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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 the presence of an infinite conducting wedge of arbitrary angle. The solution herein obviates the difficulties associated with continuous eigenfunction expansions by solving the problem in a truncated domain. A modal approximation to the fields inside an electrically small plasma reactor is presented. The author describes how the uniformity of the film deposition could be improved by coating the walls of the reactor with a lossy material. The book concludes with a modal solution to plane-wave scattering by a thin silver film perforated by a square array of circular holes.