On Equivalence of Maxwell's Equations in Differential and Integral Forms

Polat B.

2nd International Conference on Electrical, Communication and Computer Engineering, ICECCE 2020, İstanbul, Türkiye, 12 - 13 Haziran 2020 identifier


© 2020 IEEE.The analytical tools required to legitimize derivations of electromagnetic boundary conditions on an interface of singularity by using Divergence and Stokes's Theorems are presented in the Space of Schwartz-Sobolev Distributions in two steps. First, the differential and integral forms of Maxwell's Equations are demonstrated to be equally informative. By equal information it is implied that the integral/differential form of field equations can be derived when they are given in differential/integral form. Next, Divergence and Stokes's Theorems of Vector Calculus are shown to be valid in the sense of Schwartz-Sobolev distributions. This reveals that the distributional investigations of differential and integral forms of Maxwell's Equations reveal the same set of boundary conditions.