COURSE OUTLINE

Bibliography:

1- I.P. Natanson, Theory of Functions if a Real Variable (Dover)

2- W. Fleming, Functions of Several Variables (Springer)

3- J. Jost, Postmodern Analysis (Springer)

4-M. Giaquinta, G. Modica: Mathematical Analysis: An Introduction to Functions of Several Variables (Birkhauser)

TOPICS: (notes will be supplied for some topics)

1- Functions of Bounded Variation on the line [1, ch.8]

2- Lebesgue measure and integration in R^n [2, ch. 5 and 3, ch. 4; see also 1. for one variable] and 4., ch. 2]

3- L^p spaces and Sobolev Spaces [3, ch. 5]

4-Hausdorff outer measures (tentative) [4., 2.5]

5- Hypersurface area and Gauss-Green theorems [4, 2.6]