# click the upper-left icon to select videos from the playlist
source: DTUdk 2013年2月6日
01325 Mathematics 4 Real Analysis F13
Course website: http://www2.mat.dtu.dk/education/01325/
Here the link http://www2.mat.dtu.dk/education/01325/overview.htm gives all the information about the course. Each week it is updated with new files, containing the program for lectures, problem sessions and home work for the subsequent week, as well as selected solutions.
Course material: We use the book O. Christensen: Functions, Spaces, and Expansions, Birkhauser 2010. Best Regards, Ole.
Normed Vector Spaces Part 1 51:54
Lecture with Ole Christensen. Kapitler: 00:00 - Introduction; 06:45 - Vector Spaces; 07:15 - Example 1; 12:00 - Mathematical Tool - Fourier Transform; 17:00 - Example 2; 20:00 - Example 3; 23:00 - New Concept - Norm; 27:45 - Lemma 2.1.2 - The Opposite Triangle Inequality; 35:15 - Convergence; 39:30 - Exact Definition; 41:45 - Goal; 43:15 - Subspaces; 44:15 - Characterisation Of A Subspace; 46:15 - Example: A Trigonometric Polynomial;
Normed Vector Spaces Part 2 51:38
Banach Spaces part 1 48:52
Banach Spaces part 2 52:21
Hilbert Spaces part 1 50:18
Hilbert Spaces part 2 55:55
Adjoint Operator Part 1 43:08
Adjoint Operator Part 2 54:35
Lecture 5 Lp Spaces on the real line 50:59
Lp Spaces On The Real Line part 2 50:49
More On Lp And L2 Spaces Part 1 48:00
More On Lp And L2 Spaces Part 2 55:37
More On Operators On L2 Part 1 52:34
Orthonormal Bases Vs Fourier Series Part 2 46:37
Approximation Theory Part 1 48:32
Approximation Theory Part 2 53:28
The Fourier Transform Part 1 47:42
The Fourier Transform Part 2 50:20
Fourier Transform And Wavelets Part 1 47:32
The Fourier Transform And Wavelets Part 2 51:09
Wavelets And Multiresolution Analysis Part 1 51:54
Wavelets And Multiresolution Analysis Part 2 54:10
Wavelets And B-Splines Part 1 43:50
Wavelets And B-Splines Part 2 59:57
Special Functions And Diff. Equation Course Evaluation 1:16:49
Banachrum Del 2 51:25
L^p-rum Del 1 52:59
Operatorer på Hilbertrum Del 1 55:45
Lp og L2 Del 2 56:10
Lp og L2 Del 2 56:10
Fouriertransformationer Del 1 50:10
[deleted video]
L^p-rum Del 2 52:36
L^p-rum Del 2 52:36
Lp og L2 Del 1 48:52
[deleted video]
Fouriertransformationer Del 2 50:31
Fouriertransformationer Del 2 50:31
Banachrum Del 1 49:31
Banachrum Del 1 49:31
[deleted video]
Intro til Vektorrum Del 1 51:03
Operatorer på Hilbertrum Del 2 47:58
Test Del 1 0:30
Operatorer på Hilbertrum Del 2 47:58
Approximationsteori Del 1 42:19
Approximationsteori Del 1 42:19
Hilbertrum Del 1 49:45
L2 og ONB's Del 1 49:02
Intro til Vektorrum Del 2 54:44
L2 og ONB's Del 2 46:27
Hilbertrum Del 2 43:50
Approximationsteori Del 2 55:17
Anvendelse af Fouriertransformation Del 1 54:11
Anvendelse af Fouriertransformation Del 2 53:34
Wavelets Del 1 54:59
Wavelets Del 2 1:04:06
Wavelets og B-splines Del 1 37:32
Wavelets og B-splines Del 2 55:58
Specielle funktioner Del 1 1:17:32
Showing posts with label A. (subjects)-Engineering & Physical Sciences-Mathematics-Real Analysis. Show all posts
Showing posts with label A. (subjects)-Engineering & Physical Sciences-Mathematics-Real Analysis. Show all posts
2017-03-31
2016-12-22
Real Analysis I (2009-2010 at Bilkent U) by Alexandre Gontcharov
# click the up-left corner to select videos from the playlist
# click the up-left corner to select videos from the playlist
source: Bilkent Online Courses 2014年8月16日
MATH-501 Real Analysis - I (2009-2010- Fall)
Concepts of integration. Henstock-Kurzweil integral. Borel sets, Bair functions. Outer measures. Measurable sets. Lebesgue and Lebesgue-Stieltjes measures. Lebesgue density theorem. Hausdorff measures and Hausdorff dimension. Measurable functions. Lusin’s and Egorov’s theorems. Convergence in measure. Lebesgue integral. Basic theorems of Lebesgue integral. Modes of convergence. Differentiation of indefinite Lebesgue integral. Signed measures. The Radon- Nikodym theorem. Product measures. Spaces of integrable functions.
Lecture 01 Category 50:58
Lecture 02 Borel sets 51:09
Lecture 03 Baire functions 52:05
Lecture 04 Concept of measure 47:47
Lecture 05 Measurable sets 51:36
Lecture 06 Lebesgue measure 49:59
Lecture 07 Approximation of measurable sets 50:29
Lecture 08 Lebesgue density theorem 50:55
Lecture 09 Hausdorff measures 51:00
Lecture 10 Extension of premeasures 52:07
Lecture 11 Nonmeasurable sets 49:36
Lecture 12 Measurable functions 48:09
Lecture 13 Review of mid-term exam 47:57
Lecture 14 Almost uniform convergence 48:51
Lecture 15 Egorovs theorem 49:38
Lecture 16 Lusin theorem 51:09
Lecture 17 Convergence in measure 50:58
Lecture 18 Lebesgue integral for bounded functions 50:05
Lecture 19 Monotone Convergence Theorem 50:38
Lecture 20 Fatou Lemma 48:51
Lecture 21 Lebesgue Dominated Convergence Theorem 50:22
Lecture 22 Characterizations of Integrability 50:33
Lecture 23 Indefinite Lebesgue Integral 51:35
Lecture 24 Differentiation of Monotone Function 51:51
Lecture 25 Indefinite Lebesgue Integral 49:45
Lecture 26 Absolutely Continuous Functions 48:48
Lecture 27 Signed Measures 53:27
Lecture 28 Hahn Decomposition 50:54
Lecture 29 Radon-Nikodym Theorem 50:41
Lecture 30 Product Measures 53:05
Lecture 31 Fubini Theorem 46:10
Lecture 32 Applications of Fubini Theorem 48:50
Lecture 33 Spaces of Integrable Functions 51:38
Lecture 34 Rearrangement of Functions 50:33
Lecture 35 Approximation in LP 49:49
Lecture 36 Riesz' Representation Theorem 52:14
Lecture 37 Hielbert Spaces 1:19:28
# click the up-left corner to select videos from the playlist
source: Bilkent Online Courses 2014年8月16日
MATH-501 Real Analysis - I (2009-2010- Fall)
Concepts of integration. Henstock-Kurzweil integral. Borel sets, Bair functions. Outer measures. Measurable sets. Lebesgue and Lebesgue-Stieltjes measures. Lebesgue density theorem. Hausdorff measures and Hausdorff dimension. Measurable functions. Lusin’s and Egorov’s theorems. Convergence in measure. Lebesgue integral. Basic theorems of Lebesgue integral. Modes of convergence. Differentiation of indefinite Lebesgue integral. Signed measures. The Radon- Nikodym theorem. Product measures. Spaces of integrable functions.
Lecture 01 Category 50:58
Lecture 02 Borel sets 51:09
Lecture 03 Baire functions 52:05
Lecture 04 Concept of measure 47:47
Lecture 05 Measurable sets 51:36
Lecture 06 Lebesgue measure 49:59
Lecture 07 Approximation of measurable sets 50:29
Lecture 08 Lebesgue density theorem 50:55
Lecture 09 Hausdorff measures 51:00
Lecture 10 Extension of premeasures 52:07
Lecture 11 Nonmeasurable sets 49:36
Lecture 12 Measurable functions 48:09
Lecture 13 Review of mid-term exam 47:57
Lecture 14 Almost uniform convergence 48:51
Lecture 15 Egorovs theorem 49:38
Lecture 16 Lusin theorem 51:09
Lecture 17 Convergence in measure 50:58
Lecture 18 Lebesgue integral for bounded functions 50:05
Lecture 19 Monotone Convergence Theorem 50:38
Lecture 20 Fatou Lemma 48:51
Lecture 21 Lebesgue Dominated Convergence Theorem 50:22
Lecture 22 Characterizations of Integrability 50:33
Lecture 23 Indefinite Lebesgue Integral 51:35
Lecture 24 Differentiation of Monotone Function 51:51
Lecture 25 Indefinite Lebesgue Integral 49:45
Lecture 26 Absolutely Continuous Functions 48:48
Lecture 27 Signed Measures 53:27
Lecture 28 Hahn Decomposition 50:54
Lecture 29 Radon-Nikodym Theorem 50:41
Lecture 30 Product Measures 53:05
Lecture 31 Fubini Theorem 46:10
Lecture 32 Applications of Fubini Theorem 48:50
Lecture 33 Spaces of Integrable Functions 51:38
Lecture 34 Rearrangement of Functions 50:33
Lecture 35 Approximation in LP 49:49
Lecture 36 Riesz' Representation Theorem 52:14
Lecture 37 Hielbert Spaces 1:19:28
2016-10-12
P. D. Srivastava: A Basic Course in Real Analysis (IIT Kharagpur)
# playlist of the 46 videos (click the up-left corner of the video)
source: nptelhrd 2013年7月2日
Mathematics - A Basic Course in Real Analysis by Prof. P. D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
Mod-01 Lec-01 Rational Numbers and Rational Cuts 52:37
Mod-02 Lec-02 Irrational numbers, Dedekind's Theorem 54:42
Mod-03 Lec-03 Continuum and Exercises 56:11
Mod-03 Lec-04 Continuum and Exercises (Contd.) 55:00
Mod-04 Lec-05 Cantor's Theory of Irrational Numbers 53:08
Mod-04 Lec-06 Cantor's Theory of Irrational Numbers (Contd.) 55:06
Mod-05 Lec-07 Equivalence of Dedekind and Cantor's Theory 54:37
Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers 55:18
Mod-07 Lec-09 Types of Sets with Examples, Metric Space 55:02
Mod-08 Lec-10 Various properties of open set, closure of a set 55:20
Mod-09 Lec-11 Ordered set, Least upper bound, greatest lower bound of a set 56:22
Mod-10 Lec-12 Compact Sets and its properties 55:44
Mod-11 Lec-13 Weiersstrass Theorem, Heine Borel Theorem, Connected set 56:08
Mod-12 Lec-14 Tutorial - II 56:13
Mod-13 Lec-15 Concept of limit of a sequence 54:51
Mod-14 Lec-16 Some Important limits, Ratio tests for sequences of Real Numbers 51:48
Mod-15 Lec-17 Cauchy theorems on limit of sequences with examples 54:15
Mod-16 Lec-18 Fundamental theorems on limits, Bolzano-Weiersstrass Theorem 54:36
Mod-17 Lec-19 Theorems on Convergent and divergent sequences 52:42
Mod-18 Lec-20 Cauchy sequence and its properties 53:53
Mod-19 Lec-21 Infinite series of real numbers 53:16
Mod-20 Lec-22 Comparison tests for series, Absolutely convergent and Conditional convergent series 54:53
Mod-21 Lec-23 Tests for absolutely convergent series 53:01
Mod-22 Lec-24 Raabe's test, limit of functions, Cluster point 57:20
Mod-23 Lec-25 Some results on limit of functions 53:36
Mod-24 Lec-26 Limit Theorems for functions 54:09
Mod-25 Lec-27 Extension of limit concept (one sided limits) 52:26
Mod-26 Lec-28 Continuity of Functions 54:22
Mod-27 Lec-29 Properties of Continuous Functions 54:07
Mod-28 Lec-30 Boundedness Theorem, Max-Min Theorem and Bolzano's theorem 56:25
Mod-29 Lec-31 Uniform Continuity and Absolute Continuity 53:41
Mod-30 Lec-32 Types of Discontinuities, Continuity and Compactness 55:55
Mod-31 Lec-33 Continuity and Compactness (Contd.), Connectedness 55:59
Mod-32 Lec-34 Differentiability of real valued function, Mean Value Theorem 53:52
Mod-33 Lec-35 Mean Value Theorem (Contd.) 56:46
Mod-34 Lec-36 Application of MVT , Darboux Theorem, L Hospital Rule 52:54
Mod-35 Lec-37 L'Hospital Rule and Taylor's Theorem 54:06
Mod-36 Lec-38 Tutorial - III 52:42
Mod-37 Lec-39 Riemann/Riemann Stieltjes Integral 53:03
Mod-38 Lec-40 Existence of Reimann Stieltjes Integral 55:39
Mod-39 Lec-41 Properties of Reimann Stieltjes Integral 54:35
Mod-39 Lec-42 Properties of Reimann Stieltjes Integral (Contd.) 56:45
Mod-40 Lec-43 Definite and Indefinite Integral 55:39
Mod-41 Lec-44 Fundamental Theorems of Integral Calculus 52:12
Mod-42 Lec-45 Improper Integrals 55:53
Mod-43 Lec-46 Convergence Test for Improper Integrals 53:47
source: nptelhrd 2013年7月2日
Mathematics - A Basic Course in Real Analysis by Prof. P. D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
Mod-01 Lec-01 Rational Numbers and Rational Cuts 52:37
Mod-02 Lec-02 Irrational numbers, Dedekind's Theorem 54:42
Mod-03 Lec-03 Continuum and Exercises 56:11
Mod-03 Lec-04 Continuum and Exercises (Contd.) 55:00
Mod-04 Lec-05 Cantor's Theory of Irrational Numbers 53:08
Mod-04 Lec-06 Cantor's Theory of Irrational Numbers (Contd.) 55:06
Mod-05 Lec-07 Equivalence of Dedekind and Cantor's Theory 54:37
Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers 55:18
Mod-07 Lec-09 Types of Sets with Examples, Metric Space 55:02
Mod-08 Lec-10 Various properties of open set, closure of a set 55:20
Mod-09 Lec-11 Ordered set, Least upper bound, greatest lower bound of a set 56:22
Mod-10 Lec-12 Compact Sets and its properties 55:44
Mod-11 Lec-13 Weiersstrass Theorem, Heine Borel Theorem, Connected set 56:08
Mod-12 Lec-14 Tutorial - II 56:13
Mod-13 Lec-15 Concept of limit of a sequence 54:51
Mod-14 Lec-16 Some Important limits, Ratio tests for sequences of Real Numbers 51:48
Mod-15 Lec-17 Cauchy theorems on limit of sequences with examples 54:15
Mod-16 Lec-18 Fundamental theorems on limits, Bolzano-Weiersstrass Theorem 54:36
Mod-17 Lec-19 Theorems on Convergent and divergent sequences 52:42
Mod-18 Lec-20 Cauchy sequence and its properties 53:53
Mod-19 Lec-21 Infinite series of real numbers 53:16
Mod-20 Lec-22 Comparison tests for series, Absolutely convergent and Conditional convergent series 54:53
Mod-21 Lec-23 Tests for absolutely convergent series 53:01
Mod-22 Lec-24 Raabe's test, limit of functions, Cluster point 57:20
Mod-23 Lec-25 Some results on limit of functions 53:36
Mod-24 Lec-26 Limit Theorems for functions 54:09
Mod-25 Lec-27 Extension of limit concept (one sided limits) 52:26
Mod-26 Lec-28 Continuity of Functions 54:22
Mod-27 Lec-29 Properties of Continuous Functions 54:07
Mod-28 Lec-30 Boundedness Theorem, Max-Min Theorem and Bolzano's theorem 56:25
Mod-29 Lec-31 Uniform Continuity and Absolute Continuity 53:41
Mod-30 Lec-32 Types of Discontinuities, Continuity and Compactness 55:55
Mod-31 Lec-33 Continuity and Compactness (Contd.), Connectedness 55:59
Mod-32 Lec-34 Differentiability of real valued function, Mean Value Theorem 53:52
Mod-33 Lec-35 Mean Value Theorem (Contd.) 56:46
Mod-34 Lec-36 Application of MVT , Darboux Theorem, L Hospital Rule 52:54
Mod-35 Lec-37 L'Hospital Rule and Taylor's Theorem 54:06
Mod-36 Lec-38 Tutorial - III 52:42
Mod-37 Lec-39 Riemann/Riemann Stieltjes Integral 53:03
Mod-38 Lec-40 Existence of Reimann Stieltjes Integral 55:39
Mod-39 Lec-41 Properties of Reimann Stieltjes Integral 54:35
Mod-39 Lec-42 Properties of Reimann Stieltjes Integral (Contd.) 56:45
Mod-40 Lec-43 Definite and Indefinite Integral 55:39
Mod-41 Lec-44 Fundamental Theorems of Integral Calculus 52:12
Mod-42 Lec-45 Improper Integrals 55:53
Mod-43 Lec-46 Convergence Test for Improper Integrals 53:47
2016-08-30
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
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
2016-07-07
S.H. Kulkarni: Mathematics - Real Analysis (IIT Madras)
# Click the up-left corner for the playlist of the 52 videos
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
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
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