Applied Partial Differential Equations:: A Visual Approach - Hardcover

Markowich, Peter

Hardcover

ISBN 10: 3540346457 ISBN 13: 9783540346456

Publisher: Springer, 2006

Synopsis

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. Typically, these equations are highly nonlinear; in many cases they are also vectorial systems, and they represent a challenge even for the most modern and sophisticated mathematical-analytical and mathematical-numerical techniques. 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 brief in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations with a discussion of their basic mathematical properties. Illustrated with photographs taken by the author.

About this title

About the Author

Prof. Peter Markowich is the recipient of the Wittgenstein Award 2000, the highest ranking Austrian Science Prize.

From the Back Cover

This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, 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 socioeconomic 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.

Edition details

• Publisher: Springer
• Publication date: 2006
• Language: English
• ISBN 10: 3540346457
• ISBN 13: 9783540346456
• Binding: Hardcover
• Number of pages: 216