This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
An elementary function is (roughly speaking) a function of a real or complex variable which can be built up using such operations as sine, exponentiation, log, 1/tan and algebraic operations. The problem of integration in finite terms asks whether we can tell, for a given elementary function, f, whether or not the integral of f is again an elementary function. If it is elementary, then one should be able to find it in a systematic manner. In this paper, the problem is formulated precisely, the underlying theory is discussed and finally the problem is solved for those elementary functions in the subclass built up without using irrational algebraic operations. (Author).
Human Interaction with Electromagnetic Fields: Computational Models in Dosimetry presents some highly rigorous and sophisticated integral equation techniques from computational electromagnetics (CEM), along with practical techniques for the calculation and measurement of internal dosimetry. Theory is accompanied by numerical modeling algorithms and illustrative computational examples that range from academic to full real-world scenarios. Covers both deterministic and stochastic modeling Presents implementations of integral equation approaches, overcoming the limitations of the FDTD approach Presents various biomedical applications
A comprehensive guide to the latest in phased array antenna analysis and design--the Floquet modal based approach This comprehensive book offers an extensive presentation of a new methodology for phased array antenna analysis based on Floquet modal expansion. Engineers, researchers, and advanced graduate students involved in phased array antenna technology will find this systematic presentation an invaluable reference. Elaborating from fundamental principles, the author presents an in-depth treatment of the Floquet modal based approach. Detailed derivations of theorems and concepts are provided, making Phased Array Antennas a self-contained work. Each chapter is followed by several practice problems. In addition, numerous design examples and guidelines will be found highly useful by those engaged in the practical application of this new approach to phased array structures. Broadly organized into three sections, Phased Array Antennas covers: The development of the Floquet modal based approach to the analysis of phased array antennas Application of the Floquet modal based approach to important phased array structures Shaped beam array synthesis, array beam forming networks, active phased array systems, and statistical analysis of phased arrays Incorporating the most recent developments in phased array technology, Phased Array Antennas is an essential resource for students of phased array theory, as well as research professionals and engineers engaged in the design and construction of phased array antennas.
As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations. Chapter I reviews the theoretical aspects of integral equation formulations with emphasis in their mathematical aspects. The analysis of time dependent problems is presented in Chap. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm. Chapter 3 reviews the application of boundary elements for fracture mechanics analysis in the presence of thermal stresses. The chapter presents numerical results and the considerations on numerical accuracy are of interest to analysts as well as practising engineers.
The sub-domain techniques in the BEM are nowadays finding its place in the toolbox of numerical modellers, especially when dealing with complex 3D problems. We see their main application in conjunction with the classical BEM approach, which is based on a single domain, when part of the domain needs to be solved using a single domain approach, the classical BEM, and part needs to be solved using a domain approach. This has usually been done in the past by coupling the BEM with the FEM, however, it is much more efficient to use a combination of the BEM and a BEM sub-domain technique. The advantage arises from the simplicity of coupling the single domain and multi-domain solutions, and from the fact that only one formulation needs to be developed, rather than two separate formulations based on different techniques. There are still possibilities for improving the BEM sub-domain techniques. However, considering the increased interest and research in this approach we believe that BEM sub-domain techniques will become a logical choice in the future substituting the FEM whenever an efficient solution requires coupling of the BEM with a domain technique.
