Real Analysis Y2D0QDN82M

URI	`m2://res/Y2D0QDN82M`
Kind	course
Creators	S.H. Kulkarni (instructor)
Date	2016-01-18
Scope	in
Ids	course 03v0r5n49:111106053

Expressions

e1: edition

Language	en
Date	2016-01-18

m1: page, IIT Madras (record). nptel 111106053
m2: page, 2016-01-18 (record). nptel 111106053

Contents

part 1: MODULE 1: REVIEW OF SET THEORY
session 1: Introduction
session 2: Functions and Relations
session 3: Finite and Infinite Sets
session 4: Countable Sets
session 5: Uncountable Sets, Cardinal Numbers
part 2: MODULE 2: SEQUENCES AND SERIES OF REAL NUMBERS
session 6: Real Number System
session 7: LUB Axiom
session 8: Sequences of Real Numbers
session 9: Sequences of Real Numbers - continued
session 10: Sequences of Real Numbers - continued...
session 11: Infinite Series of Real Numbers
session 12: Series of nonnegative Real Numbers
session 13: Conditional Convergence
part 3: MODULE 3: METRIC SPACES - BASIC CONCEPTS
session 14: Metric Spaces: Definition and Examples
session 15: Metric Spaces: Examples and Elementary Concepts
session 16: Balls and Spheres
session 17: Open Sets
session 18: Closure Points, Limit Points and isolated Points
session 19: Closed sets
part 4: MODULE 4: COMPLETENESS
session 20: Sequences in Metric Spaces
session 21: Completeness
session 22: Baire Category Theorem
part 5: MODULE 5: LIMITS AND CONTINUITY
session 23: Limit and Continuity of a Function defined on a Metric space
session 24: Continuous Functions on a Metric Space
session 25: Uniform Continuity
part 6: MODULE 6: CONNECTEDNESS AND COMPACTNESS
session 26: Connectedness
session 27: Connected Sets
session 28: Compactness
session 29: Compactness - Continued
session 30: Characterizations of Compact Sets
session 31: Continuous Functions on Compact Sets
session 32: Types of Discontinuity
part 7: MODULE 7: DIFFERENTIATION
session 33: Differentiation
session 34: Mean Value Theorems
session 35: Mean Value Theorems - Continued
session 36: Taylor's Theorem
session 37: Differentiation of Vector Valued Functions
part 8: MODULE 8: INTEGRATION
session 38: Integration
session 39: Integrability
session 40: Integrable Functions
session 41: Integrable Functions - Continued
session 42: Integration as a Limit of Sum
session 43: Integration and Differentiation
session 44: Integration of Vector Valued Functions
session 45: More Theorems on Integrals
part 9: MODULE 9: SEQUENCES AND SERIES OF FUNCTIONS
session 46: Sequences and Series of Functions
session 47: Uniform Convergence
session 48: Uniform Convergence and Integration
session 49: Uniform Convergence and Differentiation
session 50: Construction of Everywhere Continuous Nowhere Differentiable Function
session 51: Approximation of a Continuous Function by Polynomials: Weierstrass Theorem
session 52: Equicontinuous family of Functions: Arzela - Ascoli Theorem

Catalogue records

nptel: 111106053 (manifestation)
nptel_video: 111106053 (manifestation)