Why We Wrote This Book
The rapid development and increased use of technology has required a closer scrutiny of the content of the traditional differential equations course. Because modern technology can quickly draw slope fields, graph complicated functions, and display data with just a few keystrokes, we no longer need to avoid subject matter which requires such things. Yet this same technology is capable of giving incomplete, misleading, or incorrect solutions, so it is important to look at all solutions from more than one point of view. This book does just that, equipping students with confidence because they fully understand the solution by using graphical and numerical means in addition to the traditional analytical ones. We feel that the appropriate use of technology is vital to using differential equations as a tool. Thus, we expect students to have access to mathematical software or to a calculator that draws slope fields or direction fields, generates numerical solutions, and simultaneously displays data and graphs of functions. With these tools students become active participants in the learning process and they are encouraged to think, experiment, and comprehend. By these means they understand the origins, qualitative behavior, and interpretations of solutions of ODEs.
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