Analysis II

3 Credits · Level: Graduate, Undergraduate

This course is about analysis in several dimension. 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-137). 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 in analysis. This course is expected to result in an appreciation for some of the central theorems of analysis such as the Inverse Function Theorem, Taylor's formula, the Change of Variable Formula in multiple integrals, and the Integral Theorems by Green, Gauss, and Stokes.