Linear Algebra
Eigen-elements: eigenvalues, eigenvectors, characteristic polynomial
Diagonalization
Applications
Euclidean Spaces
Scalar product: examples, properties
Orthogonality: Pythagoras theorem, orthogonal bases, orthogonal projection
Bilinear Algebra
Bilinearity
Symmetric positive definite matrices: definition, properties, characterization
Ordinary Differential Equations (ODEs) – Linear
Examples, general framework of affine ODEs
Special case of linear ODEs with constant coefficients
Multivariable Functions
Notion of differential for multivariable functions
First- and second-order optimality conditions
Multiple integrals
Numerical Analysis
Numerical resolution of ODEs
Interpolation
Numerical integration
Least squares method
Objectifs
At the end of this module, the student should have understood and be able to explain the following key concepts:
Knowledge of the main results in matrix reduction
Understanding the concept of scalar product and orthogonality
Basic notions of bilinear algebra
The concept of the differential of a multivariable function and partial derivatives
Solving linear differential equations with or without a forcing term
Calculations of integrals of functions of several variables
Finding extrema of a function
The least squares method
Numerical interpolation
Numerical integration
Numerical resolution of differential equations
List of competencies:
Code Competency
1_1 Master mathematical concepts and computational tools relevant to engineering
1_2 Develop rigorous scientific reasoning and the capacity for abstraction
2_1 Master the fundamental tools of the mathematical engineer
(Competency matrix of CTI, 2019)
Pré-requis
Linear algebra and first-year analysis, programming in Python.
Évaluation
L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…
