This web site describes a largely self-contained applied math course. The prerequisites are linear algebra, Calculus, complex analytic contour integration, and some familiarity with convolution, the Fourier transform, sampling, and the fast Fourier transform. The course provides an introduction to the numerical treatment of differential equations such as the Laplace, Helmholtz, wave, and Maxwell equations via fast multipole methods and related techniques of matrix compression. In particular, the course discusses a method that the IEEE and American Institute of Physics Computing in Science and Engineering journal deemed to be one of the top ten algorithms of the twentieth century. The syllabus is tentative and subject to revision, especially the last few topics in the syllabus, which lead into ongoing research.