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.