Introductory Course in Real Analysis 6E5BFTGZR8

URI	`m2://res/6E5BFTGZR8`
Kind	course
Creators	P D Srivastava (instructor)
Date	2016-12-27
Scope	in
Ids	course 03w5sq511:111105098

Expressions

e1: edition

Language	en
Date	2016-12-27

m1: page, IIT Kharagpur (record). nptel 111105098
m2: page, 2016-12-27 (record). nptel 111105098

Contents

part 1: Week 1
session 1: Lecture 1: Countable and Uncountable sets
session 2: Lecture 2: Properties of Countable and Uncountable sets
session 3: Lecture 3: Examples of Countable and Uncountable sets
session 4: Lecture 4: Concepts of Metric Space
session 5: Lecture 5: Open ball, Closed ball, Limit point of a set
session 6: Lecture 6: Tutorial - 1
part 2: Week 2
session 7: Lecture 7: Some theorems on Open and Closed sets
session 8: Lecture 8: Ordered set, Least upper bound, Greatest lower bound of a set
session 9: Lecture 9: Ordered set, Least upper bound, Greatest lower bound of a set (contd.)
session 10: Lecture 10: Compact Set
session 11: Lecture 11: Properties of Compact sets
session 12: Lecture 12: Tutorial - 2
part 3: Week 3
session 13: Lecture 13: Heine Borel Theorem
session 14: Lecture 14: Weierstrass Theorem
session 15: Lecture 15: Cantor set & its properties
session 16: Lecture 16: Derived set & Dense set
session 17: Lecture 17: Limit of a sequence & monotone sequence
session 18: Lecture 18: Tutorial III
part 4: Week 4
session 19: Lecture 19 : Some Important Limits of Sequences
session 20: Lecture 20 : Ratio Test Cauchy's Theorems on Limits of Sequences of Real Numbers
session 21: Lecture 21: Fundamental Theorems on Limits
session 22: Lecture 22: Some Results on Limits and Bolzano - Weierstrass Theorem
session 23: Lecture 23: Criteria for Convergent Sequence
session 24: Lecture 24: Tutorial - IV
part 5: Week 5
session 25: Lecture 25 : Criteria for Divergent Sequence
session 26: Lecture 26 : Cauchy Sequence
session 27: Lecture 27 : Cauchy Convergence Criteria for Sequences
session 28: Lecture 28 : Infinite Series of Real Numbers
session 29: Lecture 29 : Convergence Criteria for Series of Positive Real Numbers
session 30: Lecture 30 : Tutorial V
part 6: Week 6
session 31: Lecture 31: Comparison Test for Series
session 32: Lecture 32: Absolutely and Conditionally Convergent Series
session 33: Lecture 33: Rearrangement Theorem and Test for Convergence of Series
session 34: Lecture 34: Ratio and Integral Test for Convergence of Series
session 35: Lecture 35: Raabe's Test for Convergence of Series
session 36: Lecture 36 : Tutorial VI
part 7: Week 7
session 37: Lecture 37 : Limit of functions and cluster point
session 38: Lecture 38 : Limit of functions(contd.)
session 39: Lecture 39 : Divergence criteria for limit
session 40: Lecture 40 : Various properties of limit of functions
session 41: Lecture 41 : Left and Right Hand Limits for functions
session 42: Lecture 42 : Tutorial VII
part 8: Week 8
session 43: Lecture 43 : Limit of Functions at Infinity
session 44: Lecture 44 : Continuous Functions (Cauchy's Definition)
session 45: Lecture 45: Continuous Functions (Heine's Definition)
session 46: Lecture 46: Properties of Continuous Functions
session 47: Lecture 47: Properties of Continuous Functions (Contd.)
session 48: Lecture 48 : Tutorial VIII
part 9: Week 9
session 49: Lecture 49: Boundness Theorem and Max-Min Theorem
session 50: Lecture 50: Location of Root and Bolzano's Theorem
session 51: Lecture 51: Uniform Continuity and Related Theorems
session 52: Lecture 52: Absolute Continuity and Related Theorems
session 53: Lecture 53 : Types of Discontinuities
session 54: Lecture 54 : Tutorial IX
part 10: Week 10
session 55: Lecture 55 : Types of Discontinuities (Contd.)
session 56: Lecture 56 : Relation between Continuity and Compact Sets
session 57: Lecture 57 : Differentiability of Real Valued Functions
session 58: Lecture 58 : Local Max. - Min. Cauchy's and Lagrange's Mean Value Theorem
session 59: Lecture 59 : Rolle's Mean Value Theorems and Its Applications
session 60: Lecture 60 : Tutorial X
part 11: Week 11
session 61: Lecture 61 : Applications of Derivatives
session 62: Lecture 62 : Application of MVT & Darboux's theorem
session 63: Lecture 63 : L' Hospital Rule
session 64: Lecture 64 : Taylor's theorem
session 65: Lecture 65 : Riemann/Riemann Steiltjes Integral
session 66: Lecture 66 : Tutorial XI
part 12: Week 12
session 67: Lecture 67 : Riemann/Riemann Steiltjes Integral (contd.)
session 68: Lecture 68 : Existence of Riemann/Riemann Steiltjes Integral
session 69: Lecture 69 : Riemann/Riemann Steiltjes Integrable functions
session 70: Lecture 70 : Properties of Riemann Steiltjes Intergral
session 71: Lecture 71 : Various Results of Riemann Stieltjes Integral using Step Function
session 72: Lecture 72 : Some more results on Riemann Stieltjes Integral
session 73: Lecture 73 : Tutorial XII

Catalogue records

nptel: 111105098 (manifestation)
nptel_video: 111105098 (manifestation)