| Summary: | "The aim of this monograph is to present a mathematical framework which makes solving problems in multiply connected domains a very natural generalization of solving them in simply connected ones"--
Whenever two or more objects or entities-be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid-interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. Solving Problems in Multiply Connected Domains is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in a diverse range of applications; is the first monograph to focus on solving applied problems in multiply connected domains; and contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. This book is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists. It provides a rich source of project material for a range of undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
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