An introduction to the variation of a function

Abstract

{According to the brazilian dictionary, "to analyze" is to observe and to think in something. In Mathematics, “Analysis” is the name given to one of the four major areas. Namely Geometry, Algebra, Analysis and Applied Mathematics. In particular, it is possible to subdivide the third one into five large groups. They are Real Analysis, Complex Analysis, Functional Analysis, Harmonic Analysis and Numerical Analysis. In this article, a topic of Real Analysis has been introduced. More precisely, we study the concept of variation of a function will be introduced, which is extremely important while dealing with the Riemann-Stieltjes Integral and the Lebesgue Integral. The variation is a concept related to polynomial series, partitions and supreme, so the readers are supposed to be well-founded in their knowledge. After some preliminary definitions, some central propositions and theorems in the study of functions of bounded variation have been presented.