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Course Coordinated by
IIT Kharagpur
NPTEL
>>
Courses
>>
Mathematics
>> NOC:Introductory Course in Real Analysis (Video) >>
Lecture 1: Countable and Uncountable sets
Question in Lecture
Week 1
Lecture 1: Countable and Uncountable sets
Lecture 2: Properties of Countable and Uncountable sets
Lecture 3: Examples of Countable and Uncountable sets
Lecture 4: Concepts of Metric Space
Lecture 5: Open ball, Closed ball, Limit point of a set
Lecture 6: Tutorial  I
Week 2
Lecture 7: Some theorems on Open and Closed sets
Lecture 8: Ordered set, Least upper bound, Greatest lower bound of a set
Lecture 9: Ordered set, Least upper bound, Greatest lower bound of a set ( contd.)
Lecture 10: Compact Set
Lecture 11: Properties of Compact sets
Lecture 12: Tutorial II
Week 3
Lecture 13: Heine Borel Theorem
Lecture 14: Weierstrass Theorem
Lecture 15: Cantor set & its properties
Lecture 16: Derived set & Dense set
Lecture 17: Limit of a sequence & monotone sequence
Lecture 18: Tutorial 3
Week 4
Lecture 19: Some Important limits of sequences
Lecture 20: Ratio Test Cauchy’s theorems on limits of sequences of real numbers
Lecture 21: Fundamental theorems on limits
Lecture 22: Some results on limits and BolzanoWeierstrass Theorem
Lecture 23: Criteria for convergent sequence
Lecture 24: Tutorial  IV
Week 5
Lecture 25 : Criteria for Divergent Sequence
Lecture 26 : Cauchy Sequence
Lecture 27 : Cauchy Convergence Criteria for Sequences
Lecture 28 : Infinite Series of Real Numbers
Lecture 29 : Convergence Criteria for Series of Positive Real Numbers
Lecture 30 : Tutorial V
Week 6
Lecture 31 : Comparison Test for Series
Lecture 32: Absolutely and Conditionally Convergent Series
Lecture 33: Rearrangement Theorem and Test for Convergence of Series
Lecture 34: Ratio and Integral Test for Convergence of Series
Lecture 35: Raabe's Test for Convergence of Series
Lecture 36 : Tutorial VI
Week 7
Lecture 37 : Limit of Functions and Cluster Point
Lecture 38 : Limit of Functions (Contd.)
Lecture 39: Divergence Criteria for Limit
Lecture 40 : Various Properties of Limit of Functions
Lecture 41: Left and Right Hand Limits for Functions
Lecture 42: Tutorial VII
Week 8
Lecture 43 : Limit of Functions at Infinity
Lecture 44 : Continuous Functions (Cauchy's Definition)
Lecture 45 : Continuous Functions (Heine's Definition)
Lecture 46: Properties of Continuous Functions
Lecture 47: Properties of Continuous Functions (Contd.)
Lecture 48 : Tutorial VIII
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