Real Analysis part 4

Riemann Stieltjes Integral is a generalization of the Riemann Integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. It serves as an instructive and useful precursor of the Lebesgue Integral. and an invaluable tool in unifying equivalent forms of statistical theorems that apply to discrete and continuous probability.

The definition of Riemann Stieltjes Integral uses a sequence of partitions P of the given interval [a,b].The integral, the, is defined to be the limit, as the norm (the length of the longest sub interval) of the partitions

The course introduces the definition and existence of the Riemann Stieltjes integral including the concepts of the following:

Common Refinement of a partition , Upper Riemann and Lower Riemann sum, Riemann Sum, Properties of Riemann Stieltjes Integral, Integration and Differentiation, The Fundamental Theorem Of Calculus,Integration Of Vector Valued Functions,

Rectifiable Curves,that also covers the Expected Theorems and Solved Examples  based above contents.

This course also describes the various identities of Riemann Stieltjes integral.

Overall , every thing has been covered with lots of concepts and solved examples , assignments, exercises and almost all the expected theorems.

For any queries related to the course, I would be happy to assist you. Just ping me via Inbox. You will get a course completion certificate after finishing the course.