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This book consists of eleven calculus “research projects” embedded in short stories. Each project is based on some part of the curriculum of the “standard” two-semester calculus course on the differentiation and integration of functions of a single variable. The required “solution” to a problem usually consists of a report to a “client” (a hockey coach, a pirate captain, a fishing lodge owner) about how calculus can be used to solve the problem posed by the client. The recommendations in the report must be comprehensible to the client, who typically knows no calculus, and must also be supported by a detailed mathematical analysis, so that any “math expert” that the client might hire in the future can understand the reasoning leading to the recommendation.
The first goal of these projects is to develop skills in using calculus to analyze, and provide answers to, complex problems not presented in the language of mathematics. This of necessity involves having enough conceptual insight and technical ability to use calculus effectively in modeling situations. The second goal is to develop students' ability to write clear, complete accounts of how calculus has been used to solve complex problems. This requires facility at expository technical writing. Many students who use university level mathematics later in their careers will need modeling and technical writing skills more than technical mastery of concepts from more advanced areas of mathematics. “Writing across the curriculum” is in fashion nowadays, and this affords a way to implement it in a mathematics course.
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