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

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

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