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HOVEDSIDE > SIF5027
SIF5027 FOURIERANALYSE
Høsten 2001
| Om kurset | Kurset foreleses med to dobbelt-timer i uken. | |
|---|---|---|
| Foreleser | Professor Peter Lindqvist Institutt for matematiske fag Rom 1152 SB II Tlf. 73 59 35 29 lqvist@math.ntnu.no |
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| Lærebok | Utvalgte deler av Boggess & Narcowich: "A First Course in Wavelets with Fourier Analysis", Prentice Hall 2001. | |
| Forelesninger | Mandag 9-11, rom R62 Torsdag 12-14, rom K243 |
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| Øvinger | Fredag 10-11, rom R63 Begynner 31. august 2001. |
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| Pensum | Chapter 0: | "Inner Product Spaces". Sections 0.1 - 0.5. |
| Chapter 1: | "Fourier Series" (including: Gibbs' phenomenon; Fejer's theorem about the Cesàro means; Poisson's formula in exercise 36, p. 89). | |
| Chapter 2: | "The Fourier Transform" (including: oversampling in exercise 14, p. 128; Poisson's summation formula). | |
| Chapter 3: | Section 3.1 "The Discrete Fourier Transform". | |
| Chapter 4: | "Haar Wavelet Analysis". | |
| Chapter 5: | "Multiresolution Analysis", Section 5.1 and 5.3. | |
| Chapter 6: | Section 6.1 "Daubechie's Construction". | |
| Lebesgue's Integral: |
The monotone and dominated convergence theorems, Lebesgue's differentiation theorem. | |
| All the exercises (øvinger) | ||
| Eksamen | 4. desember 2001 | |
| Øvingsoppgaver | Øving 31.8.2001 Section 0.8, exercises 6, 8, 10, 15, 17, 23 and one additional exercise about the Rademacher functions. Øving 14.9.2001 Section 1.4, exercises 3, 4, 10, 15, 22, 25. Øving 21.9.2001 Section 1.4, exercises 7, 11, 16, 32. Section 2.6, exercise 5. Øving 28.9.2001 Section 2.6, exercises 1, 2, 3, 4, 13. Øving 5.10.2001 Section 2.6, exercise 14a,b,c (oversampling). Øving 12.10.2001 some examples about the Lebesgue integral will be discussed. Øving 19.10.2001 ps-fil Øving 26.10.2001 ps-fil Øving 2.11.2001 Section 4.5, Exercises 1, 4a, 5, 6 (notation on page 169). Øving 9.11.2001 Section 4.5, Exercises 7, 8. Section 5.4, Exercises 1a, 1c, 4, 5, 6, 10. Øving 16.11. 2001 Section 5.4, Exercises 8, 10, 12, 16,17. Nothing 23.11.2001 |
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