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. 


Prerequisites

Minimum grade of C- in MATH410


Level of Rigor

Advanced


Sample Textbooks

Advanced Calculus, by P.M. Fitzpatrick


Applications


If you like this course, you might also consider the following courses

MATH 437, MATH464, MATH 630, MATH 673


Additional Notes

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should consider this course 

Topics

The topology of sets  in R^n

Continuous, continuously differentiable, and C^2 functions

First and second order approximation theorems, possibly higher order approximations

The derivative matrix

The general chain rule

Inverse and implicit function theorems with applications

Smooth curves and surfaces in R^3, possibly smooth manifolds in R^n

Lagrange multipliers


Additional topics may include

Metric spaces, the contraction principle

The existence and uniqueness theorem for nonlinear first order differential equations

The Riemann integral in R^n

Introduction to integration on curves, surfaces,  Green’s theorem.