ビジュアル応用偏微分方程式 Applied Partial Differential Equations : A Visual Approach

Markowich, Peter A.

Springer（2006/12発売）

• ページ数 160 p.
• 言語 ENG
• 商品コード 9783540346456

基本説明

Shows that partial differential equations model many aspects of our natural surroundings. Beautiful photographs give a memorable and unique access to the different applications.

Full Description

This book presents topics of science and engineering which occur in nature or are part of daily life. It describes phenomena which are modelled by partial differential equations, relating to physical variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has chosen topics representing his career-long interests, including the flow of fluids and gases, granular flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is presented in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations.

Contents

Kinetic Equations: From Newton to Boltzmann.- The Navier-Stokes and Euler Equations — Fluid and Gas Dynamics.- Granular Material Flows.- Chemotactic Cell Motion and Biological Pattern Formation.- Semiconductor Modeling.- Free Boundary Problems and Phase Transitions.- Reaction-Diffusion Equations — Homogeneous and Heterogeneous Environments.- Optimal Transportation and Monge-Ampère Equations.- Wave Equations.- Digital Image Processing and Analysis — PDEs and Variational Tools.- Socio-Economic Modeling.