This classic work, on the numerical solution of boundary value problems by variational methods with special emphasis on the finite element and collocation methods, is now available in an unabridged paperback edition. Assuming only the elements of linear algebra and analysis, Prenter presents just the necessary Hilbert space theory and abstract functional analytic concepts before developing the use of splines as a fine approximating tool. This work remains one of the clearest introductions to variational methods and includes powerful applications of approximation theoretic notions to very applied problems.