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tma4170:2019v:start [2019-02-14]
xuwa [Exercises]
tma4170:2019v:start [2019-08-05] (nåværende versjon)
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 libraryalthough 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. WitomskiSpringer.**\\ 
  
-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 =====
  
-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}}+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 ​     ​|
2019-02-14, Xu Wang