Analysis of Functions of Several Variables.

Catalog description

This course rigorously develops the theory underlying the differential calculus of multivariable functions. Topics include the vector and metric space structure of n-dimensional Euclidean space; properties of multivariable functions such as continuity and differentiability; implicit and inverse function theorems; submanifolds of n-dimensional Euclidean space; optimization and the method of Lagrange multipliers. Additional topics such as multiple integrals, vector calculus, and differential equations may be covered at the discretion of the instructor.