Last updated 10 June at 11:00. Changes are marked in red.
Questions during the exam
If you have any questions during the exam, you can contact me either by e-mail or Zoom.
- I will be answering e-mails on Monday afternoon, Wednesday morning and Friday afternoon.
- I will host Zoom sessions on Monday 14–15, Wednesday 10–11 and Friday 12–13. The Zoom meeting ID can be found under the "Zoom" link in Canvas.
- In problem 5, by "\(2\pi\)-periodic" I mean simply that \(f(-\pi)=f(\pi)\).
- In problem 3b, by "\((\cos(a_i)r_i)_{i=1}^\infty\)" I mean "\(\{\cos(a_i)r_i\}_{i\in\mathbb{N}}\)", the sequence with components \(\cos(a_i)r_i\) for \(i\in\mathbb{N}\).
- In problem 5 you are asked to prove convergence of the Fourier series. The only theorem about convergence of Fourier series that we have proved in lecture (and therefore, the only theorem I expect you to use) is Fejér's Theorem (Theorem 10.4.5). Note that the exam asks for convergence of the Fourier series, while the theorem states Cesàro convergence of the Fourier series.
- In the hint for problem 2d, it should read \(\|f_n\|_{\textrm{sup}}=1\) and not \(\|f\|_{\textrm{sup}}=1\).
- In problem 3, the number p is a fixed number.
Formalities
Please consult this page (Norwegian version) for information about exams at the Faculty of Mathematics and Natural Sciences. Note in particular item 2: The exam will be graded as pass/fail based on these criteria (Norwegian version).
- The exam is made available on 8 June at 9:00, and the deadline is 15 June at 9:00. I would estimate the work load to be approximately two work days.
- To change the language in Inspera, press the menu button in the top right corner.
- The exam problems will be made available in Inspera. For more information about digital exams, see this page.
- You will submit your answers in the form of one PDF file through Inspera. The PDF can be either a scan of your handwritten answers, or be created using any program such as LaTeX, Word, etc. The only requirement is that the text is clearly written and easy to read.
- If you are planning to scan your handwritten notes, please make yourself familiar with the scanning software well in advance of the deadline in order to make your scans as legible as possible.
- Do not include the course code, your name or your candidate number in the PDF. Your candidate number will be inserted automatically by Inspera.