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, showing that the Fundamental Theorem genuinely occurs in practice. Naturally this requires differentiating each of these functions as well.

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 the course notes for this section of Math 111 is just below. To discuss with the instructor whether this section might be a good choice for you, email Jerry Shurman at jerry@reed.edu .

Course notes | Back to my home page