#### 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

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