The finite element method is a numerical procedure for solving ordinary and partial differential equations which arise in engineering and mathematical physics. This is a complete self-contained introduction to the theory and applications of finite element methods in solid mechanics, fluid mechanics, and optimization. The authors' extensive experience of the application of finite element methods gives the book a practical slant. Worked examples are scattered throughout the text. Care is taken to explain and demonstrate techniques for formatting finite element apparatus to problems. Programming techniques for solving the resulting FEM problems are also thoroughly covered. The book also contains 14 MegaBasic programs, ranging from very short introductory programs to more general programs for analysis and optimization of plane stress, plates, and shells, and fluid flows.