| Course label : | Mathematical methods |
|---|---|
| Teaching departement : | MIN / Applied Mathematics and General Computing |
| Teaching manager : | Madam AMANDINE LERICHE |
| Education language : | French |
| Potential ects : | 0 |
| Results grid : | |
| Code and label (hp) : | LE2_3_MA_MIN_MTL - Maths: Transformée de Laplace |
Education team
Teachers : Madam AMANDINE LERICHE
External contributors (business, research, secondary education): various temporary teachers
Summary
The objective of the course is to present mathematical tools dedicated to the problems of signal processing, filtering, and more generally to the problem of representation and analysis of physical systems (electrical, mechanical ...). The basic techniques of Laplace transform and Fourier analysis are presented and applied to classical physics equations. The second objective is to establish the theory of matrix reduction as well as the study of numerical series
Educational goals
At the end of the course, the student will be able to: - Use the tools wisely (Fourier and Laplace transforms) for the resolution of physical problems, - Calculate the Fourier series development of a periodic function, - Apply these tools to determine the frequency spectra of signals - Go from a time representation to a frequency representation and vice versa - Diagonalize / trigonalize a matrix independently - Contribution of the course to the skills framework; at the end of the course, the student will have progressed in: - Understanding a technical problem - Analyze and set up a scientific problem-solving approach - Provide a solution to a problem - Understand a complex project - Analyze and implement a scientific approach to solving complex projects - Provide a solution to a complex project - Analyze and compare technical solutions Knowledge worked: 1. Signal and mathematical description: step function, Dirac,ￜ 2. Development in Fourier series of a periodic function: definitions, Dirichlet's theorem, Parseval formula. 3. Fourier transform: Fourier synthesis, elementary properties, complex notation, application to usual signals 4. Study of signals and their transmission: time-frequency relationships, convolution equation, transfer within a system, power, energy, average value, autocorrelation and inter-correlation. 5. Laplace transform: definition, usual function transform, properties, inverse transform, mathematical applications, applications in physics. 6. Matrix reduction: eigenvalues, eigenvectors, diagonalization, trigonalisation of matrices and linear applications. 7. Digital series. Skills developed: - Formalize a physical problem and reformulate it using mathematical concepts. - Establish a clear and rigorous resolution of a physical problem by organizing its argument. - Put into practice theoretical results when solving an exercise. - Interpret the result of the analysis of a mathematical object. - Develop a critical sense when faced with a scientific result or a method. - Computational skills in order to apply them to other disciplines. - Work as a team, help a fellow student in difficulty, jointly think about improving the solution of a problem or a method used.
Sustainable development goals
Knowledge control procedures
Continuous Assessment / Final Exam
Comments:
Online resources
Pedagogy
Sequencing / learning methods
| Number of hours - Lectures : | 14 |
|---|---|
| Number of hours - Tutorial : | 14 |
| Number of hours - Practical work : | 0 |
| Number of hours - Seminar : | 0 |
| Number of hours - Half-group seminar : | 0 |
| Number of student hours in TEA (Autonomous learning) : | 0 |
| Number of student hours in TNE (Non-supervised activities) : | 0 |
| Number of hours in CB (Fixed exams) : | 0 |
| Number of student hours in PER (Personal work) : | 0 |
| Number of hours - Projects : | 0 |
Prerequisites
- Know how to calculate integrals, - Know how to calculate integrals by parts, - Knowing how to determine the limits of functions, the Hospital rule - Know the circular trigonometry formulas - Know the complex representation - LE1 linear algebra course