Real Analysis with Prof. S.H. Kulkarni

Video Lectures

Displaying all 52 video lectures.
I. Review of Set Theory
Lecture 1
Introduction to Real Analysis
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Introduction to Real Analysis
Lecture 2
Functions and Relations
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Functions and Relations
Lecture 3
Finite and Infinite Sets
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Finite and Infinite Sets
Lecture 4
Countable Sets
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Countable Sets
Lecture 5
Uncountable Sets, Cardinal Numbers
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Uncountable Sets, Cardinal Numbers
II. Sequences and Series of Real Numbers
Lecture 6
Real Number System
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Real Number System
Lecture 7
LUB Axiom
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LUB Axiom
Lecture 8
Sequences of Real Numbers
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Sequences of Real Numbers
Lecture 9
Sequences of Real Numbers - continued
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Sequences of Real Numbers - continued
Lecture 10
Sequences of Real Numbers - continued...
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Sequences of Real Numbers - continued...
Lecture 11
Infinite Series of Real Numbers
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Infinite Series of Real Numbers
Lecture 12
Series of nonnegative Real Numbers
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Series of nonnegative Real Numbers
Lecture 13
Conditional Convergence
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Conditional Convergence
III. Metric Spaces -- Basic Concepts
Lecture 14
Metric Spaces: Definition and Examples
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Metric Spaces: Definition and Examples
Lecture 15
Metric Spaces: Examples and Elementary Concepts
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Metric Spaces: Examples and Elementary Concepts
Lecture 16
Balls and Spheres
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Balls and Spheres
Lecture 17
Open Sets
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Open Sets
Lecture 18
Closure Points, Limit Points and isolated Points
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Closure Points, Limit Points and isolated Points
Lecture 19
Closed sets
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Closed sets
IV. Completeness
Lecture 20
Sequences in Metric Spaces
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Sequences in Metric Spaces
Lecture 21
Completeness
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Completeness
Lecture 22
Baire Category Theorem
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Baire Category Theorem
V. Limits and Continuity
Lecture 23
Limit and Continuity of a Function defined on a Metric space
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Limit and Continuity of a Function defined on a Metric space
Lecture 24
Continuous Functions on a Metric Space
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Continuous Functions on a Metric Space
Lecture 25
Uniform Continuity
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Uniform Continuity
VI. Connectedness & Compactness
Lecture 26
Connectedness
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Connectedness
Lecture 27
Connected Sets
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Connected Sets
Lecture 28
Compactness
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Compactness
Lecture 29
Compactness - Continued
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Compactness - Continued
Lecture 30
Characterizations of Compact Sets
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Characterizations of Compact Sets
Lecture 31
Continuous Functions on Compact Sets
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Continuous Functions on Compact Sets
Lecture 32
Types of Discontinuity
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Types of Discontinuity
VII. Differentiation
Lecture 33
Differentiation
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Differentiation
Lecture 34
Mean Value Theorems
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Mean Value Theorems
Lecture 35
Mean Value Theorems - Continued
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Mean Value Theorems - Continued
Lecture 36
Taylor's Theorem
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Taylor's Theorem
Lecture 37
Differentiation of Vector Valued Functions
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Differentiation of Vector Valued Functions
VIII. Integration
Lecture 38
Integration
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Integration
Lecture 39
Integrability
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Integrability
Lecture 40
Integrable Functions
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Integrable Functions
Lecture 41
Integrable Functions - Continued
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Integrable Functions - Continued
Lecture 42
Integration as a Limit of Sum
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Integration as a Limit of Sum
Lecture 43
Integration and Differentiation
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Integration and Differentiation
Lecture 44
Integration of Vector Valued Functions
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Integration of Vector Valued Functions
Lecture 45
More Theorems on Integrals
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More Theorems on Integrals
IX. Sequences and Series of Functions
Lecture 46
Sequences and Series of Functions
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Sequences and Series of Functions
Lecture 47
Uniform Convergence
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Uniform Convergence
Lecture 48
Uniform Convergence and Integration
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Uniform Convergence and Integration
Lecture 49
Uniform Convergence and Differentiation
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Uniform Convergence and Differentiation
Lecture 50
Construction of Everywhere Continuous Nowhere Differentiable Function
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Construction of Everywhere Continuous Nowhere Differentiable Function
Lecture 51
Approximation of a Continuous Function by Polynomials: Weierstrass Theorem
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Approximation of a Continuous Function by Polynomials: Weierstrass Theorem
Lecture 52
Equicontinuous family of Functions: Arzela - Ascoli Theorem
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Equicontinuous family of Functions: Arzela - Ascoli Theorem