| Course label : | Fundamental notions of Mathematics |
|---|---|
| Teaching departement : | EEA / Electrotechnics - Electronics - Control Systems |
| Teaching manager : | Mister PIERRE-ANTOINE THOUVENIN / Mister PIERRE CHAINAIS |
| Education language : | |
| Potential ects : | 0 |
| Results grid : | |
| Code and label (hp) : | MR_DS_S1_FNM - Fundamental notions of Math |
Education team
Teachers : Mister PIERRE-ANTOINE THOUVENIN / Mister PIERRE CHAINAIS
External contributors (business, research, secondary education): various temporary teachers
Summary
• Linear algebra (8h) ◦ Hermitian spaces, scalar product, projection matrices, orthogonal (unitary) and symmetric (self-adjoint) matrices. ◦ least squares problems ◦ matrix norms ◦ Singular Value Decomposition (SVD) and applications • Differential calculus and optimization (8h) ◦ functions of several variables, gradient, hessian ◦ application to gradient descent and convex problem ◦ optimization problems without and with constraints • Integration (8h) ◦ curves in R^d : line integrals and surface integrals ◦ multiple integrals: Fubini’s theorem ◦ change of variables ◦ surfaces in R^d and surface integrals ◦ Stokes theorem
Educational goals
After successfully taking this course, a student should be able to: • Think geometrically about linear algebra on Hermitian spaces • Optimize a function of several variables • Compute integrals in several variables
Sustainable development goals
Knowledge control procedures
Continuous Assessment
Comments: Exam, grading scale: (min) 0 – 20 (max)
Average passing grade = 10/20
Online resources
S Lang , Undergraduate Analysis, Springer (1997) S.DIneen, Multivariate calculus and Geometry, Springer G. Strang, Linear Algebra and Learning from Data, Wellesley-Cambridge Press
Pedagogy
24 hours, 8 lectures 4 exercises Language of instruction is specified in the course offering information in the course and program directory. English is the default language.
Sequencing / learning methods
| Number of hours - Lectures : | 12 |
|---|---|
| Number of hours - Tutorial : | 12 |
| 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
Bases of linear algebra, integration and analysis.