These notes are written for a one-semester calculus course which meets threetimes a week and is, preferably, supported by a computer lab. The courseis designed for life science majors who have a precalculus back ground, andwhose primary interest lies in the applications of calculus. We try to focuson those topics which are of greatest importance to them and use life scienceexamples to illustrate them. At the same time, we try of stay mathemat-ically coherent without becoming technical. To make this feasible, we arewilling to sacrifice generality. There is less of an emphasis on by hand cal-culations. Instead, more complex and demanding problems find their placein a computer lab. In this sense, we are trying to adopt several ideas fromcalculus reform. Among them is a more visual and less analytic approach.We typically explore new ideas in examples before we give formal definitions. In one more way we depart radically from the traditional approach to calculus. We introduce differentiability as a local property without usinglimits. The philosophy behind this idea is that limits are the a big stum-bling block for most students who see calculus for the first time, and theytake up a substantial part of the first semester. Though mathematicallyrigorous, our approach to the derivative makes no use of limits, allowingthe students to get quickly and without unresolved problems to this con-cept. It is true that our definition is more restrictive than the ordinary one,and fewer functions are differentiable in this manuscript than in a standardtext. But the functions which we do not recognize as being differentiableare not particularly important for students who will take only one semesterof calculus. In addition, in our opinion the underlying geometric idea of thederivative is at least as clear in our approach as it is in the one using limits.