This is the second edition of the book which has two additional new chapters on Maxwell's equations as well as a section on properties of solution spaces of Maxwell's equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell's equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering. <div> </div>

Boundary Integral Equations (Applied Mathematical Sciences, 164)

Science & Math

Hsiao, George C.

Wendland, Wolfgang L.

Mathematics

Springer

Diese dreisemestrige Einführung in die Analysis behandelt die Integral- und Differentialrechnung einer und mehrerer Veränderlicher. Daran anschließend werden analytische und einfache numerische Verfahren zur Lösung gewöhnlicher Differentialgleichungen besprochen. Der letzte Teil ist Methoden der komplexen Funktionentheorie gewidmet. Zentrales Anliegen dieses Lehrbuches sind die Entwicklung und Anwendung von praktischen Methoden zur Lösung mathematischer Aufgaben sowie die Konstruktion dieser Lösungen.

Analysis: Integral- und Differentialrechnung, gewöhnliche Differentialgleichungen, komplexe Funktionentheorie (German Edition)

Steinbach, Olaf

Vieweg+Teubner Verlag

This book is devoted to the mathematical foundation of boundary integral equations. The combination of ?nite element analysis on the boundary with these equations has led to very e?cient computational tools, the boundary element methods (see e.g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have con?ned ourselves to the treatment of elliptic boundary value problems. The central idea of eliminating the ?eld equations in the domain and - ducing boundary value problems to equivalent equations only on the bou- ary requires the knowledge of corresponding fundamental solutions, and this idea has a long history dating back to the work of Green [107] and Gauss [95, 96]. Today the resulting boundary integral equations still serve as a major tool for the analysis and construction of solutions to boundary value problems.

See the best price to sell, buy, or rent books by Wendland, Wolfgang L.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Wendland, Wolfgang L.

See the best price to sell, buy, or rent books by Wendland, Wolfgang L.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Boundary Integral Equations (Applied Mathematical Sciences, 164)

Boundary Integral Equations (Applied Mathematical Sciences, 164)

Analysis: Integral- und Differentialrechnung, gewöhnliche Differentialgleichungen, komplexe Funktionentheorie (German Edition)

Boundary Integral Equations (Applied Mathematical Sciences, 164)