Real Analysis Part 4

Riemann Steiltjas Integral

What you'll learn
The Real Analysis is a very important and vast branch of Mathematics, applied in Higher Studies, and Riemann Stieltjes Integral is one of its content
This course serves as an invaluable tool in unifying equivalent forms of statistical theorems that apply to discrete and continous probability.
It also serves as an instructive and useful precursor of the Lebesgue Integral.
Students will learn that Riemann sums give us the systematic way to find the area of a curved surface when we know the mathematical function for that curve.
Requirements
The only pre-requisite is a knowledge of Calculus at high school level so that students of science and engineering who want deeper understanding of calculus or want to pursue subjects such as Theoretical Physics, Computational complexity, Statistics etc. would benefit from this course.
Description
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.

Overview

Section 1: Introduction of Riemann Steiltjes Integral

Lecture 1 Riemann Stieltjes Integral Introduction

Lecture 2 Riemann Stieltjes Integral Continued….

Lecture 3 Riemann Stieltjes Integral Assignment 1

Lecture 4 Riemann Stieltjes Integral Assignment 2

Lecture 5 Riemann Stieltjes Integral Assignment 3

Lecture 6 Riemann Stieltjes Integral Assignment 4

Lecture 7 Riemann Stieltjes Integral Assignment 5

Lecture 8 Riemann Stieltjes Integral Assignment 6

Lecture 9 Riemann Stieltjes Integral Assignment 7(Expected)

Lecture 10 Riemann Stieltjes Integral Assignment 8

Lecture 11 Riemann Stieltjes Integral Assignment 9

Section 2: Properties of Riemann Stieltjes Integral

Lecture 12 Riemann Stieltjes Integral Assignment 10

Lecture 13 Riemann Stieltjes Integral Assignment 11

Lecture 14 Riemann Stieltjes Integral Assignment 12

Lecture 15 Riemann Stieltjes Integral Assignment 13

Section 3: Riemann Stieltjes Sum

Lecture 16 Riemann Stieltjes Integral Assignment 14

Lecture 17 Riemann Stieltjes Integral Assignment 15

Lecture 18 Riemann Stieltjes Integral Assignment 16

Lecture 19 Riemann Stieltjes Integral Assignment 17

Lecture 20 Riemann Stieltjes Integral Assignment 18

Section 4: Riemann Stieltjes Integral Integration and Differentiation)

Lecture 21 Integration and Differentiation Assignment 1

Lecture 22 Fundamental Theorem of Calculus Assignment 2

Lecture 23 Integration by parts Assignment 3

Lecture 24 The use of Greatest Integer Function Assignment 4

Lecture 25 Assignment 5

Section 5: Integration of Vector Valued Functions

Lecture 26 Integration of Vector Values Functions

Lecture 27 Rectifiable Curves

Section 6: Riemann Steiltjes Integral Solved Examples

Lecture 28 Riemann Steiltjes Integral Examples Assignment 1

Lecture 29 Riemann Steiltjes Integral Examples Assignment 2

Lecture 30 Riemann Steiltjes Integral Examples Assignment 3

Lecture 31 Riemann Steiltjes Integral Examples Assignment 4

Lecture 32 Riemann Steiltjes Integral Examples Assignment 5

Lecture 33 Riemann Steiltjes Integral Examples Assignment 6

Lecture 34 Riemann Steiltjes Integral Examples Assignment 7

Lecture 35 Riemann Steiltjes Integral Examples Assignment 8

Lecture 36 Riemann Steiltjes Integral Examples Assignment 9

Lecture 37 Riemann Steiltjes Integral Examples Assignment 10

BSc. Graduates , Masters in Sciences( Mathematics), CSIR UGC NET and other Entrances Exams.