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Examiner and lecturer

Hjalmar Rosengren

Literature

G. B. Folland: Fourier analysis and its applications, Wadsworth & Brooks/Cole, 1992.
Folland's book will be sold by UBS after the first lecture September 3, 15.00. The price of the book is 500 SEK.

Further material

M. Asadzadeh, Lecture notes in Fourier analysis, in preparation.
We will use these notes for the chapter on Laplace transform, and they can also be useful for supplementary reading.
A ps-file is available here, but since there may be changes, do not print it all at once (Chapter 1 is enough for a start).
Notes 1 on Laplace transform.
Notes 2 on Bessel's inequality.
Notes 3 on the Gibbs phenomenon and periodic solutions to ODE.
Notes 4 on L2 theory of Fourier series.
Notes 5 on filters.
Corrections to Folland's book.
Some additional problems in Swedish and English. These exercises do not reflect the course content precisely.
Course contents and theory check-list.
Additional material may become available later.

Preliminary programme

F refers to Folland's book, A to Asadzadeh's lecture notes, N to my own notes.

Day	Chapter	Content	Exercises
W 3/9	A 1.1 (see also F 8.1)	Introduction, Laplace transform
Th 4/9	A 1.2-1.3, N1 (see also F 7.1, 8.3)	Applications of Laplace transform, convolution	Exercises 1
M 8/9	N1, F 1.3 (see also A 2)	Applications of Laplace transform Separation of variables (an example)	Exercises 2
Th 11/9	F 2.1, N2 (see also A 3.1-3.4)	Fourier series: Definition, Bessel's inequality	Exercises 3
M 15/9	F 2.2-2.4 (see also A 3.5-3.8)	Fourier series: Proof of inversion theorem, further properties	Exercises 4
Th 18/9	F 2.5	Separation of variables (again)	Exercises 5
M 22/9	N3	Gibbs phenomenon Periodic solutions to ODE	Exercises 6
Th 25/9	N4, see also F 3.1-3.3	Inner product spaces and complete orthonormal systems Norm convergence of Fourier series	Exercises 7
M 29/9	N4, F 7.2, example on pp. 226-227	Hilbert spaces and L2 spaces Fourier transform: Elementary properties	Exercises 8
Th 2/10	F 7.2, see also pp. 266-267	Fourier transform: Inversion theorem Fourier transform on L2	Exercises 9
M 6/10	N5, F pp. 229-231, 249-252	Applications in signal processing: Filters, sampling, discrete Fourier transform	Exercises 10
Th 9/10	F 3.5-3.6, example on pp. 101-103	Sturm-Liouville problems	Exercises 11
M 13/10	F 4.1-4.3	Techniques for inhomogeneous boundary value problems	F: 4.2.2, 4.2.4, 4.2.5, 4.3.5, 4.3.6, 4.3.7
Th 16/10	F 4.4, p. 228	Harmonic functions, Dirichlet problem
week 43		Reserve, Repetition

Examination

The exam will consist of 6 problems, giving a maximum of 24 points.
For MMG710 (GU students), grades are G (12-17 points) and VG (18-24 points).
For TMA362 (Chalmers students), grades are 3 (12-14 points), 4 (15-17 points) and 5 (18-24 points).
The exam takes place on October 25, 08.30-13.30.
No calculator or handbook is allowed at the exam.

Tag med giltig legitimation och kvitto på erlagd kåravgift!
Meddelande om resultat fås med epost via LADOK. (Detta sker automatiskt så fort tentan är rättad och resultaten är registrerade.)
Rättade tentor återfås på expeditionen för matematik.
Kontrollera att Du har fått rätt betyg och att poängsumman stämmer.
Eventuella klagomål på rättningen ska lämnas skriftligt (på expeditionen finns en blankett till hjälp).

Old exams

Some old exams have been handed out at the lecture October 6.