  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.
