Numerical analysis
Summary
This course presents numerical methods for the solution of mathematical problems such as systems of linear and non-linear equations, functions approximation, integration and differentiation, and differential equations.
Content
- Polynomial approximation: interpolation and least squares
- Numerical differentiation and integration
- Direct methods for solving systems of linear equations
- Iterative methods for solving systems of linear and non-linear equations
- Numerical approximation of differential equations.
In the exercise the students will implement and test the studied methods using Python.
Keywords
Numerical algorithms, polynomial interpolation, numerical integration, numerical linear algebra, numerical solution of ODEs, iterative methods.
Learning Prerequisites
Required courses
- Analyse
- Algèbre linéaire
Recommended courses
Programmation
Learning Outcomes
By the end of the course, the student must be able to:
- Choose a method for solving a specific problem
- Interpret in the light of theory the results obtained from a computation
- Estimate numerical errors
- Prove theoretical properties of numerical methods
- Implement numerical algorithms
- Apply numerical algorithms to specific problems
- Describe numerical methods
- State the theoretical properties of mathematical problems and numerical methods
Transversal skills
- Use both general and domain specific IT resources and tools
- Access and evaluate appropriate sources of information.
Teaching methods
Ex cathedra lectures, exercices in class and with computers
Expected student activities
- Attendance to lectures
- Exercises resolution
- Resolution of elementary problem with computers
Assessment methods
Written exam. The exam may require the resolution of problems in a computer using Python.
Supervision
| Office hours | Yes |
| Assistants | Yes |
| Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
Yes
Bibliography
- Course's notes (English and French versions available).
- A. Quarteroni, P. Gervasio et F. Saleri : « Calcul Scientifique : Cours, exercices corrigés et illustrations en MATLAB et OCTAVE », Springer, 2010, ISBN 978-88-470-1676-7.
- A. Quarteroni et F. Saleri et P. Gervasio: « Scientific Computing with MATLAB and OCTAVE », Springer, 2014, ISBN 978-3-642-45367-0.
- A. Quarteroni, R. Sacco et F. Saleri : « Numerical Mathematics », Springer, 2007, ISBN 978-3-540-49809-4.
- J. Rappaz et M. Picasso: "Introduction à l'analyse numérique", PPUR - Collection: Enseignement des mathématiques - 2017
Ressources en bibliothèque
- Calcul scientifique / Quarteroni
- Scientific computing with MATLAB and OCTAVE / Quarteroni
- Numerical Mathematics / Quarteroni
- Introduction à l'analyse numérique / Rappaz & Picasso
Notes/Handbook
Available on the Moodle (English and French versions).
Moodle Link
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: mandatory