#### Description

Analysis of functions of several variables. (Credit will only be granted for one of Math 411 and 412.)

#### Prerequisites

A C- or better in MATH 410

#### Topics

**Preliminary Notions**

The topology of sets and sequences in Rn

Continuity and its ramifications for functions of several variables

**Potential Functions**

Directional derivatives

Gradient

Differentiability

Weak and strong Mean Value Theorems

Chain rule

Tangent plane

**Mappings**

Differentiability

General Mean Value Theorem

Inverse and implicit function theorems with applications

**Multiple Integration**

Potential function integration

Area measure

Iterated integrals

**Line Integration**

Arc length

Line integration

Conservative vector fields

Green's Theorem and Green's Identities

**Surfaces (time permitting)**

Simple smooth surface elements

Orientation

Surface area

Divergence theorem

Stokes' theorem