Foreword
This site contains an introduction to the theory of Riemann integration for real functions of one real variable.
This theory can be introduced in several different, but completely equivalent, ways: by means of upper and lower sums, of Cauchy sums, of step functions. We prefer the last one (use of step functions) because it puts in evidence from the real beginning some facts that are very important in this theory, of which the most important one is that also discontinuous functions can be Riemann integrable.
The proof of the theorems in this theory is not
always simple; for this reason, in many cases, the proofs are
not included in this site: you may find them in good analysis
textbooks.
Extensive use of graphical and computational capabilities of personal computers is employed in the following pages, but, as usual, be careful: computer graphics can only help us in the comprehension of this subject, and it is not possible to construct a satisfactory theory only on this basis.
Some of the Tom & Jerry cliparts are
downloaded from the Hanna & Barbera Pages.
These pages collect all the materials on this subject prepared by Luciano Battaia for the students of class VB of Liceo Scientifico Grigoletti, school year 2002/2003.