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9780898715316 Academic Inspection Copy

Ordinary Differential Equations in Theory and Practice

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Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modelling 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 modelling, where such ODEs often play a significant role. Although 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 modelling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained.
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.
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