## 2017-03-31

### Real Analysis with Ole Christensen

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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
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