See here my previous teaching activities.

Numerical Analysis

This is the website for the course Numerical Analysis at Ecole des Ponts. Lecture notes and assignments will be posted here weekly.

Practical information

Lectures

Monday and Wednesday 15:00-16:15 Paris time, Room 608.

Recitation

Monday 16:30-18:00 Paris time, Room 608.

Office hours

Wednesday 16:30-17:30 Paris time in Room 608 or by email appointment.

Key dates

Midterm on Monday 23 Oct, Final exam on Monday 11 Dec.

Reference textbook

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

Assessment

The final grade is calculated as .6 A + .4 E, where A is the average assignment grade and E is the exam grade. The latter is calculated as E = max{FE, .4 ME + .6 FE}, where ME is the midterm exam grade and FE is the final exam grade.

Lecture notes

• Lecture notes: [pdf]

  Last modified: 30 Oct 2023.

• Syllabus: [pdf]

  Last modified: 18 Sep 2023.

• Introduction: [pdf]

  Last modified: 18 Sep 2023.

• Chapter 1: Floating point arithmetic: [pdf]

  Last modified: 30 Oct 2023.

• Chapter 2: Interpolation and approximation: [pdf]

  Last modified: 18 Sep 2023.

• Chapter 3: Numerical integration: [pdf]

  Last modified: 30 Oct 2023.

• Chapter 4: Solving linear equations: [pdf]

  Last modified: 18 Sep 2023.

• Chapter 5: Solving nonlinear equations: [pdf]

  Last modified: 18 Sep 2023.

• Chapter 6: Calculating eigenvalues and eigenvectors: [pdf]

  Last modified: 18 Sep 2023.

• Appendix A: Linear algebra: [pdf]

  Last modified: 04 Oct 2023.

• Appendix B: Introduction to Julia: [pdf]

  Last modified: 18 Sep 2023.

• Appendix C: Chebyshev polynomials: [pdf]

  Last modified: 18 Sep 2023.

• Bibliography: [pdf]

  Last modified: 18 Sep 2023.

Jupyter notebooks

• Chapter 2: Interpolation and Approximation: [Jupyter]

  Last modified: 18 Sep 2023.

• Midterm revision notebook: Interpolation, integration, linear systems: [Jupyter]

  Last modified: 18 Oct 2023.

• Chapter 4: Linear systems: [Jupyter]

  Last modified: 30 Oct 2023.

• Chapter 5: Nonlinear systems: [Jupyter]

  Last modified: 04 Dec 2023.

• Chapter 6: Eigenvalue problems: [Jupyter]

  Last modified: 20 Nov 2023.

• Exam revision notebook: [Jupyter]

  Last modified: 08 Dec 2023.

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.

• Fall 2023: Midterm: [pdf]

  Last modified: 23 Oct 2023.

• Fall 2023: Midterm answer sheet: [Jupyter]

  Last modified: 23 Oct 2023.

• Fall 2023: Final exam: [Jupyter]

  Last modified: 11 Dec 2023.

Slides

• Chapter 4: Solving linear systems: [HTML]

  Last modified: 18 Sep 2023.

• Chapter 5: Solving nonlinear systems: [HTML]

  Last modified: 18 Sep 2023.

• Chapter 6: Eigenvalue problems: [HTML]

  Last modified: 18 Sep 2023.

• Chapter 7: Ordinary differential equations: [HTML]

  Last modified: 18 Sep 2023.

Homework

Unless otherwise specified, the due time for assignments is the Monday of the following week at 11:59PM. All the assignments carry an equal weight. Submit your work to Brighspace.

• Homework 1: Complete Task 4 in Appendix B and Exercise 1.6. You may return either a file hw1.jl or a notebook hw1.ipynb.

  Extra credit: +2/10 if you complete Task 6 in Appendix B.

• Homework 2: Complete the second exercise (on interpolation nodes) of the Jupyter notebook.

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

• Homework 3: Complete exercise 2.15.

• Homework 4: Complete exercise 3.11.

• Homework 5: Complete exercise 3 in review notebook.

• Homework 6: Complete the penultimate exercise, on the steepest descent method, in the notebook 4_linear.ipynb.

• Homework 7: Complete the notebook on nonlinear equations

• Homework 8: Complete the notebook on eigenvalue problems

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.

Miscellaneous documents

• Calendar of Fall term 2023: [pdf]

Useful links

• Introduction to Julia by Jane Herriman. See [Link to video] and [Link to notebooks].