Numerical Analysis II
Table of Contents
General Information
| Lecturer: | Prof. Habib Ammari | Coordinators: | Alice Vanel | ||
| Bryn Davies | |||||
| First lecture: | Mon. 17.02.2020 | First Exercise Class: | Thu. 20.02.2020 |
Remote Teaching Arrangements
All classroom teaching has been suspended for the rest of the semester, meaning the rest of the course will be completed remotely under the following arrangements.
Prof. Ammari will record his lectures for students to view in their own time. Links to these recordings, as well as the lecture notes and the slides from the lectures, can be found below.
Exercise classes will continue to happen at the same time each Thursday but will be hosted on the web conferencing platform Zoom. Your tutor will contact you with details. We strongly encourage you to familiarise yourselves with Zoom and take part in these classes, as they will be the most effective way to have any questions answered.
Assignments will continue to be published each week. You should submit all your solutions using the SAM Upload Tool, including scans or photos of any handwritten solutions. Students are strongly enocuraged to complete the assignments, particularly since the Python programming skills they develop will form a large part of the final exam.
This year, bonus points can be earnt by completing the "Mid-term summary assignment" and "End-term summary assignment". These replace the mid-tem and end-term tests of previous years. See below for details.
Lecture Recordings
Here, you can find the recordings of Prof. Ammari's lectures. The titles correspond to the slides, given below.
16 March: Lecture 4, slides 1-17: explicit one-step method
20 March: Lecture 4, slides 18-21: explicit Euler scheme
23 March: Lecture 4, slides 22-39: high-order methods
27 March: Lecture 4, slides 40-46: linear systems
30 March: Lecture 4, slides 47-64: Runge-Kutta methods
3 April: Lecture 4, slides 65-83: Runge-Kutta methods as collocation methods
6 April: Lecture 4, slides 84-103: multistep methods
4 May: Lecture 5, slides 1-24: geometrical numerical integration methods
11 May: Lecture 5, slides 25-48: geometrical numerical integration methods
18 May: Lecture 5, slides 49-78: geometrical numerical integration methods
Lecture Notes
Here, you can find the lecture notes:
Here are the slides used in the lectures:
Assignments
There will be weekly homework assignments available for download from the course web page each Wednesday afternoon. Homework will include theoretical problems and programming problems, which are to be prepared using Python 3 (available at the student computer pools at ETH).
All solutions (both codes and scans or photos of written solutions) should be submitted using the SAM Upload Tool. Since we are not using a server for permanent storage, everything on the server might disappear after several weeks so please don't rely on it for storing files. Instructions on how to use the upload tool can be found in the User Guide.
Programming problems
Here is a Python cheat sheet, it contains instructions on how to install Python 3 and gives some useful commands. We also recommend these scipy lecture notes and Python for Scientists by John Stewart (available as a pdf on the ETH network) as other resources for learning Python.
Testate condition
As testate conditions are not in place anymore, it is not compulsory to hand in the assignments for correction. It is, however, recommended to submit the assignments as this will develop your understanding of the material and help you be better prepared for the exams.
Assignments
You can download the assignments (with templates) and solutions here:
| Problem Set | Templates | Published on | Submit by | Solutions |
|---|
Exercise Groups
All registered students should have received an email with the registration link (for MyStudies) to exercise groups.
| Group | Time | Classroom | Tutor |
|---|---|---|---|
| 1 | Thu. 10:15-12:00 | Zoom | He Yanchen |
| 2 | Thu. 10:15-12:00 | Zoom | Renggli Aaron |
| 3 | Thu. 10:15-12:00 | Zoom | Salib Anthony |
| 4 | Thu. 10:15-12:00 | Zoom | Schlagenhauf Dominik |
| 5 | Thu. 13:15-15:00 | Zoom | Bosselmann Viola |
| 6 | Thu. 13:15-15:00 | Zoom | Guzzi Emanuele |
Summary Assignments
Students will have the opportunity to earn bonus points by completing the "Mid-term summary assignment" and "End-term summary assignment". These will be two additional assignments consisting of simple and routine problems. Completing these assignments is not compulsory but doing so to a good standard will earn a student bonus points. Suppose a student gets x points (out of 60 points) in the mid-term summary assignment and y points (out of 60 points) in the end-term summary assignment, then they will get 0.25 bonus points added to their final grade if x+y > 80.
No programming problems will be involved in the mid-term and end-term summary assignments. The problems will focus on the important definitions and theorems from the course, with some examples.
The mid-term summary assignment will take place on 27th, April (Monday) and the end-term summary assignment will take place on 25th, May (Monday). In both cases, the assignments will be published here at 9am (Zurich time) and students will need to submit solutions via the SAM Upload Tool within 24 hours (i.e. by 9am on Tuesday). You will need to take photos or scans of your handwritten solutions. You can either fill in the white boxes or use your own paper. The assignments are designed to take around an hour to complete and will be similar to the mid-term and end-term tests of previous years (see below).
Mid-term summary assignment - please submit via the SAM Upload Tool by 9am on Tuesday, 28 April.
End-term summary assignment - please submit via the SAM Upload Tool by 9am on Tuesday, 26 May.
Exam
The final exam will be a (computer-aided) written exam. Programming with Python will be involved. Spyder will be available as the default editor. The lecture notes (in the form of the pdf, as given above) will be available during the exam.
The exam will take place on Friday 7th August, starting at 14:30. Registered students have been emailed details of the room allocation as well as relevant safety measures.
Previous Exams
| Exam | Templates |
|---|---|
| Winter 2014 | Not available |
| Summer 2014 | Summer 2014 |
| Winter 2015 | Winter 2015 |
| Summer 2015 | Summer 2015 |
| Winter 2016 | Not available |
| Summer 2016 | Summer 2016 |
| Winter 2017 | Winter 2017 |
| Summer 2017 | Summer 2017 |
| Winter 2018 | Winter 2018 |
| Summer 2018 | Summer 2018 |
| Winter 2019 | Not available |
| Summer 2019 | Summer 2019 |
| Winter 2020 | Winter 2020 |
| Summer 2020 | Summer 2020 |
Literature
Note: Extra reading is not considered important for understanding the course subjects.
- Deuflhard and Bornemann: Numerische Mathematik II - Integration gewohnlicher Differentialgleichungen, Walter de Gruyter & Co., 1994.
- Hairer and Wanner: Solving ordinary differential equations II - Stiff and differential-algebraic problems, Springer-Verlag, 1996.
- Hairer, Lubich and Wanner: Geometric numerical integration - Structure-preserving algorithms for ordinary differential equations}, Springer-Verlag, Berlin, 2002.
- L. Gruene, O. Junge "Gewoehnliche Differentialgleichungen", Vieweg+Teubner, 2009.
- Hairer, Norsett and Wanner: Solving ordinary differential equations I - Nonstiff problems, Springer-Verlag, Berlin, 1993.
- Walter: Gewöhnliche Differentialgleichungen - Eine Einuhrung, Springer-Verlag, Berlin, 1972.
- Walter: Ordinary differential equations, Springer-Verlag, New York, 1998.