The book contains the theory, techniques, and applications covered in the traditional introductory courses in differential equations. A major feature of this text is the quantity and variety of applications of current interest in physical, biological, and social sciences. We have furnished a wealth of applications from such diverse fields as astronomy, bioengineering, biology, botany, chemistry, ecology, economics, electric circuits, finance, geometry, mechanics, medicine, meteorology, pharmacology, physics, psychology, seismology, sociology, and statistics. The goal of this book, then, is to make elementary differential equations more useful, more meaningful, and more exciting to the student. To accomplish this, we strive to demonstrate that differential equations are very much ”alive” in present-day applications. We have tried to make the presentation direct, yet informal. Definitions and theorems are stated precisely and rigorously, but theory and rigor have been minimized in favor of comprehension of technique. The general approach is to use a larger number of routine examples to illustrate the new concepts, definitions, methods of solution, and theorems. Thus, it is intended that the material will be easily accessible to the student. Hopefully the presence of modern applications in addition to the traditional applications of geometry, physics, and chemistry will be refreshing to the teacher. Numerous routine exercises in each section will help to test and strengthen the student’s understanding of the new methods under discussion. There are over 1600 exercises in the text with answers to odd-numbered exercises provided.
The first eight chapters of this book are reproduced from our text ”Ordinary differential equations with modern applications”, second edition (1981; Zbl 0507.34002).
The additional chapters 9, 10, and 11 treat difference equations, Fourier series, and partial differential equations, respectively. Each of these chapters provides a thorough introduction to its respective topic. We feel that the chapters on difference equations and partial differential equations are more extensive than one usually finds at this level. Our purpose for including these topics is to allow more course options for users of this book.