Books in the Differential and Integral Equations and Their Applications series

Starting from an elementary level and finishing with the most recent results, this book gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. The presentation includes a review of the main techniques of the theory of elliptic equations, offers a comparative analysis of various approaches to differential equations on manifolds with singularities, and devotes considerable attention to applications of the theory. A glossary, numerous illustrations, and many examples help readers master the subject. Clear exposition, up-to-date coverage, and accessibility lay the groundwork for continuing studies and further advances in the field.

Presents a survey of methods and results in an application area of Lie groups to difference equations and difference meshes (lattices). This work focuses on the formulation and mathematical substantiation of exact symmetry preservation in difference models, such as difference equations and meshes.

A reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences, this title contains about 3000 first order partial differential equations with solutions.

Focuses on the analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. This book provides estimates of the operator norms for various ranges of the wave number variation, and then examines the spectral properties of these operators.