Calculus III - Vector Calculus

Service Description

Third course in calculus and analytic geometry including: vector analysis, Euclidean space, partial differentiation, multiple integrals, line and surface integrals, the integral theorems of vector calculus. Earns 4 credit hours in Calculus from the Univeristy of Illinois. Prerequisite: Calculus II (or equivalent), or 4 or 5 on Calculus BC test, or 5 or higher on IB Mathematics HL with a score of 5 or higher Topics: • Vectors o Tangent and velocity vectors o Length of a vector, dot product, and cross product o Velocity and acceleration applications • Perpendicularity o Planes in three dimensions o Plotting curves on planes • The Gradient o The gradient as a normal vector o Maximization and minimization • Gauss-Green Formula o 2D integrals for area and volume measurements o Correct parameterization in non-ideal situations • Vector fields and their trajectories o Flow along and flow across o The gradient test in 2D and 3D o Line integrals and path integrals o Sources, sinks, divergence, and rotation of a vector field • Transforming 2D and 3D integrals o Area and volume conversion factors o Measurements of volume, mass, and density o Integrating on cylinders, spheres, and tubes • Spherical Coordinates o Integrating with spherical coordinates o Applications including ice cream cones and a flower • 3D Surface Measurements o Sources, sinks and Gauss’s formula in 3D o Measuring area on surfaces o Surface integrals and applications o Stokes’ formula • 3D Flow Along Measurements o Curl of a 3D vector field o Applying Stokes’ formula to measure the swirl o Path dependence and independence Format Course content is drawn from Vector Calculus written by Bill Davis, Horacio Porta and Jerry Uhl ©2006‐2010. Math 241 utilizes the CAS-ILE system. See https://cas-ile.illinois.edu/ for more information. This online system helps students learn math topics through dynamic exploration and visualization.