Course Description

This course is a continuation of MATH 302 Elements of Analysis I, focusing on further exploration of integration and related ideas. One part of the course will be devoted to Lebesgue theory where integration of more general functions over more general domains than those encountered in MATH 302 is considered. Connections between analysis and linear algebra will be explored during the functional analysis part of the class. These will include a study of normed spaces, such as function and Hilbert spaces, and linear maps between them. Applications to Fourier series will also be discussed. The last topic of the class will be tensors and tensor algebras, leading to the study of differential forms and culminating in a generalization of Stokes’ Theorem.  This part will also feature an exciting interplay between integration and algebra.