# Mathematics Department

## Math 111 Descriptions

Descriptions of some Fall 2021 Math 111 sections

F03 MWF (Nick Davidson)
This section of Math 111 is for students interested in applications of calculus to natural sciences, especially biology, chemistry, and related fields.  This course will develop the standard tools of calculus (limits, continuity, derivatives, and integrals), and use them to analyze problems with a biological or chemical motivation.   For example, we will use differential equations to describe the growth of populations in the presence of limited resources, as well as the diffusion of a chemical through a membrane. Even though this course will use natural sciences as a source of examples and applications, no prior experience with these subjects is required.

F04 MTuWF  (Jerry Shurman)
This section of Math 111 meets four days a week. It is meant for students who have already taken an AP/IB style calculus course and want to see a variant approach to the subject, but it should also serve students who found high school algebra fluid and comfortable, and who are motivated to engage with calculus in part through analytic arguments--i.e., arguments that use symbols substantively. The earliest example of integration is Archimedes's quadrature of the parabola, and so we will begin there. After that, we will introduce the rational power function, the logarithm function, the exponential function, and basic trigonometric functions, taking care with their definitions and making explicit how these functions rely on fundamental properties of the number system of calculus. We will integrate each of these functions without using the Fundamental Theorem of Calculus; computing each integral reduces to computing a related derivative, showing that the Fundamental Theorem genuinely manifests in practice. Also we will differentiate each of these functions. Toward the end of the semester we will cover some standard topics: optimization and related rates problems, basic methods of antidifferentiation, and possibly the Taylor series of the functions mentioned above. Because these topics will come at the end, students who aren't conversant with AP/IB calculus and take this course concurrently with freshman physics may need to do some separate reading for the calculus being used in that course. To preview the notes for this section of Math 111, see http://people.reed.edu/~jerry/111/calc.html