Course Description
Calculus of functions of two and three variables. Topics include parametric curves, partial derivatives, gradient vectors, multivariable optimization, multiple integration in various coordinate systems, line and surface integrals, and multivariable versions of the Fundamental Theorem of Calculus. This accelerated course emphasizes core concepts with less depth than Calculus III for Science and Mathematics.
Athena Title
Calculus III for Engineering H
Equivalent Courses
Not open to students with credit in MATH 2270, MATH 2270H, MATH 2500, MATH 2500E
Prerequisite
(MATH 2260 or MATH 2260E or MATH 2260H or MATH 2310H or MATH 2410 or MATH 2410H) and permission of Honors
Semester Course Offered
Offered spring
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.
