This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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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