S. H. Kulkarni: Real Analysis (IIT Madras)

# playlist of the 52 videos (click the up-left corner of the video)

source: nptelhrd     2016年1月18日
Mathematics - Real Analysis by Prof. S. H. Kulkarni, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Mod-01 Lec-1 Introduction 52:45
Mod-01 Lec-02 Functions and Relations 51:36
Mod-01 Lec-3 Finite and Infinite Sets 51:34
Mod-01 Lec-4 Countable Sets 50:09
Mod-01 Lec-5 Uncountable Sets, Cardinal Numbers 50:05
Mod-02 Lec-06 Real Number System 52:16
Mod-02 Lec-7 LUB Axiom 51:41
Mod-02 Lec-08 Sequences of Real Numbers 52:36
Mod-02 Lec-09 Sequences of Real Numbers - continued 52:23
Mod-02 Lec-10 Sequences of Real Numbers - continued... 50:59
Mod-02 Lec-11 Infinite Series of Real Numbers 51:53
Mod-02 Lec-12 Series of nonnegative Real Numbers 53:26
Mod-02 Lec-13 Conditional Convergence 53:44
Mod-03 Lec-14 Metric Spaces: Definition and Examples 52:56
Mod-03 Lec-15 Metric Spaces: Examples and Elementary Concepts 52:09
Mod-03 Lec-16 Balls and Spheres 52:03
Mod-03 Lec-17 Open Sets 51:29
Mod-03 Lec-18 Closure Points, Limit Points and isolated Points 52:20
Mod-03 Lec-19 Closed sets 51:14
Mod-04 Lec-20 Sequences in Metric Spaces 51:44
Mod-04 Lec-21 Completeness 49:20
Mod-04 Lec-22 Baire Category Theorem 53:38
Mod-05 Lec-23 Limit and Continuity of a Function defined on a Metric space 53:27
Mod-05 Lec-24 Continuous Functions on a Metric Space 54:19
Mod-05 Lec-25 Uniform Continuity 51:01
Mod-06 Lec-26 Connectedness 40:05
Mod-06 Lec-27 Connected Sets 54:53
Mod-06 Lec-28 Compactness 51:22
Mod-06 Lec-29 Compactness - Continued 51:59
Mod-06 Lec-30 Characterizations of Compact Sets 56:29
Mod-06 Lec-31 Continuous Functions on Compact Sets 53:20
Mod-06 Lec-32 Types of Discontinuity 54:44
Mod-07 Lec-33 Differentiation 52:41
Mod-07 Lec-34 Mean Value Theorems 50:19
Mod-07 Lec-35 Mean Value Theorems - Continued 51:35
Mod-07 Lec-36 Taylor's Theorem 50:13
Mod-07 Lec-37 Differentiation of Vector Valued Functions 50:59
Mod-08 Lec-38 Integration 51:02
Mod-08 Lec-39 Integrability 50:43
Mod-08 Lec-40 Integrable Functions 51:23
Mod-08 Lec-41 Integrable Functions - Continued 52:33
Mod-08 Lec-42 Integration as a Limit of Sum 52:25
Mod-08 Lec-43 Integration and Differentiation 54:25
Mod-08 Lec-44 Integration of Vector Valued Functions 51:51
Mod-08 Lec-45 More Theorems on Integrals 52:35
Mod-09 Lec-46 Sequences and Series of Functions 51:34
Mod-09 Lec-47 Uniform Convergence 53:24
Mod-09 Lec-48 Uniform Convergence and Integration 52:50
Mod-09 Lec-49 Uniform Convergence and Differentiation 52:06
Mod-09 Lec-50 Construction of Everywhere Continuous Nowhere Differentiable Function 53:42
Mod-09 Lec-51 Approximation of a Continuous Function by Polynomials: Weierstrass Theorem 50:58
Mod-09 Lec-52 Equicontinuous family of Functions: Arzela - Ascoli Theorem 53:24

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