John Ockendon - Böcker

This new edition, interspersed with numerous footnotes and topical exercises, is aimed at students of mathematics, engineering and physics seeking a comprehensive text in the applications of PDEs.

Partial differential equations are a central concept in mathematics. They are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of the well-known text by Ockendon et al., providing an enthusiastic and clear guide to the theory and applications of PDEs, provides timely updates on: transform methods (especially multidimensional Fourier transforms and the Radon transform); explicit representations of general solutions of the wave equation; bifurcations; the Wiener-Hopf method; free surface flows; American options; the Monge-Ampere equation; linear elasticity and complex characteristics; as well as numerous topical exercises.This book is ideal for students of mathematics, engineering and physics seeking a comprehensive text in the modern applications of PDEs

Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

The world around us, natural or man-made, is built and held together by solid materials. Understanding their behaviour is the task of solid mechanics, which is in turn applied to many areas, from earthquake mechanics to industry, construction to biomechanics. The variety of materials (metals, rocks, glasses, sand, flesh and bone) and their properties (porosity, viscosity, elasticity, plasticity) is reflected by the concepts and techniques needed to understand them: a rich mixture of mathematics, physics and experiment. These are all combined in this unique book, based on years of experience in research and teaching. Starting from the simplest situations, models of increasing sophistication are derived and applied. The emphasis is on problem-solving and building intuition, rather than a technical presentation of theory. The text is complemented by over 100 carefully-chosen exercises, making this an ideal companion for students taking advanced courses, or those undertaking research in this or related disciplines.