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

Math 2248; 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 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.

You should have a solid working knowledge of first year calculus at the level of math 021, math 022 We will meet four times a week. The MWF meetings will be 50 minutes while the Tuesday meetings will be between 50 minutes and 75 minutes. You will need some form of the textbook; Calculus by James Stewart; 9th edition. If you took math 021 at UVM during fall semester of 2021, you probably already have the book. You will need Webassign to do the course. You may already have a contract with Webassign from math 021. You should expect to spend about 8 to 10 hours on the course per week outside of class.

Your grade will be based on five tests with the lowest test grade dropped, a mandatory comprehensive final exam and homework. All graded work will be on webassign.