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: 15 Jan 2023.* - Syllabus: [pdf]
*Last modified: 04 Sep 2022.* - List of examinable proofs: [pdf]
*Last modified: 08 Dec 2022.* - Introduction: [pdf]
*Last modified: 13 Sep 2022.* **Chapter 1**: Floating point arithmetic: [pdf]*Last modified: 06 Oct 2022.***Chapter 2**: Interpolation and approximation: [pdf]*Last modified: 27 Dec 2022.***Chapter 3**: Numerical integration: [pdf]*Last modified: 27 Dec 2022.***Chapter 4**: Solving linear equations: [pdf]*Last modified: 17 Nov 2022.***Chapter 5**: Solving nonlinear equations: [pdf]*Last modified: 27 Dec 2022.***Chapter 6**: Calculating eigenvalues and eigenvectors: [pdf]*Last modified: 11 Dec 2022.***Appendix A**: Linear algebra: [pdf]*Last modified: 17 Nov 2022.***Appendix B**: Introduction to Julia: [pdf]*Last modified: 15 Jan 2023.***Appendix C**: Chebyshev polynomials: [pdf]*Last modified: 15 Jan 2023.*- 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.**Homework 4:**Complete Exercise 3.11. Return a file*hw4.jl*.*Extra credit:*+2/10 if your confidence interval is better than the one in the example solution.**Homework 5:**Complete Exercise 4.24. Return a file*hw5.jl*.*Extra credit:*+2/10 if you also complete the part that says "Extra credit".**Homework 6:**Complete Exercise 4.25. Return a file*hw6.jl*.*Extra credit:*+2/10 if you have the fastest code.**Homework 7:**Complete Exercise 5.13 Return a file*hw7.jl*.*Extra credit:*+2/10 if you have the fastest code.**Homework 8:**Complete Exercise 6.1. Return your work in a file called*hw8.ipynb*. Dataset: [data.tar.gz]*Extra credit:*+1/10 if you complete the part that says 'extra credit'.

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.

## Midterms and final exams

- Spring 2022: Midterm: [pdf]
*Last modified: 31 Mar 2022.* - Spring 2022: Final exam: [pdf]
*Last modified: 12 May 2022.* - Spring 2022: Final exam with solutions: [pdf]
*Last modified: 23 Oct 2022.* - Fall 2022: Midterm: [pdf]
*Last modified: 30 Oct 2022.* - Fall 2022: Midterm with solutions: [pdf]
*Last modified: 02 Dec 2022.* - Fall 2022: Final exam: [pdf]
*Last modified: 13 Dec 2022.*

## 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 Sep (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 Sep (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 26 Sep (lecture)**: End of Chapter 2 and beginning of Chapter 3. [Recording]**Mon 26 Sep (recitation)**: Exercise 2.14.**Wed 28 Sep (lecture)**: Error estimates in chapter 3. [Recording]

### Week 5

**Mon 3 Oct (lecture)**: Richardson extrapolation. [Recording]**Mon 3 Oct (recitation)**: Exercises from Chapter 3.**Wed 5 Oct (lecture)**: End of Chapter 3: Gaussian quadrature. [Recording]

### Week 6

**Mon 10 Oct (lecture)**: Numerical integration using the Monte Carlo method. [Recording]**Wed 12 Oct (lecture)**: Section 4.1, on conditioning for linear systems. [Recording]**Wed 12 Oct (recitation)**: Exercises from Chapter 3

### Week 7

**Mon 17 Oct (lecture)**: Conditioning and direct methods for linear systems. [Recording]**Mon 17 Oct (recitation)**: Exercise in Chapter 4: vector and matrix norms.**Wed 19 Oct (lecture)**: End of Section 4.2 [Recording]

### Week 8

**Mon 24 Oct (lecture)**: Midterm.**Wed 26 Oct (lecture)**: Beginning of Section 4.3 [Recording]

### Week 9

**Wed 2 Nov (lecture)**: Section 4.3, convergence of basic iterative metods. [Recording]

### Week 10

**Mon 7 Nov (lecture)**: Section 4.3, convergence of Jacobi and Gauss-Seidel. [Recording]**Mon 7 Nov (recitation)**: Exercises 4.12, 4.13, 4.14, 4.15, 4.16.**Wed 9 Nov (lecture)**: Section 4.3, introduction to gradient methods. [Recording]

### Week 11

**Mon 14 Nov (lecture)**: End of Chapter 4 and beginning of Chapter 5. [Recording]**Mon 16 Nov (recitation)**: Exercises 4.18, 4.27, 4.28, 4.20.**Wed 16 Nov (lecture)**: Fixed point methods [Recording]

### Week 11

**Mon 21 Nov (lecture)**: Convergence results for fixed-point methods. [Recording]**Mon 21 Nov (recitation)**: Exercises from Chapter 5.**Wed 23 Nov (lecture)**: Proof of quadratic convergence for Newton-Raphson. [Recording]

### Week 13

**Mon 28 Nov (lecture)**: Beginning of Chapter 6: power iteration. [Recording]**Wed 30 Nov (lecture)**: Inverse and subspace iterations. [Recording]**Wed 30 Nov (recitation)**: Exercises from Chapter 6.

### Week 14

**Mon 5 Dec (lecture)**: End of Chapter 6. [Recording]**Mon 5 Dec (recitation)**: Exercises from Chapter 6.**Wed 7 Dec (lecture)**: Revisions. [Recording]