Calculus of functions of two and three variables: Parametric
curves, derivatives, gradient, Lagrange multipliers. Multiple
integration, area, volume, polar, cylindrical, and spherical
coordinates. Line integrals and Green's Theorem. Introduction to
surface integrals and Stokes's and Divergence Theorems. This is
an accelerated version of Calculus III for Science and
Engineering that covers fewer topics and applications.
Athena Title
Calculus III for Engineering
Equivalent Courses
Not open to students with credit in MATH 2270, MATH 2270H, MATH 2500E, MATH 2500H
Prerequisite
MATH 2260 or MATH 2260E or MATH 2260H or MATH 2310H or MATH 2410 or MATH 2410H
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Student learning Outcomes
Students will learn to visualize and work in 3D space. They will sketch curves, surfaces, and regions in three dimensions, and choose the most effective coordinate system (polar, cylindrical, spherical) to set up and solve problems involving area and volume.
Students will solve optimization problems, finding maximum and minimum values of functions with multiple variables, including solving constrained optimization problems using Lagrange multipliers, with applications in science, engineering, and economics.
Students will learn to analyze changing systems, by calculating how quantities change along paths in space, determining work done by forces, and measuring the flow of fluids and electromagnetic fields through curves and surfaces.
Near the end of the course, students will learn to connect concepts from throughout the semester by applying the major Green's Theorem, Stokes' Theorem, and the Divergence Theorem to relate different types of integrals and simplify complex calculations in physics and engineering contexts.
Students will learn to translate between different kinds of representations of mathematical ideas, moving between geometric descriptions, algebraic equations, and computational solutions when modeling phenomena involving multiple variables.
Topical Outline
This course takes the calculus students already know and applies it to problems involving two or three variables at once. Students learn to work with curves and surfaces in 3D space, measure how things change in different directions using partial derivatives and the gradient, and find maximum and minimum values for real-world problems with multiple factors using techniques like Lagrange multipliers. Students calculate areas and volumes of irregular shapes by integrating in polar, cylindrical, and spherical coordinates. The course ends with vector calculus—learning to measure flow along curves and across surfaces—and brings everything together with Green's, Stokes', and Divergence Theorems, which are the big ideas used in physics and engineering.
