Analysis II

3 Credits · Level: Graduate, Undergraduate

Prerequisite: MATH 3310 . Description: This course is about analysis in n-dimensional Euclidean spaces. Topics include the Euclidean spaces, metric spaces, functions of several variables, differentiation and integration of functions of several variables, and the theorems of vector calculus. Most of the topics will be familiar from Multivariable Calculus (MATH-2370). Many proofs will be presented and discussed. Students will be made familiar with some concepts of topology, the basic theory of metric spaces as well as the importance of compact sets and connected sets in analysis. This course is expected to result in an appreciation for some of the central theorems of analysis such as the Inverse and Implicit Function Theorems, the Change of Variable Formula in multiple integrals, and the Integral Theorems by Green, Gauss, and Stokes.