ABSTRACT
Integral theorems borrowed from the differential geometry of curves, surfaces and connected regions turn out to be useful and perhaps even indispensable for a thorough understanding of elementary electromagnetic theory. Not only are they quite helpful in converting the differential form of Maxwell’s equations into their equivalent integral form, but they also offer a convenient tool to define a discretized version of the field variables in the framework of numerical simulation. Moreover, they naturally bridge the gap between the microscopic interaction of the electromagnetic fields and charges in a solid-state conductor and the global circuit models envisaged on the macroscopic level. This chapter summarizes the first three integral theorems. The fourth one is the Helmholtz theorem, which allows one to decompose any well-behaved vector field into a longitudinal and a transverse part.
