# Numerical Analysis II

## Table of Contents

## General Information

Lecturer: | Prof. Habib Ammari | Coordinators: | Andrea Scapin | ||

Lorenzo Baldassari | |||||

First lecture: | Mon. 22.02.2021 | First Exercise Class: | Thu. 25.02.2021 |

## Remote Teaching Arrangements

The course will be held remotely in Zoom under the following arrangements.

Prof. Ammari will inform the students of the URL of the meeting in Zoom. He will also 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 be hosted on Zoom. Your tutor will contact you with details. We strongly encourage you to take part in these classes, as they will be the most effective way to have any questions answered.

Assignments will 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.

As last 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.

## Prof. Habib Ammari's Lecture Recordings in 2021

Here, you can find the recordings of Prof. Ammari's lectures. The titles correspond to the slides, given below.

22 February 2021: Lecture 1, part i: Some basics

26 February 2021: Lecture 1, part ii: Some basics

1 March 2021: Lecture 2: Existence, uniqueness, and regularity in the Lipschitz case

5 March 2021: Lecture 3, part i: Linear systems

8 March 2021: Lecture 3, part ii: Linear systems

12 March 2021: Lecture 4, part i: Numerical solution of ordinary differential equations

15 March 2021: Lecture 4, part ii: Numerical solution of ordinary differential equations

19 March 2021: Lecture 4, part iii: Numerical solution of ordinary differential equations

22 March 2021: Lecture 4, parti iv: Numerical solution of ordinary differential equations

26 March 2021: Lecture 4, part v: Numerical solution of ordinary differential equations

29 March 2021: Lecture 4, part vi: Numerical solution of ordinary differential equations

16 April 2021: Lecture 5, part i: Geometrical numerical integration methods for differential equations

23 April 2021: Lecture 5, part ii: Geometrical numerical integration methods for differential equations

26 April 2021: Lecture 5, part iii: Geometrical numerical integration methods for differential equations

30 April 2021: Lecture 5, part iv: Geometrical numerical integration methods for differential equations

3 May 2021: Lecture 5, part v: Geometrical numerical integration methods for differential equations

10 May 2021: Lecture 6, part ii: Finite difference methods

14 May 2021: Lecture 6, part iii: Finite difference methods

17 May 2021: Lecture 6, part iv: Finite difference method

## 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 |
---|---|---|---|---|

Assignment 0 | no templates | 17th Feb 2021 | Completed in class | Solution 0 Code 0 |

Assignment 1 | Template 1 | 24th Feb 2021 | 4th Mar 2021 | Solution 1 Code 1 |

Assignment 2 | Template 2 | 3th Mar 2021 | 11th Mar 2021 | Solution 2 Code 2 |

Assignment 3 | no templates | 10th Mar 2021 | 18th Mar 2021 | Solution 3 |

Assignment 4 | Template 4 | 17th Mar 2021 | 25th Mar 2021 | Solution 4 Code 4 |

Assignment 5 | Template 5 | 24th Mar 2021 | 1st Apr 2021 | Solution 5 Code 5 |

Assignment 6 | Template 6 | 31th Mar 2021 | 15th Apr 2021 | Solution 6 Code 6 |

Assignment 7 | No template | 14th Apr 2021 | 22th Apr 2021 | Solution 7 |

Assignment 8 | Template 8 | 21th Apr 2021 | 29rd Apr 2021 | Solution 8 Code 8 |

Assignment 9 | Template 9 | 28th Apr 2021 | 6th May 2021 | Solution 9 Code 9 |

Assignment 10 | No template | 5th May 2021 | 20th May 2021 | Solution 10 |

Assignment 11 | Template 11 | 19th May 2021 | 27th May 2021 | Solution 11 Code 11 |

Assignment 12 | No template | 26th May 2021 | 3rd June 2021 | Solution 12 |

### Exercise Groups

All registered students will receive an email with the registration link (for MyStudies) to exercise groups before the starting of the first exercise class (25th February).

Group | Time | Classroom | Tutor |
---|---|---|---|

1 | Thu. 10:15-12:00 | Zoom | V. Bosselmann |

2 | Thu. 10:15-12:00 | Zoom | P. Herkenrath |

3 | Thu. 10:15-12:00 | Zoom | T. Winstral |

4 | Thu. 14:15-16:00 | Zoom | A. Salib |

5 | Thu. 14:15-16:00 | Zoom | K. Shakhnovich |

## 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 **12th, April (Monday)** and the end-term summary assignment will take place on **31th, 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, 13 April**.

End-term summary assignment - please submit via the SAM Upload Tool by **9am on Tuesday, 1 June**.

## 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.

### 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 |

Winter 2021 | Winter 2021 |

## Prof. Habib Ammari's Lecture Recordings in 2020

Here, you can find the previous recordings of Prof. Ammari's lectures. The titles correspond to the slides, see above.

16 March 2020: Lecture 4, slides 1-17: explicit one-step method

20 March 2020: Lecture 4, slides 18-21: explicit Euler scheme

23 March 2020: Lecture 4, slides 22-39: high-order methods

27 March 2020: Lecture 4, slides 40-46: linear systems

30 March 2020: Lecture 4, slides 47-64: Runge-Kutta methods

3 April 2020: Lecture 4, slides 65-83: Runge-Kutta methods as collocation methods

6 April 2020: Lecture 4, slides 84-103: multistep methods

4 May 2020: Lecture 5, slides 1-24: geometrical numerical integration methods

11 May 2020: Lecture 5, slides 25-48: geometrical numerical integration methods

18 May 2020: Lecture 5, slides 49-78: geometrical numerical integration methods

## 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.