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Simple and efficient numerical methods are developed for treating electromagnetic problems of scattering and radiation from surfaces. Special consideration is given to the treatment of edges so that rather arbitrary geometrical configurations may be handled. For the conducting body problems considered, an electric field integral formulation is used, and the method of moments is applied using pulse expansions to represent both the current and the charge. It is demonstrated that proper placement of the current and charge subdomains relative to edges not only is important in treating edges but also yields a convenient numerical procedure. A simple testing scheme is used which is almost as efficient as point-matching. Numerical results indicate that the approach is free of anomalies in the behavior of current near edges and of other previously observed numerical instabilities. Problems considered include conducting strips (both TM and TE), a bent rectangular plate, and both material and conducting bodies of revolution.