See here my previous teaching activities.

# Numerical Analysis

This is the website for the course MATH-UA 9252: *Numerical Analysis.* Lecture notes and assignments will be posted here weekly.
All the lectures will be hybrid: in room 406 and online at the Zoom link indicated below.

## Practical information

**Lectures**- Monday and Wednesday 15:00-16:15 Paris time, Room 406.
**Recitation**- Monday 16:30-18:00 Paris time, Room 406.
**Office hours**- Thursday 10:00 Paris time at the usual Zoom link or by email appointment.
**Zoom link**- https://nyu.zoom.us/j/2341268713.
**Assessment**- 60% assignments, 40% final exam.
**Reference textbook**https://link.springer.com/book/10.1007/b98885.

There will be an additional online lecture on **Friday 23 Sep** 15:00-18:00,
which is the make up day for Monday 31 Oct

## Lecture notes

- Lecture notes: [pdf]
*Last modified: 28 Sep 2022.* - Syllabus: [pdf]
*Last modified: 04 Sep 2022.* - List of examinable proofs: [pdf]
*Last modified: 26 Sep 2022.* - Introduction: [pdf]
*Last modified: 13 Sep 2022.* **Chapter 1**: Floating point arithmetic: [pdf]*Last modified: 27 Sep 2022.***Chapter 2**: Interpolation and approximation: [pdf]*Last modified: 28 Sep 2022.*- Animation: polynomial interpolation: [HTML]
- Animation: polynomial interpolation for the cosine function: [HTML]
- Animation: polynomial interpolation for the Runge function: [HTML]
- Animation: Comparison between global polynomial interpolation and local interpolation using cubic splines: [HTML]
**Chapter 3**: Numerical integration: [pdf]*Last modified: 28 Sep 2022.***Appendix A**: Linear algebra: [pdf]*Last modified: 21 Sep 2022.***Appendix B**: Introduction to Julia: [pdf]*Last modified: 09 Sep 2022.***Appendix C**: Chebyshev polynomials: [pdf]*Last modified: 27 Sep 2022.*- Bibliography: [pdf]
*Last modified: 05 Sep 2022.*

## Homework

Unless otherwise specified, the due time for assignments is the Saturday following the day of handing out. All the assignments carry an equal weight. You can send your work by email to urbain.vaes@inria.fr.

**Homework 1:**Complete one of the items of Task 5 in Appendix B. You may return either a file*hw1.jl*or a notebook*hw1.ipynb*.*Extra credit:*+2/10 if you complete all three items.**Homework 2:**Complete Exercise 1.23. Return a file*hw2.pdf*.*Extra credit:*+2/10 if you complete also exercise 1.5 (in this case, please send a file*hw2.jl*)**Homework 3:**Complete Exercise 2.15. Return a file*hw3.jl*.*Extra credit:*+2/10 if your code is the fastest.

At any time during the course, you can earn bonus points for the next assignment, with a maximum of +2 out of 10, if you spot typos in the lecture notes (only in the sections explicitly listed): +0.4 for an English or formatting typo, and +1 for a mathematical error. To communicate that you found a typo, just send me an email with [TYPO] in the subject line.

## Detailed log (adjusted a posteriori)

### Week 1

**Mon 5 Sep (lecture x2)**: Introduction and Sections 1.1 to 1.3. [Recording]**Wed 7 Sep (recitation)**: Introduction to Julia in Appendix B. [Recording]

### Week 2

**Mon 12 (lecture)**: Beginning of Chapter 2. [Recording]**Mon 12 Sep (recitation)**: Exercises 1.6, 1.20, 1.22 and 1.24.**Wed 14 Sep (lecture)**: Section 2.1: Newton interpolation and interpolation error. [Recording]

### Week 3

**Mon 19 (lecture)**: Interpolation error and Chebyshev polynomials. [Recording]**Wed 21 Sep (lecture)**: Hermite interpolation and approximation. [Recording]**Wed 21 Sep (recitation)**: Exercises 2.1, 2.2, 2.6, 2.7 and C.5.**Fri 23 Sep (lecture)**: Section 2.2.1, approximation of data points. [Recording]**Fri 23 Sep (recitation)**: Exercises 2.8, 2.11 and 2.13.

### Week 4

**Mon 27 (lecture)**: End of Chapter 2 and beginning of Chapter 3. [Recording]

**Mon 27 Sep (recitation)**: Exercise 2.14.