Course Description
Calculus of functions of two and three variables: Parametric curves and applications to planetary motion. Derivatives, the gradient, Lagrange multipliers. Multiple integration, area, volume, and physical applications; polar, cylindrical, and spherical coordinates. Line and surface integrals; Green's, Stokes', and Divergence theorems, with applications to physics.
Athena Title
Calc III Sci and Math Honors
Equivalent Courses
Not open to students with credit in MATH 2270, MATH 2500, MATH 2500E, MATH 2500H
Prerequisite
(MATH 2260 or MATH 2260E or MATH 2310H or MATH 2410 or MATH 2410H) and permission of Honors
Grading System
A - F (Traditional)
Student learning Outcomes
- Students will be able to calculate partial derivatives, directional derivatives, and gradients.
- Students will be able to solve maximum and minimum problems using Lagrange multipliers.
- Students will learn to calculate area, volume, center of mass, and moment of inertia using multiple integrals.
- Students will understand integrals along curves and surfaces, culminating in various generalizations of the Fundamental Theorem of Calculus.
- Students will apply the tools learned in this course to areas such as planetary motion, gravitation, data fitting, Gauss's Law, and fluid dynamics.
Topical Outline
- 1. Review of vector algebra.
- 2. Parametric curves; Kepler's laws.
- 3. Partial differentiation: directional derivatives, gradients, tangent planes, chain rule, maximum/minimum problems, and Lagrange multipliers.
- 4. Multiple integration: double and triple integrals, change of order of integration, applications to computations of areas, volumes, center of mass and moments of inertia. Polar, cylindrical, and spherical coordinates.
- 5. Line integrals, work, path-independence, and Green's Theorem.
- 6. Surface integrals and flux. Curl, divergence, Stokes's and Divergence Theorems and their applications.
General Education Core
CORE III: Quantitative Reasoning
