http://www.math.chalmers.se/Math/Grundutb/CTH/mallar/Style/mven.png

 

MMG710 (GU)/TMA362 (Chalmers), Fourier Analysis, Autumn 17

Latest news

                  Welcome to the course. This is a GU/Chalmers-combined course. (TEST)

                  The schedule for the course can be found in TimeEdit.

                   Exam 2018-Aug-23. Solution 2018-Aug-23. Exam 2017-Oct-21. Solution-p1, p2, p3, p4

Teachers

                   Genkai Zhang, email: genkai@chalmers.se, office MVH5023 (The H-building of Math. Sciences)

Course literature

               G. Folland, Fourier Analysis and Its Applications. Amer. Math. Soc., 1992.

              (Some supplementary texts by my colleague Hjalmar Rosengren on Filter and Gibbs    Phenomenon

Program

            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

1.1-1.3

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.

2.2-2.4

Inversion/Convergence Theorem

Thurs.

2.3-2.4

Convergence.

Further Properties of Fourier Series (FS): Differentiation and Integration of F.S.

W3. 11/9-

Tu.

2.5-2.6

Application of FS to Heat and Wave Equations, Gibbs phenomenon

Th.

3.1-3.4

Hilbert spaces, L2 theory of Fourier series

W4. 18/9

Mon.

3.2-3.4

More on Hilbert spaces and  L^2 spaces. Completeness. Parseval theorem.

Tu

3.5

Sturm-Liouville problems

Th.

4.1

Inhomogeneous boundary value problems

W5. 25/9

Tu

7.1-7.2

Fourier Transform (FT)

Th

7.1-7.2

Properties of FT. Riemann-Lebesgue Lemma. Inversion and Plancherel formula.

W6. 2/10

Tu

8.1-8.2

Laplace Transform (LT)

Th

7.3 pp. 229-231. 8.3 pp 273-279

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, 8:30-12:30

 

 

 

 

 

 

 

 

 

                 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): Suppl-Ex-1 (on Fourier Series), Suppl-Ex2 (on L^2-convergence) Supplem-Ex3

            

           (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] 8-10, 31-32.

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]16-18, 36-37, 51-52.

W5, Sept. 25-

Mon

[F] 3.4.2, 3.5.1,    3.5.2,    [E] 52-53

Mon. Wedn

[F] 4.2.3,   4.2.5,   4.3.6,                 [E]25-28

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 74-76, 78-79, 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

Repetition exercises

Course requirements

            The learning goals of the course can be found in the course plan.

             Check-list of main theorems.

Assignments

              Homework with bonus points.



                  Three sets of home-work-exercises for hand-in, on weeks 3, 5, 7. You may work in teams (of max. 3 team members) and submit you team’s work.

Assignment-1

Assignment-2

Assignment-3

Examination

                  Written examination.

Examination procedures

                   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 re-examination:
                  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.

Old exams

Exam2017Jan  Exam2017Jan-Solution  

Exam2016Oct  Exam2016Oct-Sol

Exam2015Aug  Exam2015Aug-Sol

Exam2015-JAN  Solution

2014-OCT  Solution

2014-Aug-with-Solution

2014-Jan-with-Sol.

2013-Oct-with-Sol.

 

Computer labs

                          Not included in the course. However you are encouraged to use Math. Softwares to compute Fourier Series/Transforms graphically/symbolically.

                      Reference literature:

Learning MATLAB, Tobin A. Driscoll ISBN: 978-0-898716-83-2 (The book is published by SIAM).