School of Mathematics and Computing Sciences, Chalmers University of Technology and Goteborg University


Fourier Analysis for Kf2, Lp2, Fall 2000


General information:

This is a support course equivalent to a 2 credit points of 5 for the F2/Kf2 Fourier Analysis. The reason for this splitting is some schema collisions for Kf2 in period 3. The content of the course will be kept identical to the corresponding part that is scheduled for F2/Kf2, so that except the current "time splitting" there will be no differences between the two corresponding parts.


Teacher:

Mohammad Asadzadeh (Lectures/Exercises)
telephone: 7723517,
e-mail:mohammad@math.chalmers.se
URL:http://www.math.chalmers.se/~mohammad
Matematiskt Centrum, Eklandagatan, room 2331


Where and when:

Tuesdays and Fridays: 10-12 (during first 6 weeks of period 2) in FL51, (except Friday Nov. first; in FL52).


Literature:

G.B. Folland: Fourier analysis and its applications, Wadsworth & Cole 1992.
Can be purchased through UBS (University Book Service),
Vasagatan 36, tel. 711 60 39


K. Holmåker: Tillämpningar av komplex analys och Fourieranalys, 1994.


Some handouts


Preliminary weekly program:

$\circ$ Week 1: Introduction, separation of variables, Fourier series

$\circ$ Week 2: Fourier series, termvise derivatives and integrals, applications

$\circ$ Week 3: Fourier transforms, definition, inverse Fourier transform, ect.

$\circ$ Week 4: Applications of Fourier transforms

$\circ$ Week 5: More on applications, discrete and fast Fourier transforms (Introducing the computer assignment)

$\circ$ Week 6: Orthogonality, convergence, completeness, etc.



Preliminary plan for problems:

The following problems are considered for demonstrated during exercise hours (D) and hone assignments (H). The problems maked by an "ö" are from "Extra Övningar (ps-fil), (pdf-fil)" which will be distributed during the week 1.

Week 1:
D: 2.1:8, 16; Ö1; 2.2:4, 6, 7; 2.3:2

H: 1.1:6; 2.1:18; 2.2:3, 5; Ö2; 2.3:3,4

Week 2:
D: 2.4:8; Ö4, 6, 7

H: 2.4:9, 10; Ö14, 15

Week 3:
D: ö10, 11, 13; 7.2:13a,b, 1, 9

H: 7.2:3, 12; Ö8, 9, 12

Week 4:
D: Ö16, 18, samplingsteoremet nr 2

H: Ö17; 7.6:3

Week 5:
D: 3.3:1, 9, 10a,b; ö21, 22; 7.2:6

H: 3.3:2, 10c,d; 3.4:2, 3, 7a

Week 6:
D: 3.5:4, 7, 10; ö24

H: 3.5:3, 5, 11, 12; ö23

Reserve:
D: 4.2:1, 2, 6; 4.3:3, 7

H: 4.2:5, 7, (8); 4.3:6; Ö26, 27


Project:
FFT(ps-fil)
FFT(pdf-fil)


M. Asadzadeh
December 04, 2000