Many electromagnetic geophysical systems employ a spatially extended source (i.e., a large rectangular horizontal loop or a long grounded wire) to generate the electromagnetic (EM) field. In forward or inverse modeling, the theory and computational algorithms are usually derived for infinitesimal electric or magnetic dipole sources, or infinite line currents. However, it is often not sufficiently accurate to approximate an extended source in such a manner. Also, in many instances topographic and access problems can force the use of a source which has a complicated shape. Conceptually, there is no difficulty in expressing the actual source as an integral (line or surface) of the appropriate elementary source. However, if the integration is carried out numerically, the algorithm for calculating the field of the elementary source may have to be evaluated many times, and the calculation may become impractically long.