Transverse electric scattering on inhomogeneous objects: Singular integral equation, symbol of the operator, and matrix elements

This is a companion report for the paper “Transverse electric scattering on inhomogeneous objects: Spectrum of integral operator and preconditioning” by the present authors. In this report we formulate the two-dimensional transverse electric scattering problem as a standard singular integral equation, derive the symbol of the integral operator for H"older-continuous contrasts, and calculate the elements of the system matrix obtained after discretization via the mid-point rule.