Number of hours
- Lectures 24.0
- Projects -
- Tutorials 24.0
- Internship -
- Laboratory works -
- Written tests -
ECTS
ECTS 4.0
Goal(s)
To provide students admitted through academic qualifications with the fundamentals of analysis for engineers, which will be useful throughout their studies in applied mathematics.
Our goal is to introduce the Lebesgue integral, focusing primarily on computational techniques to equip students with the practical skills necessary for further studies in applied mathematics. We will then present Hilbert spaces, including an application to Fourier series. To conclude the semester, we will introduce numerical methods for solving linear systems and nonlinear equations.
Responsible(s)
Valerie PERRIER, Emmanuel MAITRE
Content(s)
1. Lebesgue Integral
– Computational tools (antiderivatives, dominated convergence, Fubini’s theorem, parameter-dependent integrals, change of variables)
– L^p spaces on R. Convolution. Example applications
2. Hilbert Spaces
– Hilbert bases, projection onto closed convex sets
– Periodic functions, Fourier series
3. Basic Numerical Methods
– Iterative methods for solving linear systems
– Nonlinear equations (Newton and quasi-Newton methods)
Mathematics curriculum second-year undergraduate level with a major different from mathematics
Test
Evaluation : 50% of Examen Ecrit and 50% of Examen Ecrit (2H)
Resit : Examen Ecrit (2H)
Written exam, closed book.
Calendar
The course exists in the following branches:
- Curriculum - Core curriculum - Semester 6
Additional Information
Course ID : 3MMACI
Course language(s): 
You can find this course among all other courses.
Bibliography
- Le cours d'analyse de Terence Tao, Dunod
- Analyse réelle et complexe, Walter Rudin
- Real and complex analysis, Walter Rudin
- Introduction à l’analyse numérique matricielle et à l’optimisation, P.G. Ciarlet, Masson
- Patrick Lascaux et Raymond Théodor, Analyse numérique matricielle appliquée à l'art de l'ingénieur
- Iterative solution methods : Owe Axelsson, Cambridge University Press
- Analyse numérique - Une approche mathématique, Michelle Schatzmann
- Analysis (AMS, Graduate Studies in Mathematics), Elliott H. Lieb, Michael Loss
- An Introduction to Measure Theory (AMS, Graduate Studies in Mathematics), by Terence Tao