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; Open to Degree and PACE students

Calculus III (Multivariable Calculus) is the third course in our three-course calculus sequence. Successful completion of Calculus II (MATH 022 or MATH 023) is a prerequisite for Calculus III. The course topics include vector functions, with a discussion of derivatives, velocity, acceleration, arc length and curvature; functions of several variables, where we extend the basic ideas of differential calculus to these functions; the concept of the definite integral is extended to double and triple integrals, with applications such as volume, mass and centroids, while introducing two new coordinate systems in three-dimensional space (cylindrical coordinates and spherical coordinates); a study of vector fields, line integrals and surface integrals, leading to a discussion of Stokes’ Theorem and the Divergence Theorem. Topics will be presented with a level of depth and rigor appropriate for students pursuing degrees in technical fields such as mathematics, statistics, engineering, or the physical sciences. The computer algebra system Mathematica will be used throughout the course.

Grades will be based on WebAssign homework, Mathematica labs, quizzes, exams, and a cumulative final exam.