Description

An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections of the course will use the software package MATLAB. Credit will be granted for only one of the following: MATH 241 or MATH 340.

Prerequisites

a C- or better in MATH 141

Topics

(by chapter)

XI. Vectors, Lines and Planes.

Cartesian coordinates of space
Vectors
Lines
Planes
Dot and cross product

XII. Vector-valued Functions

Vector-valued functions
Tangents
Normals
Curvature

XIII. Partial Derivatives

Quadric surfaces
Partial derivatives
Chain rule
Directional derivatives
Gradients
Extreme values
Lagrange multipliers

XIV. Multiple Integrals

Double and triple integrals
Change of variable
Volume
Surface area
Moments and centers of gravity

XV. Calculus of Vector Fields

Line and surface integrals
Green's theorem
Stokes' theorem
Divergence theorem