Calculus II

April 2, 2025 June 15, 2025

University of Denver

Undergraduate

Calculus, which is covered at DU with the courses MATH 1951, 1952, 1953 and 2080, is the study of infinitesimal change. Whereas MATH 1951 is focused on the derivative, MATH 1952 is focused on integrals. Both of these concepts are defined in terms of a limit, which is a central idea that underlies all of Calculus. It turns out that these two special limits, the integral and the derivative, are closely related, and in particular the integral is tied to the idea of an antiderivative. This will force us to learn to 'undo' the derivative rules which we learned in 1951. Integrals have several important applications. The most fundamental is that an integral gives the area under the graph of a positive function on an interval. Beyond measuring area under the curve, we can use the integrals to compute many other important quantities such as the volume or surface areas of an object, the average value of a continuous function, the amount of work done by a force (as in physics) or the probability of a certain random event.