The curriculum is covered mainly by the lectures based on the following notes and everything handed out during the lectures.
1. part one
2. part two (renewed from time to time)
3. Errata
The Fourier analysis part of the notes is based on the following two books:
E. M. Stein & R. Shakarchi: Fourier Analysis, An Introduction, Princeton University Press, 2003
H. Dym & H. P. McKean: Fourier Series and Integrals, Academic Press, 1972
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.
We also recommend the following standard textbook on Fourier analysis and wavelets:
Fourier Analysis and Applications, by G. Gasquet and P. Witomski, Springer.
TBA
TBA
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 Part 1 of the notes. There are some mistakes, see the Errata for the corrections.
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.
NOTE: The exams from 2014 and older are written with a slightly different curriculum in mind and as such may contain exercises not covered by the current curriculum!
Week 2 | 1.1-1.5 | |
Week 3 | 1.5, Appendix 2 | |
Week 4 | 1.6-1.7 | |
Week 5 | 1.7-1.8 | |
Week 6 | 2.1-2.3 | |
Week 7 | 2.4 | |
Week 8 | 2.5-2.6 | |
Week 9 | 2.7-2.8 | |
Week 10 | B&N Ch.4 | |
Week 11 | B&N Ch.5 | |
Week 12 | B&N Ch.6 | |
Week 13 | B&N Ch.7 | |
Week 14 | Repetition | |
Week 15 | Repetition |
Week 2 | Fourier series, Pointwise and Mean square convergence | Xu |
Week 3 | Lebesgue integral, elementary solution of D+s | Xu |
Week 4 | Sec 1.7.1, 1.7.2 Sec 1.8.1 | Helge |
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 7 | 2.4.3-2.4.5 | Xu |
Week 8 | Exercise set 6 on complex analysis | Xu |
Week 9 | 2.5 | Xu |
Week 10 | 2.6-2.7 | Xu |
Week 11 | 2.8, 1.7.3, 1.8.2 | Xu |
Week 12 | Mon: Ch 4 in BN, Thu: Se 5.1 | Xu(Monday), Ho Cheung Pang(Thursday) |
Week 13 | Mon: Sec 5.2 (p. 204-214) in Boggess & Narcowich. Thu: Sec. 5.3 (up to p. 222) | Helge |
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 | Repetition based on exercises | Xu |