This article gathers useful, simple algorithms and their physical interpretations for field solutions from incremental sources in three-dimensional (3-D) spatial, two-dimensional (2-D) spectral, and one-dimensional (1-D) spectral domains. The interpretations of the 1-D spectral Green's functions are visualized in space as fields from current sheets, tubes, and shells for the planar, circular cylindrical, and spherical cases, respectively. A joint algorithm is presented for solving the multilayer case for all three cases. Similarly, field problems involving cylindrical objects or bodies of revolution (BOR) are structured into spectrums of 2-D spatial solutions from line sources and ring sources, respectively. The formulations and physical images are pedagogical and open up for new creative ways of teaching electromagnetic (EM) field theory as well as structuring numerical algorithms for field solutions that take known symmetries into account. It is also shown that the 3-D spatial Green's functions can be approximated to improve physical interpretation by omitting higher-order 1/r terms when r>2λ.