Introduction -- Mathematical preliminaries, integral formulations, and variational methods -- Second-order differential equations in one dimension : finite element models -- Second-order differential equations in one dimension applications -- Beams and frames -- Eigenvalue and time-dependent problems -- Computer implementation -- Single-variable problems in two dimensions -- Interpolation functions, numerical integration, and modeling considerations -- Flows of viscous incompressible fluids -- Plane elasticity -- Bending of elastic plates -- Computer implementation of two-dimensional problems -- Prelude to advanced topics