Self-patch integrals in transient electromagnetic scattering

The self-patch integrals that arise in the integral equations of electromagnetic scattering are evaluated analytically for general orthogonal coordinate systems to first order in the linear size of the patch. There are terms that contain spatial derivatives of the surface fields, and these terms may not be negligible. Although the formulas are derived for transient waves, the same integrals appear for monochromatic waves.