William Cox - Ordinary Differential Equations

The style of presentation is novel, and is intended to engage the reader at crucial points. The problems within the text are exercises designed to lead the reader into the subsequent text - it prepares them for what is to come. Some of these are quite simple, while others form substantial pieces of work which the impatient reader may avoid by continuing with the text. I refer to this approach as ask and answer (a question leads you into the answer, encouraging you to discover the ideas for yourself if you wish) as opposed to tell and test (we tell you in the text, then test what you have learnt in the exercises). Most sections have reinforcement exercises, and all chapters but the last have end-of-chapter exercises. These include essay type questions, which exercise your appreciation and understanding of the material.

These may also provide small group discussion topics. Also you are encouraged to write your own verbal summary of each chapter, as concisely as possible, and compare your result with the Appendix. Writing such summaries is surprisingly instructive, and provides you with an overview of the topic of the chapter, and the interrelations between its components. While answers to most exercises are included, you are encouraged to verify your answers for yourself where possible. This develops confidence and provides plenty of exercise in manipulative skills. Some sections, and exercises, are projects.

These give you the opportunity to develop material for yourself, by reference to other books such as those in the bibliography, or by your own work. Such material is optional and provides opportunities for the enthusiastic reader to delve deeper. Lastly, I have tried to make the material enjoyable. That doesnt mean it will always be easy! Bill Cox, September 1995

Bill Cox, Computer Science and Applied Mathematics, Aston University