Welcome to the course. This is a GU/Chalmerscombined course. (TEST)
The schedule for the course can be found in TimeEdit.
Exam 2018Aug23.
Solution 2018Aug23.
Exam 2017Oct21.
Solutionp1, p2, p3, p4
Genkai Zhang, email: genkai@chalmers.se,
office MVH5023 (The Hbuilding of Math. Sciences)
G. Folland, Fourier Analysis and Its Applications. Amer. Math. Soc., 1992.
(Some supplementary texts by my colleague Hjalmar Rosengren on Filter and Gibbs Phenomenon
The course spans a total period of 8 weeks, the first seven weeks being teaching, the last week repetition and examination.
Dag/Day 
Avsnitt/Chapter 
Innehåll/Content 
Week 1. 28/8 Tues. 29/8 
1.11.3 
Introduction/Motivation. Wave equations/heat equations. Method of Separation of Variables for Solving PDE. 
Wedn. & Thurs 
1.3, 2.1 
Separation of varibles. Fourier series 
W2. 4/9 Tues. 
2.22.4 
Inversion/Convergence Theorem 
Thurs. 
2.32.4 
Convergence. Further Properties of Fourier Series (FS): Differentiation and Integration of F.S. 
W3. 11/9 Tu. 
2.52.6 
Application of FS to Heat and Wave Equations, Gibbs phenomenon 
Th. 
3.13.4 
Hilbert spaces, L2 theory of Fourier series 
W4. 18/9 Mon. 
3.23.4 
More on Hilbert spaces and L^2 spaces. Completeness. Parseval theorem. 
Tu 
3.5 
SturmLiouville problems 
Th. 
4.1 
Inhomogeneous
boundary value problems 
W5. 25/9 Tu 
7.17.2 
Fourier Transform (FT) 
Th 
7.17.2 
Properties of FT. RiemannLebesgue Lemma. Inversion and Plancherel formula. 
W6. 2/10 Tu 
8.18.2 
Laplace Transform (LT) 
Th 
7.3 pp. 229231. 8.3 pp 273279 
Applications of FT and LT. Diff. Eqs on the real line/half line. 
W7. 9/10 Tu 
4.4 
Laplace equations, Harmonic functions. Dirichlet problems. 
Th 
4.4 
Poisson formula for solutions of Dirichlet problem on the disc. 
W8. 16/10 Mon.

Repetition 
Repetition. Solving earlier examination problems. 
Exam. Sat. 21/10,
8:3012:30 


Rekommenderade
övningsuppgifter/Recommended Exercises
We will have three collections of exercises:
[F] exercises in Folland’s book which are a bit more conceptual,
[E] additional exercises
(more computational), and
[S] supplementary
exercises (more elementary/introductory): SupplEx1
(on Fourier Series), SupplEx2 (on
L^2convergence) SupplemEx3
(We shall solve some of the
exercise below for the demonstration on the blackboard. Please try yourself
before the class, and try those unsolved ones afterwards.)
Dag/Day 
Uppgifter/Exercises 
W1, Aug. 28 Wedn 
[E]
1,2, [F] 1.1.1, 1.1.5, 1.1.6, 1.2.4, 1.3.1,
1.3.4, 1.3.7 
W2, Sept. 4 Mon. 
[F] Table 1: 2, 8, 20, [E]3, 4 
Wedn 

[F]
2.2.2, 2.2.4, 2.4.3, 2.4.7,
2.4.11, [E] 5, 6, 86 

W3, Sept. 11 Mon 
F]
2.3.2, 2.3.3, 2.3.5, [E] 810,
3132. 
Wedn 
F.
2.3.2, 2.3.5, 2.3,7,
[E] 13, 15 
W4, Sept. 18 Mon.
Wedn 
[F] 2.5.1, 2.5.5, 3.3.1, 3.3.2, 3.3.9, 3.3.10, 3.4.6, 3.4.7, [E]1618, 3637, 5152. 
W5, Sept. 25 Mon 
[F]
3.4.2, 3.5.1, 3.5.2, [E] 5253 
Mon.
Wedn 
[F]
4.2.3, 4.2.5, 4.3.6,
[E]2528 
W6. Oct. 2 Mon 
[F]
7.1.1, 7.2.2,
7.2.3, 7.2.12, [E]54ace,
56, 58. 
Wedn 
[F]
7.2.13ab, 7.3.1, [E] 60ab(cde), 64, 65, 67, 76. 
W7. Oct. 9 Mon 
[E] E 7476, 7879, 81, [F]8.1.8, 8.2.3, 8.2.5 
Wedn. 
[F] 4.4.1, 4.4.2, 4.4.6, [E]22, 30. 
W8. Oct .
16 Mon 
The learning goals of the course can be found in the course plan.
Homework with bonus points.
Three sets of
homeworkexercises for handin, on weeks 3, 5, 7. You
may work in teams (of max. 3 team members) and submit you team’s work.
Written examination.
In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.
Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.
At the exam, you should be able to show valid identification.
After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.
At the annual
(regular) examination:
When it is practical, a separate review
is arranged. The date of the review will be announced here on the course
homepage. Anyone who can not participate in the
review may thereafter retrieve and review their exam at the Mathematical
Sciences Student office. Check that you have the right grades and score.
Any complaints about the marking must be submitted in writing at the office,
where there is a form to fill out.
At reexamination:
Exams are reviewed and
retrieved at the Mathematical
Sciences Student office. Check that you have the right grades and score.
Any complaints about the marking must be submitted in writing at the office,
where there is a form to fill out.
Not included in the course. However you are encouraged to use Math. Softwares to compute Fourier Series/Transforms graphically/symbolically.
Learning MATLAB, Tobin A.
Driscoll ISBN: 9780898716832 (The book is published by SIAM).