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Applied Partial Differential Equations: A Visual Approach: A Visual Approach ******************************************************************************* ------------------------------------------------------------------------------- General Information ------------------------------------------------------------------------------- Type.................: Ebook Part Size............: 16,912,303 bytes ------------------------------------------------------------------------------- Post Information ------------------------------------------------------------------------------- Posted by............: ~tqw~ ------------------------------------------------------------------------------- Release Notes ------------------------------------------------------------------------------- This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socio-economic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity and energy to their spatial and temporal variations. Typically, these equations are highly nonlinear; in many cases they are systems, and they represent challenges even for the most modern and sophisticated mathematical and numerical-analytic techniques. The selected topics reflect the longtime scientific interests of the author. They include flows of fluids and gases, granular-material flows, biological processes such as pattern formation on animal skins, kinetics of rarified gases, free boundaries, semiconductor devices, and socio-economic processes. Each topic is briefly introduced in its scientific or engineering context, followed by a presentation of the mathematical models in the form of partial differential equations with a discussion of their basic mathematical properties. The author illustrates each chapter by a series of his own high-quality photographs, which demonstrate that partial differential equations are powerful tools for modeling a large variety of phenomena influencing our daily lives. Table of Contents Foreword V Introduction 1 Kinetic Equations: From Newton to Boltzmann 5 The Navier-Stokes and Euler Equations - Fluid and Gas Dynamics 21 Granular Material Flows (with G. Toscani) 37 Chemotactic Cell Motion and Biological Pattern Formation (with D. Olz) 55 Semiconductor Modeling 73 Free Boundary Problems and Phase Transitions 87 Reaction-Diffusion Equations - Homogeneous and Heterogeneous Environments 109 Optimal Transportation and Monge-Ampere Equations 129 Wave Equations 149 Digital Image Processing and Analysis - PDEs and Variational Tools 167 Socio-Economic Modeling (with G. Toscani) 185 Product Details * ISBN: 3540346457 * ISBN-13: 9783540346456 * Format: Hardcover, 206pp * Publisher: Springer-Verlag New York, LLC * Pub. Date: September 2006 ------------------------------------------------------------------------------- Install Notes ------------------------------------------------------------------------------- PDF Reader Sharing Widget |