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. Apart from the first few lectures which will be fully online, all the lectures will be hybrid: in room 406 and online at the Zoom link indicated below.

Practical information

Lectures

Tuesday and Thursday 14:15-15:30 Paris time, Room 406.

Recitation

Thursday 15:45-17:15 Paris time, Room 406.

Office hours

Tuesday 15:40, or by email appointment.

Zoom link

https://nyu.zoom.us/j/2341268713.

Assessment

70% assignments, 30% final exam.

Reference textbook

https://link.springer.com/book/10.1007/b98885.

There will be an additional online lecture on Friday 18 Feb 14:15-15:30, which is the make up day for Tuesday 25 Jan.

Lecture notes

• Lecture notes: [pdf]

  Last modified: 01 Jul 2022.

• Syllabus: [pdf]

  Last modified: 02 Feb 2022.

• List of examinable proofs: [pdf]

  Last modified: 04 May 2022.

• Introduction: [pdf]

  Last modified: 01 Jul 2022.

• Chapter 1: Floating point arithmetic: [pdf]

  Last modified: 27 Mar 2022.

• Chapter 2: Solving linear equations: [pdf]

  Last modified: 13 Apr 2022.

• Chapter 3: Solving nonlinear equations: [pdf]

  Last modified: 10 Jul 2022.

• Chapter 4: Calculating eigenvalues and eigenvectors: [pdf]

  Last modified: 04 May 2022.

• Chapter 5: Interpolation and approximation: [pdf]

  Last modified: 10 Jul 2022.

• Chapter 6: Numerical integration: [pdf]

  Last modified: 06 May 2022.

• Appendix A: Vectors and matrices: [pdf]

  Last modified: 04 May 2022.

• Appendix B: Introduction to Julia: [pdf]

  Last modified: 05 May 2022.

• Bibliography: [pdf]

  Last modified: 21 Apr 2022.

Midterm and final exam

• Practice midterm: [pdf]

  Last modified: 31 Mar 2022.

• Final exam: [pdf]

  Last modified: 12 May 2022.

• Final exam with solutions: [pdf]

  Last modified: 10 Jul 2022.

Homework

Unless otherwise specified, the due time for assignments is the Friday of the following week, end of the day. All the assignments carry an equal weight. You can send your work by email to urbain.vaes@nyu.edu.

• Homework 1: Complete task 4 in Appendix B. You may return either a file hw1.jl or a Jupyter notebook hw1.ipynb.

  Extra credit: +2/10 if you also provide a working implementation for task 5. [solution]

• Homework 2: Complete Exercises 1.6 and 1.16. Return your work in a Jupyter notebook called hw2.ipynb.

  Extra credit: +2/10 if you complete also Exercise 1.17.

• Homework 3: Complete Exercise 2.7. Return your work in a file called hw3.jl.

  Extra credit: ... if you complete the part that says 'extra credit', and if your code is reasonably fast.

• Homework 4: Complete Exercise 2.18. Return your work in a file called hw4.jl.

  Extra credit: Find a formula for the optimal ω in the relaxation method.

• Homework 5: Complete Exercises 2.22 and 2.23. Return your work in a file called hw5.ipynb.

  Starting point: this julia file [hw5.jl]

• Homework 6: Complete Exercises 3.12. Return your work in a file called hw6.jl.

  Extra credit: +2/10 if you complete also exercise 3.5.

• Homework 7: Complete Exercise 4.1. Return your work in a file called hw7.ipynb before Thu 14 Apr. Dataset: [data.tar.gz]

  Extra credit: +1/10 if you complete the part that says 'extra credit'.

• Homework 8: Complete Exercise 5.11. Return your work in a file called hw8.jl before Thu 28 Apr.

  Extra credit: +1/10 if you implement the polyonmial interpolation yourself, without relying on a package.

• Homework 9: Complete exercise 2.1 in the Jupyter notebook of week 13. Return your work before Sun 8 May.

  Accompanying documents: [Jupyter notebook][dataset1][dataset2]

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, you can either send me an email with [TYPO] in the subject line, or fix the typo directly in the LaTeX source. (For the latter option, you will need a Github account.)

Julia codes

• Chapter 1: Floating point arithmetic: [Julia] [Jupyter] [HTML]

  Last modified: 27 Mar 2022.

• Chapter 2: Solving linear systems: [Julia] [Jupyter] [HTML]

  Last modified: 27 Mar 2022.

Detailed log (adjusted a posteriori)

Week 1

• Thu 27 Jan (lecture): Introduction, Section 1.1, and beginning of Section 1.2. [Recording]
• Thu 27 Jan (recitation): Appendix B.

Week 2

• Tue 01 Feb (lecture): Sections 1.2 and 1.3. We will not cover Sections 1.4 and 1.5 during the lectures. [Recording]
• Thu 03 Feb (lecture): Sections 2.1 and background material in Sections A.2 and A.3. [Recording]
• Thu 03 Feb (recitation): Exercises 1.3, 1.4, 1.7 and 1.14.

Week 3

• Tue 08 Feb (lecture): Sections 2.1 and 2.2. [Recording]
• Thu 10 Feb (lecture): Section 2.2. [Recording]
• Thu 10 Feb (recitation): Exercises 2.1, 2.2, 2.4 and 2.5.

Week 4

• Tue 15 Feb (lecture): End of 2.2. [Recording]
• Thu 17 Feb (lecture): Section 2.3. [Recording]
• Thu 10 Feb (recitation): Exercices 2.9 to 2.15.
• Thu 18 Feb (online lecture): Section 2.3. [Recording]

Week 5

• Tue 22 Feb (lecture): Section 2.3.1: convergence results for Jacobi's method and the relaxation method. [Recording]
• Thu 24 Feb (lecture): End of Section 2.3.1 and beginning of Section 2.3.2. [Recording]
• Thu 24 Feb (recitation): Exercise 2.12, 2.13 and 2.19. Then 2.18 if time permits.

Week 6

• Tue 1 Mar (lecture): Section 2.3.2. [Recording]
• Thu 3 Mar (lecture): End of Section 2.3.2. [Recording]
• Thu 3 Mar (recitation): Exercises 2.20 and 2.21.

Week 7

• Tue 8 Mar (lecture): End of Section 2.3.2 and beginning of Chapter 3. [Recording]
• Thu 10 Mar (lecture): Beginning of Section 3 [Recording]
• Thu 10 Mar (recitation): Exercise 2.24 and Exercises 3.1 to 3.4.

Week 8

• Tue 21 Mar (lecture): Section 3.3. [Recording]
• Thu 24 Mar (lecture): Section 3.4. [Recording]
• Thu 24 Mar (recitation): Exercise 3.6 to 3.10.

Week 9

• Tue 29 Mar (lecture): Introduction to Chapter 4. [Recording]
• Thu 31 Mar (lecture): Practice midterm and end of Section 4.2.

Week 10

• Tue 5 Apr (lecture): Section 4.3 and 4.4. [Recording]
• Thu 7 Apr (lecture): End of Chapter 4. [Recording]
• Thu 7 Apr (recitation): Exercises of Chapter 4.

Week 11

• Tue 12 Apr (lecture): Beginning of Chapter 5, introduction to interpolation. [Recording]
• Thu 14 Apr (lecture): Sections 5.1.3 and 5.1.4. [Recording]
• Thu 14 Apr (recitation): Exercises of Chapter 5.

Week 12

• Tue 19 Apr (lecture): Sections 5.1.5 and 5.1.6. [Recording]
• Thu 21 Apr (lecture): End of Section 5.1 and beginning of Section 5.2. [Recording]
• Thu 21 Apr (recitation): Exercises of Chapter 5.

Week 13

• Tue 26 Apr (lecture): Beginning of Chapter 6. [Recording]
• Thu 28 Apr (lecture): Guest lecture on machine learning approaches to function approximation.
• Thu 28 Apr (recitation): Exercises in this Jupyter notebook. Accompanying datasets: [dataset1][dataset2]

Week 14

• Tue 3 May (lecture): Composite integration methods and Richardson's extrapolation. [Recording]
• Thu 5 May (lecture): End of Chapter 6. [Recording]
• Thu 5 May (recitation): Exercises of Chapter 6.

Miscellaneous documents

• Calendar of Spring term 2022: [pdf]
• Slides 28 April: [pdf]