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 Notes

Here, you can find the lecture notes:

Lecture Notes

Here are the slides used in the lectures:


Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6


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.


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.


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 Mid-term and End-term Exams

Mid Term End Term
2017 2017
2018 2018
2019 2019


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.