For final year graduate and postgraduate courses in the finite element method, this book introduces the method as applied to linear, non-linear and one- and two-dimensional problems of engineering and applied sciences. It includes a step-by-step systematic approach to the formulation and analysis of differential and integral equations in variational forms. The book adopts a differential equation approach, avoiding the need for knowledge of the variational principles of solid mechanics in the development of the finite element models. The need for the weighted-integral formulation of differential equations is explained clearly, providing the student with logical reasons for the recasting of differential equations into variational form.