Abstract
A general description of boundary value problems including the definitions of the concepts of domain and boundary are given. Distinction between the domain and the boundary are emphasized and essential and natural boundary conditions are introduced. The mathematical tools used in the solution of boundary value problems are briefly introduced with emphasis on functionals and calculus of variations. The connections between the differential equation of equilibrium and the extremal value of the associated functional are established. The weighted residual integral and the weak form of the boundary value problems are introduced for problems that involve Sturm–Liouville type differential operators. Examples include deformation of a one-dimensional bar and deflection of an Euler–Bernoulli beam. Method of weighted residuals, in particular, the Rayleigh–Ritz and Galerkin's methods are presented with relevant examples.
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