The growing computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by leading to closed-form solutions for many boundary value problems that arise in science and engineering. It includes discussion of the Laplace equation, plane strain, and the bending of plates with transverse shear deformation and considers each with Dirichlet, Neumann, and Robin boundary conditions.