Weiglhofer W.S., Lindsay K.A. Ordinary Differential Equations and Applications: Mathematical Methods for Applied Mathematicians, Physicists, Engineers and Bioscientists

Woodhead Publishing, 1999. - 216 pages. ISBN: 1898563578A thorough understanding of and an ability to solve ordinary differential equations are essential cornerstones in most areas of mathematical science: from applied mathematics to physics, from engineering to biosciences. This book aims to provide a solid foundation for the reader who wishes to solve problems in the mathematical and applied sciences that can be expressed in terms of ordinary differential equations or through the calculus of variations.
We approach the study of ordinary differential equations from two directions. Firstly, there is, in the more traditional setting, the provision of solution techniques for various types of ordinary differential equations; and secondly, we give a practical and more modern approach to mathematical modelling leading to ordinary differential equations.
The text presents ordinary differential equations and calculus of variations (a topic intimately connected to differential equations) from an applied perspective. The book is based on the lecture notes compiled by the authors for the undergraduate course Mathematical Methods taken in the third year of the honours mathematics programme at the Department of Mathematics, University of Glasgow. This course was introduced in the academic year 1994/95 and comprises 25 lectures and 10 tutorials. Like the original lecture notes, the present book aims to provide a self-contained and solid introduction into ordinary differential equations and their applications. Needless to add, the theory and practice of ordinary differential equations is a vast topic in mathematical science. Even a cursory glance at the shelves of any university library will produce dozens of treatments of this topic in one form or another.1 The material covered in the book is suitable for undergraduates (from their second year at a university onwards) and graduate students of applied mathematics, physics, engineering, chemistry and biosciences. Because of the way it was developed, the book lends itself naturally to a course spanning 20-25 lectures during a term or semester. It provides a spring-board for advanced study and research in the applied mathematical sciences.
The book is structured into ten chapters that develop the theme of ordinary differential equations of first, of second and of higher order plus detailed applicational aspects that arise with these equations. Boundary value problems and calculus of variations round off the main part of the text. An important feature for students and other readers is the wide variety of examples. There are many worked examples embedded directly into the text and each chapter is supplemented by a section containing additional tutorial examples. Extended solutions to these tutorial examples are given in an appendix.
A second appendix specifies a small number of projects. These are more complex than the tutorial examples and will therefore require a longer period of effort through self-study or group work.