USFKAD: An expert system for partial differential equations

USFKAD is an encoded expert system for the eigenfunction expansion of solutions to the wave, diffusion, and Laplace equations: both homogeneous and nonhomogenous; one, two, or three dimensions; Cartesian, cylindrical, or spherical coordinates; Dirichlet, Neumann, Robin, or singular boundary conditions; in time, frequency, or Laplace domain. The user follows a menu to enter his/her choices and the output is a LaTeX file containing the formula for the solution together with the transcendental equation for the eigenvalues (if necessary) and the projection formulas for the coefficients. The file is suitable for insertion into a book or journal article, and as a teaching aid. Virtually all cases are covered, including the Mellin, spherical harmonic, Bessel, modified Bessel, spherical Bessel, Dini, Hankel, Weber, MacDonald, and Kantorovich-Lebedev expansions, mixed spectrum, and rigid body modes.