JACOB NIELS

Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great det...

This is the second volume of A Course in Analysis and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed a...

In this third volume of A Course in Analysis, two topics indispensible for every mathematician are treated: Measure and Integration Theory; and Complex Function Theory. In the first part m...

In the part on Fourier analysis , we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a firs...