by
Mike MestertonGibbons Professor Department of Mathematics Florida State University Tallahassee, Florida 323064510 Phone: (850) 6442580 Email: mesterto@math.fsu.edu 
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Biocalculus introduces the fundamental ideas of calculus from the perspective of a biologist, i.e., it uses biological data to motivate and elucidate concepts that are essential for constructive use of Mathematica (or any other mathematical software) in solving biological problems. The approach is heuristic, but systematic. One can develop a great deal of mathematical maturity with remarkably little exposure to mathematical rigor, and in these lectures I encourage students to develop as much as possible of the first with as little exposure as possible to the second.
This is not, however, a nobrainer calculus for those who have drifted into biology under the illusion that it offers an escape from mathematics. On the contrary, calculus plays an increasingly central role in biology, and so its concepts must be mastered, despite  or, rather, because of  the widespread availability of powerful mathematical software. Every application of mathematics involves formulation (of a relevant problem), calculation (of requisite quantities) and interpretation (of results); and insofar as concepts and methods can be separated, formulation and interpretation require understanding of concepts, whereas calculation requires knowledge of method. Mathematica, in essence, is a magical black box for performing calculations. Although its graphical output may facilitate interpretation, Mathematica neither formulates nor interprets, and to that extent there is a greater need than ever before for biology majors to know the concepts thoroughly. This course addresses that need.
On the other hand, concepts and method are not so readily separated. Because all black boxes  even magical black boxes  are fallible, one cannot in general use mathematical software wisely unless one develops reliable instincts about whether it has truly yielded an answer to the problem one gave it (or meant to give it). Although using the software may refine such instincts, the only way to acquire them in the first instance is through extensive experience of solving problems without the software's help. In other words, there is still a need to enter the black box, which this course addresses as well.
An exception to the rule of fallibility, however, is that mathematical software is extraordinarily reliable for plotting simple graphs, in particular those of polynomials. I exploit that reliability by assuming at the outset that plotting graphs is a computer task, so that early exercises can introduce the software by requiring graphs to be drawn. In each set of exercises, an asterisked number indicates that a relevant Mathematica program can be downloaded from this site, and a number in bold refers to answers or hints at the end. All other problems can be solved by modifying an existing program or solution.
In sum, this course straddles the contentious divide between reform and tradition in calculus. Its goal is to mould biology majors into better scientists by enabling them to use Mathematica (or similar software) wisely, but its approach embodies a firm conviction that skill in using high technology for complex procedures requires skill in using low technology (e.g., pencil and paper) for simple procedures. So its outlook is thoroughly modern. But its style is deliberately oldfashioned.

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