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The application of the method of moments usually requires a minimum degree of differentiability for basis and testing functions. Through the solution of the electric field integral equation (EFIE) for scattering by a perfect conducting cylinder illuminated by a TE wave, however, it is shown that such a restriction can be loosed. Theoretically, pulse basis functions and point matching are usually considered to be not suitable for the solution of the TE EFIE for lack of sufficient degrees of differentiability. Nevertheless proper treatment still permits their application. The basic idea is to avoid or eliminate all the nonphysical terms in the discretized equations produced by point matching. Several methods to tackle this problem are theoretically investigated and validated through numerical results for cylinders of various geometries.