Ordinary Differential Equations in Theory and Practice (Classics in Applied Mathematics)

图书介绍

In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role.

Originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained.


Audience
The book is intended as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.

Contents
Preface to the Classics Edition;
Preface;
Chapter 1: Introduction;
Chapter 2: Existence, Uniqueness, and Dependence on Parameters;
Chapter 3: Numerical Analysis of One-Step Methods;
Chapter 4: Linear Systems;
Chapter 5: Stability;
Chapter 6: Chaotic Systems;
Chapter 7: Numerical Analysis of Multistep Methods;
Chapter 8: Singular Perturbations and Stiff Differential Equations;
Chapter 9: Differential-Algebraic Equations;
Chapter 10: Boundary Value Problems;
Chapter 11: Concepts from Classical Mechanics;
Chapter 12: Mathematical Modelling;
Appendices;
References;
Index.

About the Author
Robert Mattheij is a Professor of Scientific Computing in the Department of Mathematics and Computer Science at Technische Universiteit Eindhoven, The Netherlands. He heads the Scientific Computing Group, which specializes in modeling and simulation of problems arising in an industrial context. His present research involves viscous flow and local defect correction methods.

Jaap Molenaar is a Professor of Applied Analysis in the Department of Mathematics and Computer Science at Technische Universiteit Eindhoven, The Netherlands, and in the Department of Applied Mathematics at the University of Technology, Twente, The Netherlands. His research is centered around differential equations and recently has focused on mathematical aspects of polymer flow.