ECTS
6 credits
Component
Faculty of Science
Description
This course is intended for first year PCSI students. It is an introduction to linear algebra as well as to the solution of linear differential systems (matrix calculus, solution of linear systems, eigenvalues and diagonalization, solution of linear differential systems).
Objectives
- Matrices: operations, power, properties, calculation. Remarkable matrices. The vector space of matrices. Notion of vector subspace. The space Rn seen as the space of matrix-columns.
- Linear systems and pivot method. Space of solutions.
- Determinant in dimension 2 and 3 - Invertible matrices - Application to linear systems.
- Bases of Rn - coordinates. Intuitive notion of dimension. Change of base - transition matrix.
- Linear applications Rp → Rn. Matrix relative to a basis. Formula for change of basis.
- Elementary diagonalization (exercises and examples will be limited to the case of 2×2 and 3×3 matrices).
- Application of diagonalization to the solution of linear differential systems.
- (Optional: Matrix exponential. Introduction to non-linear differential systems)
Necessary pre-requisites
Required prerequisites*: High school mathematics program + UE Mathematical tools 1.
Recommended prerequisites*: Expert mathematics option in high school. It is also strongly recommended to have followed the Calculus course in semester 1 or - at least - to have a basic knowledge of polynomials and complex numbers.
Knowledge control
1 continuous assessment (written) + 1 final exam (written).
Additional information
Content manager: laurent.guieu@umontpellier.fr