3 courses in electromagnetic fundamentals at BYU. The sequence begins with basic principles and concludes with advanced concepts, including Greens functions, asymptotic methods, and anisotropic materials. In addition to these basic principles courses, we offer applications courses in antennas, microwave circuit design, remote sensing, radar, nonlinear and Fourier optics, and fiber optics. We have found that expressing basic electromagnetic principles in terms of differential forms as a supplement to vector analysis aids the students at all levels in understanding electromagnetic theory.

The use of differential forms is widespread in the physics community, particularly in gravitation and relativistic electrodynamics problems. Several researchers advocate the use of differential forms in electrical engineering, among the most outspoken is Burke.

The test of a mathematical formalism is shown in the applications. Although I have long been convinced of this, it was emphasized to me again when I decided to teach a graduate electrodynamics course using differential forms instead of the usual vector notation. I expected only modest gains, but in fact it made a tremendous improvement. The mathematics became "transparent" and the underlying physical structures became visible. (William L. Burke, Applied Differential Geometry, Cambridge University Press, 1985)

Proponents point out that forms provide additional insight into the nature of electromagnetics, simplify derivations, and provide notational compactness.

If differential forms are as beneficial as proponents claim, why have they not come into more widespread use in electrical engineering electromagnetics? One opinion is expressed by Georges A. Deschamps:

The differential forms approach has not yet had any impact on engineering in spite of its convenience, compactness, and many other qualities. The main reason for this is, of course, the lack of exposure in engineering publications: the entire literature on the subject of electromagnetics is written in vector calculus notation. It is hoped that this article will help remove this obstacle to a wider use of these techniques, and demonstrate some of the real advantages of this new notation. (Georges A. Deschamps, Fellow IEEE, Electromagnetics and Differential Forms, Proceedings of the IEEE, Vol. 69, No. 6, June 1981)

1996 ASEE Annual Conference Proceedings

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Selfridge, R. H., & Warnick, K. F., & Arnold, D. V. (1996, June), Enhancing The Teaching Of Electromagnetic Using Differential Forms Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6034