Accurate and efficient solutions to scattering problems are essential to many areas of electromagnetic research. In this volume, the mode-matching technique is used to solve scattering problems in eddy-current nondestructive evaluation, thin-film deposition, and nanophotonics. In addition to being fast and accurate, the discrete eigenfunction solutions provide insight into the physics of each problem. After establishing the validity of discrete eigenfunction expansions for geometries of finite extent, the author derives an expression for the impedance of a tangential eddy-current coil in...