#### 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.

#### Prerequisites

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