Math 111 F01 Fall 202425 MTuWF 12:0012:50 (Jerry Shurman)This class is not technical like an honors class for ambitious incoming mathematics students at a large university. Incoming Reed students who are confident of majoring in mathematics and who can place out of Math 111 probably should take Math 112 immediately. But students with a range of interests who want to engage actively with a more causal treatment of calculus than AP/IB may enjoy how this class treats the subject. The earliest example of integration is Archimedes' 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 calculus number system. We will integrate each of these functions without using the Fundamental Theorem of Calculus; computing each integral reduces to computing a related normalized derivative value obtained by algebra or geometry, showing that the Fundamental Theorem is an actual phenomenon. The general derivatives of these functions follow from the normalized values. 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 late in the term, students who aren't conversant with AP/IB calculus and take this course concurrently with introductory physics at Reed may need to do some separate reading for the calculus being used in that course. A link to an html wrapper page for the course notes for this section of Math 111 is just below, with a link from there to the notes as pdf. To discuss with the instructor whether this section might be a good choice for you, email Jerry Shurman at jerry@reed.edu .
