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
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]

• Syllabus: [pdf]

• Introduction: [pdf]

• Chapter 1: Floating point arithmetic: [pdf]

• Chapter 2: Interpolation and approximation: [pdf]

• Chapter 3: Numerical integration: [pdf]

• Chapter 4: Solving linear equations: [pdf]

• Chapter 5: Solving nonlinear equations: [pdf]

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

• Appendix A: Linear algebra: [pdf]

• Appendix B: Introduction to Julia: [pdf]

• Appendix C: Chebyshev polynomials: [pdf]

• Bibliography: [pdf]

## Jupyter notebooks

• Chapter 2: Interpolation and Approximation: [Jupyter]

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

• Chapter 4: Linear systems: [Jupyter]

• Chapter 5: Nonlinear systems: [Jupyter]

• Chapter 6: Eigenvalue problems: [Jupyter]

• Exam revision notebook: [Jupyter]

## Midterms and final exams

• Spring 2022: Midterm: [pdf]

• Spring 2022: Final exam: [pdf]

• Spring 2022: Final exam with solutions: [pdf]

• Fall 2022: Midterm: [pdf]

• Fall 2022: Midterm with solutions: [pdf]

• Fall 2022: Final exam: [pdf]

• Fall 2023: Midterm: [pdf]

• Fall 2023: Midterm answer sheet: [Jupyter]

• Fall 2023: Final exam: [Jupyter]

## Slides

• Chapter 4: Solving linear systems: [HTML]

• Chapter 5: Solving nonlinear systems: [HTML]

• Chapter 6: Eigenvalue problems: [HTML]

• Chapter 7: Ordinary differential equations: [HTML]

## 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]