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tma4170:2019v:start [2019-02-13]
xuwa [Actual Lecture Plan] 		tma4170:2019v:start [2019-08-05]
xuwa [TMA4170 Mathematics 4D autumn 2018]
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-====== TMA4170 Fourier analysis, spring 2019 ====== +====== TMA4170 Fourier analysis 2019======
- +
-[[http://www.ntnu.no/studier/emner/TMA4170|Course description]] can be found here.+
  
  
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   * Week 5 exercise has two parts and can be found in the notes now, <color #ed1c24>solutions for Week 3 and 4 exercises will be presented on 5th Feb, 16:15-18:00, S21</color>.   <color #ed1c24> There is an error in the last exercise for Week 4, sgn(x) should be -1 when x is negative </color>   * Week 5 exercise has two parts and can be found in the notes now, <color #ed1c24>solutions for Week 3 and 4 exercises will be presented on 5th Feb, 16:15-18:00, S21</color>.   <color #ed1c24> There is an error in the last exercise for Week 4, sgn(x) should be -1 when x is negative </color>
   * <color #ed1c24>There will be no Exercise Session on 12 Feb</color>   * <color #ed1c24>There will be no Exercise Session on 12 Feb</color>
 +  * We will need some complex analysis results form the {{ :tma4170:2019v:6.pdf |Exercise for week 6}}, please have a look if you haven't taken the complex analysis course.  
 +  * Exercise set for week 7 is online now. 
 +  * Exercise set for week 8 is online now.
 +  * {{ :tma4170:2019v:fourier_2.pdf |Part 2 of the notes}} is online now. Next week (11-17 March) we will do central limit theorem, equidistribution theorem and random walks. 
 +  * An {{ :tma4170:2019v:errata.pdf |errata}} for part 1 of the notes (also contains a list of errors in the weekly exercises).
 +  * The Exercise session for 26th March will by in Xu's office (942 S2), the same time.
 +  * Complete version of {{ :tma4170:2019v:fourier_2.pdf |Part 2 of the notes}} is online now.
 +  * The final week will be repetition based on the exercises (<color #ed1c24>No Exercise Session on 9 April</color>)
 +  * {{ :tma4170:2019v:summary_solution.pdf |A short summary}} of the course and solutions to several exercises
 ===== Course Information ===== ===== Course Information =====
  
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 === SYLLABUS-Notes === === SYLLABUS-Notes ===
  
-The curriculum is covered mainly by the lectures based on the notes found in {{ :tma4170:2019v:fourier_1.pdf |TMA4170 notes}} +The curriculum is covered mainly by the lectures based on the following notes and everything handed out during the lectures. 
-(renewed from time to time) and everything handed out during the lectures. + 
 +1. {{ :tma4170:2019v:fourier_1.pdf |part one}} 
 + 
 +2. {{ :tma4170:2019v:fourier_2.pdf |part two}} (renewed from time to time) 
 + 
 +3. {{ :tma4170:2019v:errata.pdf |Errata}}
  
  
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 The wavelet part of the notes is based on the following book: The wavelet part of the notes is based on the following book:
  
-**A. Boggess & F. Narcowich: A first course in Wavelets with Fourier Analysis, Wiley, 2nd Edition, 2009**.\\ The book is available as an eBook through the university library, although restricted to only one person at a time. \\ +**A. Boggess & F. Narcowich: A first course in Wavelets with Fourier Analysis, Wiley, 2nd Edition, 2009**. 
 + 
 +We also recommend the following standard textbook on Fourier analysis and wavelets: 
 + 
 +** Fourier Analysis and Applications, by G. Gasquet and  P. Witomski, Springer.**\\ 
  
-As mentioned on page 160 of Boggess & Narcowich, **Yves Meyer, Wavelets, Algorithms and Applications, SIAM, 1993** is interesting reading. **Ingrid Daubechies: Ten Lectures on Wavelets, SIAM, 1992** is a classic that goes more deeply into the various aspects of wavelet theory. 
  
 === LECTURER === === LECTURER ===
 +
   * Helge Holden:     Office 1156 in SB II,  [[helge.holden@ntnu.no]]    * Helge Holden:     Office 1156 in SB II,  [[helge.holden@ntnu.no]] 
   * Xu Wang:    Office 942 in SB II, [[xu.wang@ntnu.no]]    * Xu Wang:    Office 942 in SB II, [[xu.wang@ntnu.no]] 
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 TBA TBA
 +
 ===== Exercises ===== ===== Exercises =====
  
-We will hand out the exercise every week, on the other hand all the exercises can be found at the end of notes, they are NOT mandatory, but strongly recommended. +Usually we will hand out the exercise, but you can also find the exercises at the end of the notes. The first five exercise sets are in page 53--59 in {{ :tma4170:2019v:fourier_1.pdf |Part 1 of the notes}}. There are some mistakes, see the {{ :tma4170:2019v:errata.pdf |Errata}} for the corrections. 
 + 
 +{{ :tma4170:2019v:6.pdf |Week 6 Exercise}} 
 + 
 +{{ :tma4170:2019v:7.pdf |Week 7 Exercise}} 
 + 
 +{{ :tma4170:2019v:8.pdf |Week 8 Exercise}} 
 + 
 +{{ :tma4170:2019v:9.pdf |Week 9 Exercise}} 
 + 
 +{{ :tma4170:2019v:10_11.pdf |Week 10-11 Exercise}} 
 + 
 +Wavelet Exercise (Week 12-14): from Boggess--Narcowich 
 + 
 +Ch.4: 1, 3, 4, 5  
 +  
 +Ch.5: 5, 6, 10, 12 
 + 
 +Ch.5: 8, 17, 18 
 + 
 + 
 +Solutions can be found in the 2018 TMA4170 course page. 
  
  
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 ===== Tentative Lecture Plan (according to the notes) ===== ===== Tentative Lecture Plan (according to the notes) =====
  
-| Week 2   | 1.1-1.5 |   | +| Week 2   | 1.1-1.5          |   | 
-| Week 3   | 1.5, Appendix 2 |                                                   | +| Week 3   | 1.5, Appendix 2  |   | 
-| Week 4   | 1.6-1.7 |                     | +| Week 4   | 1.6-1.7          |   | 
-| Week 5   | 1.7-1.8 |          | +| Week 5   | 1.7-1.8          |   | 
-| Week 6   | 2.1-2.3  |                     | +| Week 6   | 2.1-2.3          |   | 
-| Week 7   |  2.4  |                                                      | +| Week 7   |  2.4             |   | 
-| Week 8   | 2.5-2.6|                                                                           | +| Week 8   | 2.5-2.6          |   | 
-| Week 9   | 2.7-2.8|                                                                                | +| Week 9   | 2.7-2.8          |   | 
-| Week 10  | TBA   |                                                                              | +| Week 10  | B&N Ch.4         |   | 
-| Week 11  | TBA   |                                                                   | +| Week 11  | B&N Ch.5         |   | 
-| Week 12  | TBA   |                                    | +| Week 12  | B&N Ch.6         |   | 
-| Week 13  | TBA   |                                                                          | +| Week 13  | B&N Ch.7         |   | 
-| Week 14  | TBA   |                                          | +| Week 14  | Repetition       |   | 
-| Week 15  | Repetition |   +| Week 15  | Repetition       |   |
 ===== Actual Lecture Plan ===== ===== Actual Lecture Plan =====
  
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 | Week 5   | Sec 2.1-2.3                                 | Helge(Monday), Ho Cheung Pang(Thursday)   | | Week 5   | Sec 2.1-2.3                                 | Helge(Monday), Ho Cheung Pang(Thursday)   |
 | Week 6   | 2.4.1-2.4.2                                     |   Helge(Monday), Xu(Thursday)     | | Week 6   | 2.4.1-2.4.2                                     |   Helge(Monday), Xu(Thursday)     |
-| Week 7   |     TBA         |        | +| Week 7   | 2.4.3-2.4.5        |   Xu     | 
-| Week 8   | TBA                                         |        | +| Week 8   | Exercise set 6 on complex analysis          |    Xu    | 
-| Week 9   | TBA                                         |        | +| Week 9   | 2.5                                         |   Xu     | 
-| Week 10  | TBA                                         |        | +| Week 10  | 2.6-2.7                                         |   Xu     | 
-| Week 11  | TBA                                         |        | +| Week 11  | 2.8, 1.7.3, 1.8.2                                         |   Xu     | 
-| Week 12  | TBA                                         |        | +| Week 12  | Mon: Ch 4 in BN, Thu: Se 5.1                                         |   Xu(Monday), Ho Cheung Pang(Thursday)     | 
-| Week 13  | TBA                                         |        | +| Week 13  | Mon: Sec 5.2 (p. 204-214) in Boggess & Narcowich.  Thu: Sec. 5.3 (up to p. 222)                                 |    Helge    | 
-| Week 14  | TBA                                         |        | +| Week 14  | Mon: The remaining part of Ch. 5, and Ch. 6 up to and incl. p. 237 , Thu: wavelet transform                                       |  Helge(Monday), Xu(Thursday)      | 
-| Week 15  | TBA                                         |        |+| Week 15  | Repetition based on exercises                                         |  Xu      |
2019-08-05, Xu Wang