Mathematics: Calculus III

Vector-valued functions. Calculus of functions of several variables: partial derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes' and Green's theorems. Prerequisite: C- or better in MATH 1248 or MATH 1242.

Prereqs enforced by the system: MATH 1248 or MATH 1242;

MATH 2248 (Calculus III) is a course in Multivariable Calculus. In this course, we take the ideas encountered in the first year of calculus to the third dimension. We will begin with a discussion of vector functions, which are needed to describe curves and surfaces in space. From there, we will learn how the standard topics of differential calculus (limits, continuity, derivatives, and optimization) apply to functions of several real variables. We will extend the idea of the definite integral to double and triple integrals, which we shall use to compute volumes, masses, and centroids. We will see that polar coordinates are useful in the evaluation of double integrals, and will introduce cylindrical and spherical coordinates to help us with triple integrals. Next, we will study vector fields, line integrals, and surface integrals, and towards the end of the course we will understand how everything we have learned is connected through the higher-dimensional versions of the Fundamental Theorem - Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.

Students are expected to attend class and complete the assignments on time. Participation in class is encouraged. In the case where a student is struggling, they are urged to seek help from the instructor, either by attending office hours or scheduling an appointment.

Students will be evaluated through homework and in-class quizzes and exams.