This book is an outgrowth of the sixth international conference on integral methods in science and engineering. The chapters focus on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes.

Integral Methods in Science and Engineering describes the construction and application of various analytic and numerical integration techniques. Problem solving in areas such as solid mechanics, fluid dynamics, thermoelasticity, plates and shells, liquid crystals, diffusion and diffraction theory, Hamiltonian systems, resonance, nonlinear waves, plasma, flight dynamics, and structural networks are presented in an accessible manner. The book offers a vehicle for the quick dissemination of new results in these domains, and will help create an ideal environment for investigative interdisciplinary study among a variety of research areas.

Topics:

* Offers an illustration by prominent researchers of efficient methods of solution with numerical results and rigorous analytic methods

* Presents applications of integral methods to a wide variety of mathematical and physical problems

* Provides new results in the study of various physical and mechanical models

* A clear, concise focus on a class of methodologies rather than a specific field of study

This book is a practical resource for a broad audience of professionals, researchers, and practitioners in applied mathematics, mechanical engineering, and theoretical physics, who are interested in current research in ordinary and partial differential equations, integral equations, numerical analysis, mechanics of solids, fluid mechanics, and mathematical physics.Graduate students will find this a helpful guide to the wide range of applications that integral methods have in science and engineering.

This book is an outgrowth of the sixth international conference on integral methods in science and engineering. The chapters focus on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes. Integral Methods in Science and Engineering describes the construction and application of various analytic and numerical integration techniques. Problem solving in areas such as solid mechanics, fluid dynamics, thermoelasticity, plates and shells, liquid crystals, diffusion and diffraction theory, Hamiltonian systems, resonance, nonlinear waves, plasma, flight dynamics, and structural networks are presented in an accessible manner. The book offers a vehicle for the quick dissemination of new results in these domains, and will help create an ideal environment for investigative interdisciplinary study among a variety of research areas.Topics: * Offers an illustration by prominent researchers of efficient methods of solution with numerical results and rigorous analytic methods * Presents applications of integral methods to a wide variety of mathematical and physical problems * Provides new results in the study of various physical and mechanical models * A clear, concise focus on a class of methodologies rather than a specific field of study This book is a practical resource for a broad audience of professionals, researchers, and practitioners in applied mathematics, mechanical engineering, and theoretical physics, who are interested in current research in ordinary and partial differential equations, integral equations, numerical analysis, mechanics of solids, fluid mechanics, and mathematical physics. Graduate students will find this a helpful guide to the wide range of applications that integral methods have in science and engineering.

Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl,"" Ym) into a vector-valued function I = (h, ..., II). We assume at first that all the functions, as well as the coefficients of the differen tial operator, are defined in an open domain Jl in the n-dimensional Euclidean n space IR, and that they are smooth (infinitely differentiable). A is called an overdetermined operator if there is a non-zero differential operator A' such that the composition A' A is the zero operator (and underdetermined if there is a non-zero operator A" such that AA" = 0). If A is overdetermined, then A'I = 0 is a necessary condition for the solvability of the system Ay = I with an unknown vector-valued function y. 3 A simple example in 1R is the operator grad, which maps a scalar func tion Y into the vector-valued function (8y/8x , 8y/8x2, 8y/8x3)' A necessary solvability condition for the system grad y = I has the form curl I = O."