The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration. The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 24, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures. The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.