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Abstract-Mathematical frameworks for representing fields and waves and expressing Maxwell's equations of electromagnetism include vector calculus, differential forms, dyadics, bivectors, tensors, quaternions, and Clifford algebras. Vector notation is by far the most widely used, particularly in applications. Of the more sophisticated notations, differential forms stand out as being close enough to vectors that most practitioners can readily understand the notation, yet at the same time offering unique visualization tools and graphical insight into the behavior of fields and waves. We survey recent papers and book on differential forms and review the basic concepts, notation, graphical representations, and key applications of the differential forms notation to Maxwell's equations and electromagnetic field theory.

Abstract. In this paper the characteristics of small carbon nanotube (CNT) dipole antennas are investigated on the basis of the thin wire Hallén integral equation (IE). A surface impedance model for the CNT is adopted to account for the specific material properties resulting in a modified kernel function for the integral equation. A numerical solution for the IE gives the current distribution along the CNT. From the current distribution the antenna driving point impedance and the antenna efficiency are computed. The presented numerical examples demonstrate the strong dependence of the antenna characteristics on the used material and show the limitations of nanoscale antennas.