Numerical analysis

MATH-251(b)

Media

MATH-251(b) Numerical analysis

MATH-251(b) Numerical Analysis - Week 13 - Boundary Value Problems

20.05.2025, 11:48

This recording covers the Lecture 13 - Boundary Value Problems from the course syllabus.
It corresponds to the Chapter 12 of the course Notebook.

Recorded on 20.05.2025

MATH-251(b) Numerical Analysis - Week 7 - Direct Methods for Linear Systems

13.05.2025, 20:43

This recording covers the Lecture 7 - Direct Methods for Linear Systems (continued) from the course syllabus.
It corresponds to the Chapter 6 of the course Notebook.

Recorded on 01.04.2025

MATH-251(b) Numerical Analysis - Week 12 - Eigenvalue Problems

13.05.2025, 11:50

This recording covers the Lecture 12 - Eigenvalue Problems from the course syllabus.
It corresponds to the Chapter 8 of the course Notebook.

Recorded on 13.05.2025

MATH-251(b) Numerical Analysis - Week 4 - Interpolation

07.05.2025, 13:03

This recording covers the Lecture 4 - Interpolation from the course syllabus.
It corresponds to the Chapter 4 of the course Notebook.

Recorded on 11.03.2025

MATH-251(b) Numerical Analysis - Week 11 - Numerical Integration

06.05.2025, 11:53

This recording covers the Lecture 11 - Numerical Integration from the course syllabus.
It corresponds to the Chapter 9 of the course Notebook.

Recorded on 06.05.2025

MATH-251(b) Numerical Analysis - Week 10 - Initial Value Problems

29.04.2025, 11:56

This recording covers the Lecture 10 - Initial Value Problems from the course syllabus.
It corresponds to the Chapter 11 of the course Notebook.

Recorded on 29.04.2025

MATH 251(b) Numerical Analysis - Week 9 - Numerical Differentiation - 2nd Half

15.04.2025, 11:48

This recording covers the 2nd half of the Lecture 9 - Numerical Differentiation from the course syllabus.
It corresponds to the Chapter 10 of the course Notebook.

Unfortunately, the 1st half of the lecture could not be recorded due to technical issue with the audiovisual system.

Recorded on 15.04.2025

MATH-251(b) Numerical Analysis - Week 8 - Iterative Methods for Linear Systems

08.04.2025, 14:20

This recording covers the Lecture 8 - Iterative Methods for Linear Systems from the course syllabus.
It corresponds to the Chapter 7 of the course Notebook.

Recorded on 08.04.2025


This file is part of the content downloaded from Numerical analysis.

General Information

The Numerical Analysis lecture will be divided in 14 weekly lectures, with the following approximate syllabus (subject to change).

Syllabus

  • Lecture 1 (18.02.2025): introduction to Julia and to fixed-point iteration.
  • Lecture 2 (25.02.2025): fixed-point iteration.
  • Lecture 3 (04.03.2025): Newton's method.
  • Lecture 4 (11.03.2025): interpolation.
  • Lecture 5 (18.03.2025): interpolation, continued.
  • Lecture 6 (25.03.2025): regression and direct methods linear systems.
  • Lecture 7 (01.04.2025): direct methods for linear systems, continued.
  • Lecture 8 (08.04.2025): iterative methods for linear systems.
  • Lecture 9 (15.04.2025): numerical differentiation.
  • (22.04) no lecture (Easter)
  • Lecture 10 (29.04.2025): initial value problems.
  • Lecture 11 (06.05.2025): numerical integration.
  • Lecture 12 (13.05.2025): eigenvalue problems.
  • Lecture 13 (20.05.2025): boundary value problems.
  • Lecture 14 (27.05.2025): revision, non-linear approximations.

Admin

The course is taught by Prof. Michael Herbst, with Bruno Ploumhans (bruno.ploumhans@epfl.ch) serving as head teaching assistant.
  • Lectures take place on Tuesday from 10:15 to 12:00 in room CM 1 4.
  • Exercice sessions take place on Wednesday from 10:15 to 12:00 in room BC 07-08.
  • Teaching assistants for the lecture are: 
  •     Alessio Siviglia alessio.siviglia@epfl.ch
  •     Andrea Pintus andrea.pintus@epfl.ch
  •     Divya Suman divya.suman@epfl.ch
  •     Leo Digonzelli leo.digonzelli@epfl.ch
  •     Lorenzo Piersante lorenzo.piersante@epfl.ch
  •     Théodore Decaux theodore.decaux@epfl.ch


Lecture notes

The rendered lecture notes, a list of recommended books and further resources can be found on


https://teaching.matmat.org/numerical-analysis


If you spot an error feel free to make a pull request to the github repository generating this website.

Recording of the lectures

Some lectures were recorded, and are provided to you in case it's helpful:

Link to lecture recordings


Disclaimer: Some parts of the lecture might be missing or of poor quality due to technical problems. Future recordings are also not guaranteed.

Exam and Grade

Towards the end of the semester, there will be a graded exercise sheet. That will contribute to 20% of the final grade. The remaining 80% will be determined by a written exam during the summer exam session.

Exam consultations

The consultation for the written exam will take place on 18th July, organised centrally by CePro. You will be contacted by CePro closer to this date to register for this session. Only the registered participants will be able to consult their exam copy. Note that this will be the only possibility to consult your exam, as we will not organise additional sessions.

Exercises

The exercise sheets/notebooks are released on Tuesday at noon every week. Reference solutions will be released after a week.

Programming Language

The lecture will rely on coding exercices that demonstrate how theoretical concepts are implemented in practice. Students are strongly encouraged to solve the exercices and code solutions by themselves.
The lecture will use the Julia Programming Language. The first exercise session will be devoted to introducing the language and helping students set up a proper coding environment, which for us will be using Pluto notebooks in a web browser.
There you will also learn how to get help on using Julia. After this exercise session we will assume all students are able to work with the Pluto notebooks we provide. 

Note that this is not a programming lecture. Hence, exercises are designed to be doable by understanding and using code, with less emphasis on programming per se.

Given that some of you might have trouble installing Pluto, the contents of the first week are also provided in HTML format. The next weeks will be only available as Pluto notebooks, so please ask for help from the assistants if you have trouble installing Pluto.

Julia & Pluto Installation

On this Moodle page, you can find a working Julia & Pluto installation, provided as a VirtualBox image.

See the Virtual Machine Installation Instructions document.

Alternatively, you can install Julia on your own computer. It is not difficult and will be a nicer experience than working inside a Virtual Machine, however assistants will only be able to provide limited help with installation problems.

Assistants are there to provide support during the first week and you are welcome to ask for help. After that, Julia is assumed to be installed and working, and there will be a check in the second exercise session.

Julia Resources: 

Get started with coding Julia


Ed Forum

You are welcome to ask and answer questions on the Ed forum. As a general rule, the teaching team will not answer questions before 2 days have passed.

Make sure to install Julia and Pluto this week. Instructions for the Virtual Machine are available in the Virtual Machine Installation Instructions document above.

The 02_Julia chapter of the notes contains more information about Julia.

You are welcome to ask for help if you have trouble with the installation.