The fourth week we will revisit the concept of integration and extended it to multivariable functions.  In particular, the theoretical part of 4th week's material corresponds to the material described in the second section of Chapter 8 of the BG book, titled ``Integration for second time''.

This includes the following concepts:

1) Integration of multivariate functions;

2)  Multiple integrals;

3) Extension of Fubini's theorem;

4) Change of coordinates;

5) Riemann measurable sets.

Examples and applications related to these notions are described in the corresponding left column of the BG book, and in particular in Section I with title  ``Volumes, areas, centroids and solids''.