Many computational methods for solving continuous or infinite-dimensional problems with a high-speed digital computer exist. One of these, the
finite-element method, seems to be almost universally applicable. In this book I discuss, in elementary terms, a unified and mathematically rigorous approach to the finite-element method. My primary aim is to present enough practical and theoretical details to enable the reader either to
implement the method intelligently on a digital computer in order to solve practical problems, or to pursue theoretical studies knowledgeably. Included in the presentation are applications to interpolation problems, integral equations, least squares or regression problems, elliptic differential equations, eigenvalue problems, parabolic problems, and optimal control problems.