C.M. Linton - Böcker

How are maps created? What is the process that enables a location on the Earth's surface to become a point on a sheet of paper? The answer lies in map projections. This book provides a highly readable account of the theory that underpins all major map projections, starting from the concept of map distortion, which all flat maps necessarily possess. The engaging exposition is enhanced by the extensive use of diagrams, including over sixty maps. The opening chapters set the scene, covering the mathematical background, the notion of map distortion and the classification of map projections. The book then turns its attention to the different types of projection, including cylindrical, azimuthal, and conical projections. Following a modern analytic approach, the author uses the tools of multivariable calculus to derive the equations defining these map projections. The book ends with a chapter utilizing complex variables to study conformal projections, and a final summary chapter to wrap up the material. Each chapter is interwoven with a compelling historical narrative enriching the text. A Mathematical Exploration of Map Projections assumes only a prior knowledge of elementary calculus, and is an excellent resource for anyone curious about the mathematics underlying map projections.

Although a wide range of mathematical techniques can apply to solving problems involving the interaction of waves with structures, few texts discuss those techniques within that context-most often they are presented without reference to any applications. Handbook of Mathematical Techniques for Wave/Structure Interactions brings together some of the most important techniques useful to applied mathematicians and engineers.Each chapter is dedicated to a particular technique, such as eigenfunction expansions, multipoles, integral equations, and Wiener-Hopf methods. Other chapters discuss approximation techniques and variational methods. The authors describe all of the techniques in terms of wave/structure interactions, with most illustrated by application to research problems. They provide detailed explanations of the important steps within the mathematical development, and, where possible, physical interpretations of mathematical results.Handbook of Mathematical Techniques for Wave/Structure Interactions effectively bridges the gap between the heavy computational methods preferred by some engineers and the more mathematical approach favored by others. These techniques provide a powerful means of dealing with wave/structure interactions, are readily applied to relevant problems, and illuminate those problems in a way that neither a purely computational approach nor a straight theoretical treatment can.