Ordinary differential equations in theory and practice

Robert Mattheij, Jaap Molenaar9780898715316, 0898715318

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.

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Table of contents :
Ordinary Differential Equations in Theory and Practice……Page 1
Contents……Page 10
Preface to the Classics Edition……Page 14
Preface……Page 16
I Introduction……Page 20
II Existence, Uniqueness,and Dependence on Parameters……Page 44
III Numerical Analysis of One-Step Methods……Page 70
IV Linear Systems……Page 98
V Stability……Page 126
VI Chaotic Systems……Page 156
VII Numerical Analysis of Multistep Methods……Page 190
VIII Singular Perturbations and Stiff Differential Equations……Page 218
IX Differential-Algebraic Equations……Page 250
X Boundary Value Problems……Page 276
XI Concepts from Classical Mechanics……Page 298
XII Mathematical Modelling……Page 320
Appendix A……Page 396
References……Page 416
Index……Page 420