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Full-Text Articles in Engineering
Teaching Electromagnetic Field Theory Using Differential Forms, Karl F. Warnick, Richard H. Selfridge, David V. Arnold
Teaching Electromagnetic Field Theory Using Differential Forms, Karl F. Warnick, Richard H. Selfridge, David V. Arnold
Faculty Publications
The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory. First, films clarify the relationship between field intensity and flux density, by providing distinct mathematical and graphical representations for the two types of fields. Second, Ampere's and Faraday's laws obtain graphical representations that are as intuitive as the representation of Gauss's law. Third, the vector Stokes theorem and the divergence theorem become special cases of a single relationship that is easier for the student to remember, apply, and visualize than their vector formulations. Fourth, computational simplifications result from the use …
Electromagnetic Boundary Conditions And Differential Forms, Karl F. Warnick, Richard H. Selfridge, David V. Arnold
Electromagnetic Boundary Conditions And Differential Forms, Karl F. Warnick, Richard H. Selfridge, David V. Arnold
Faculty Publications
A new representation for electromagnetic boundary conditions involving a boundary projection operator defined using the interior and exterior products of the calculus of differential forms is developed. This operator expresses boundary conditions for fields represented by differential forms of arbitrary degree. With vector analysis, the field intensity boundary conditions require the cross product, whereas the flux boundary conditions use the inner product. With differential forms, the field intensity and flux density boundary conditions are expressed using a single operator. This boundary projection operator is readily applied in practice, so that this work extends the utility of the calculus of differential …