Analysis III (for IC)

Lecture title: Analysis III - MATH-203(d) 

Instructor: Pablo Antolin

Main assistant: Mohamed Ben Abdelouahab

• Link for Tuesdays broadcasting: https://mediaspace.epfl.ch/media/0_04hr1tf7
• Link for Thursdays broadcasting: https://mediaspace.epfl.ch/media/0_o839m5w2
• Link for Wednesday December 3: https://epfl.zoom.us/j/7450071839?omn=62464466500
• Link for Thursday December 4: https://epfl.zoom.us/j/7450071839?omn=67713824868

The lectures' recordings will be available in this channel (possibly with a few days delay).

Exercise sessions: Thursday 14:15-16:00 (in CE1103, CE15, CM1104, GC A1 416, GC C3 30).

Office hour instructor: Tuesday 13:45-14:15 (upon request)

After each course, the associated handwritten notes will be published on this moodle page.

General remarks:

Access to STCC:

Information and instructions for the exam:

• The exam will last 120 minutes.
• It will be a combination of (MCQ) multiple choice questions (around ~2/3 of the exam, but not fully decided yet) and open questions.
  • Incorrect answers to MCQ  will have negative points. No answer -> 0 points.
  • Only one correct answer.
  • Not all the MCQ value the same points.
  • No True/False questions.
  • No proofs of theorems in the exam.
• You can bring a cheat sheet to the exam: A single A4 written on both sides. Fourier transforms table will be provided in the exam booklet.

• Before the exam, make sure you know which is your assigned room and seat by looking at the map and at the student list.
• Check the PDF below regarding what to do and what not to do when marking MCQs.
• Do not unstaple the booklet.
  
• Scratch paper will be provided during the exam (it will be collected at the end of the exam). 
  
• Using a calculator or any electronic device is not permitted during the exam.
  
• The scoring system of each question will be indicated in the exam booklet.
• Use a black or dark blue ball-pen and clearly erase with correction fluid if necessary.

This mock exam is a representative sample of what the course exam will look like in January.  However, the length of each section may vary.

Here we provide a collection of previous years' exams.

This collection is only for the purpose of preparing for the exam. However, there is no guarantee that this year's exam will follow the same structure as these exams.

Note that most of these exams were prepared for a 3h duration. This year the exam will be 2h and we will reduce the exam length.

In addition, some solutions may be missing and there may be errors. WE WILL NOT PROVIDE MISSING SOLUTIONS.

In addition to the Fourier transforms table, some exams provided an extra formulaire. However, this year only the Fourier transforms table will be provided. You can bring your own cheat sheet (a double-sided A4 sheet).

ERRATUM

• 2018 (Correction), Question 15.  $a_{0\ }=\frac{2}{\pi} \int_0^\pi \sin x \,dx \quad \text{and} \quad a_{n }=\frac{2}{\pi} \int_0^\pi \sin x \cos(nx) \,dx$
  
• 2020 (Correction), Question 5. i.  2pi/n + 8/(pi n^3) if n is odd, and −2pi/n if n is even.
• 2025 (Correction), Question 3. "Les deux paramétrisations données parcourent les courbes de gauche à droite. Or, pour laisser le domaine à gauche, la partie du dessus (soit Γ2) doit être parcourue de droite à gauche".
• 2022 (Correction), Question 7. Instead of $\phi(3,2,-1)$, we should have $\phi(3,1,-2)$, and instead of 9 + 15 - 18 - 2 + $\alpha_3$ = ,0 we should have 9 +15 - 18 - 2 - 8 + $\alpha_3$ = 0.
• 2023 (Correction), Question 15. The computed curl is wrong, at it should be (-1, -1, 0). This changes the sign of the integral. This error gets compensated with another error in the sense of circulation of the boundary for the line integral. To circulate the boundary in the positive sense, according to the chosen parameterization, the integral limits should be pi/2, -pi/2, and not the other way around
• 2018, Question 13. There is a typo in the boundary conditions on v. The boundary condition should be at 1, and not a pi.
• 2025, Question 12. There is a typo in the definition of f(x): it should be e^{-4x}, and not e^{-4t}.

The purpose of this polycopy is to help students in engineering sections with their second year Analysis III course. However, it is not an alternative to the course itself, nor is it guaranteed to cover all the material in the course. You should always refer to the material covered in the lectures.

This polycopy has not been proofread, so we urge students who use it to apply appropriate scientific skepticism when reading it. We will be grateful if you report any typos or errors you find, as well as any other constructive comments. Note that as errors are discovered and fixed, new versions of the document will be released.

This document is currently only available in French. An English version may be published in future editions of this course.

The lectures on December 3rd and 4th will be in CO1.

The recordings of Tuesday's lecture can be found in the following mediaspace links (3 parts)

• Part 1
• Part 2
• Part 3