Course Description
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
Prerequisite
MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Course Objectives
Students should understand the concept of continuity and differentiability in two and three variables. They should be able to calculate partial derivatives, directional derivatives and gradients. Students should be able to solve maximum and minimum problems using Lagrange multipliers. Students are introduced to multiple integrals and are expected to be able to calculate volumes and areas using multiple integrals. They are expected to understand and apply Green's theorem.
Topical Outline
1. Review of vector algebra and geometry. 2. Parametric curves, velocity, acceleration. 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, and physical applications as time allows. Polar, cylindrical, and spherical coordinates. 4. Line integrals, work, path-independence, and Green's Theorem. 5. Brief survey of surface integrals and flux, curl, divergence, Stokes's and Divergence Theorems.
General Education Core
CORE III: Quantitative ReasoningSyllabus