  This paper presents a class of boundary integral equations for the solution
of problems of electromagnetic and acoustic scattering by two dimensional
homogeneous penetrable scatterers with smooth boundaries. The new integral
equations, which, as is established in this paper, are uniquely solvable
Fredholm equations of the second kind, result from representations of fields as
combinations of single and double layer potentials acting on appropriately
chosen regularizing operators. As demonstrated in this text by means of a
variety of numerical examples (that resulted from a high-order Nystrom
computational implementation of the new equations), these "regularized combined
equations" can give rise to important reductions in computational costs, for a
given accuracy, over those resulting from previous boundary integral
formulations for transmission problems.
