This chapter and the subsequent 27 chapters are about differential equations and how they are applied by biologists. As the branch of mathematics called differential equations is a direct application of ideas from calculus, and as this is a mathematics text, I should begin by telling you a little bit about what is meant by the term differential equation. However, I'll digress first to begin an argument for including mathematics in the tool kit of a working biologist.

Modeling in the Biological Sciences

First, I freely admit to not being a biologist. In fact, until I started teaching the course on which this book was based, I knew very little of recent work in biology. I took biology in high school, dissected a worm and a frog, and happily found other interests. Subsequently, I kept minimally abreast of the subject by reading articles from popular science journals such as Science News and Scientific American. However, since I started teaching this course, I have endeavored to educate myself about modern biology and have found it to be a glorious thing. In fact, I would be happy to argue the case that our understanding of biology now ranks as the (or at least one of the) crowning achievements of human knowledge.

My recent and ongoing education in biology has taught me the following lesson: With some notable exceptions, biology at the cusp of the twenty-first century is very much an experimentally driven science. Life is extremely complicated, and sorting out these complications is the task at hand.