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Course11110506946 lectures

A Basic Course in Real Analysis

Prof. P.D. Srivastava · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

Rational Numbers and Rational Cuts

  1. Rational Numbers and Rational Cuts Video

Irrational numbers, Dedekind\'s Theorem

  1. Irrational numbers, Dedekind's Theorem Video

Continuum and Exercises

  1. Continuum and Exercises Video
  2. Continuum and Exercises (Contd.) Video

Cantor\\\'s Theory of Irrational Numbers

  1. Cantor's Theory of Irrational Numbers Video
  2. Cantor's Theory of Irrational Numbers (Contd.) Video

Equivalence of Dedekind and Cantor\'s Theory

  1. Equivalence of Dedekind and Cantor's Theory Video

Finite, Infinite, Countable and Uncountable Sets of Real Numbers

  1. Finite, Infinite, Countable and Uncountable Sets of Real Numbers Video

Types of Sets with Examples, Metric Space

  1. Types of Sets with Examples, Metric Space Video

Various properties of open set, closure of a set

  1. Various properties of open set, closure of a set Video

Ordered set, Least upper bound, greatest lower bound of a set

  1. Ordered set, Least upper bound, greatest lower bound of a set Video

Compact Sets and its properties

  1. Compact Sets and its properties Video

Weiersstrass Theorem, Heine Borel Theorem, Connected set

  1. Weiersstrass Theorem, Heine Borel Theorem, Connected set Video

Tutorial - II

  1. Tutorial - II Video

Concept of limit of a sequence

  1. Concept of limit of a sequence Video

Some important limits, Ratio tests for sequences of Real Numbers

  1. Some Important limits, Ratio tests for sequences of Real Numbers Video

Cauchy theorems on limit of sequences with examples

  1. Cauchy theorems on limit of sequences with examples Video

Fundamental theorems on limits, Bolzano-Weiersstrass Theorem

  1. Fundamental theorems on limits, Bolzano-Weiersstrass Theorem Video

Theorems on Convergent and Divergent sequences

  1. Theorems on Convergent and divergent sequences Video

Cauchy sequence and its properties

  1. Cauchy sequence and its properties Video

Infinite series of real numbers

  1. Infinite series of real numbers Video

Comparison tests for series, Absolutely convergent and Conditional convergent series

  1. Comparison tests for series, Absolutely convergent and Conditional convergent series Video

Tests for absolutely convergent series

  1. Tests for absolutely convergent series Video

Raabe\\\'s test, limit of functions, Cluster point

  1. Raabe's test, limit of functions, Cluster point Video

Some results on limit of functions

  1. Some results on limit of functions Video

Limit Theorems for functions

  1. Limit Theorems for functions Video

Extension of limit concept (one sided limits)

  1. Extension of limit concept (one sided limits) Video

Continuity of Functions

  1. Continuity of Functions Video

Properties of Continuous Functions

  1. Properties of Continuous Functions Video

Boundedness Theorem, Max-Min Theorem, and Bolzano\'s Theorem

  1. Boundedness Theorem, Max-Min Theorem and Bolzano's theorem Video

Uniform Continuity and Absolute Continuity

  1. Uniform Continuity and Absolute Continuity Video

Types of Discontinuities, Continuity and Compactness

  1. Types of Discontinuities, Continuity and Compactness Video

Continuity and Compactness (Contd.), Connectedness

  1. Continuity and Compactness (Contd.), Connectedness Video

Differentiability of real valued function, Mean Value Theorem

  1. Differentiability of real valued function, Mean Value Theorem Video

Mean Value Theorem (Contd.)

  1. Mean Value Theorem (Contd.) Video

Application of MVT, Darboux Theorem, L Hospital Rule

  1. Application of MVT , Darboux Theorem, L Hospital Rule Video

L\' Hospital Rule and Taylor\'s Theorem

  1. L'Hospital Rule and Taylor's Theorem Video

Tutorial - III

  1. Tutorial - III Video

Riemann/Riemann Stieltjes Integral

  1. Riemann/Riemann Stieltjes Integral Video

Existence of Reimann Stieltjes Integral

  1. Existence of Reimann Stieltjes Integral Video

Properties of Reimann Stieltjes Integral

  1. Properties of Reimann Stieltjes Integral Video
  2. Properties of Reimann Stieltjes Integral (Contd.) Video

Definite and Indefinite Integral

  1. Definite and Indefinite Integral Video

Fundamental Theorems of Integral Calculus

  1. Fundamental Theorems of Integral Calculus Video

Improper Integrals

  1. Improper Integrals Video

Convergence Test for Improper Integrals

  1. Convergence Test for Improper Integrals Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. P.D. Srivastava
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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