Unified matrix presentation of Maxwellʹs and wave equations using generalized differential matrix operators [EM engineering education]

In this paper, we introduce the concept of generalized differential matrix operators (GDMO’s) that are useful for the formulation of electromagnetic boundary value problems in arbitrary orthogonal coordinate systems, e.g., Cartesian, cylindrical, and spherical. The most significant attribute of the GDMO approach is that their use helps to simplify the complicated manipulation of vector differential equations, especially in problems dealing with an anisotropic media. We show that the use of the GDMO’s enable one to replace, for most problems in electromagnetics, the complicated vector differential operations with manipulation of 3 3 matrices. In addition, we demonstrate GDMO’s are convenient for deriving many differentiation identities and integral theorems which find extensive applications in electromagnetics.