ECTS
6 credits
Component
Faculty of Science
Description
This course is designed for first-year PCSI students. It provides an introduction to linear algebra and the resolution of linear differential systems (matrix calculus, resolution of linear systems, eigenvalues and diagonalization, resolution of linear differential systems).
Objectives
- Matrices: operations, power, properties, calculation. Remarkable matrices. 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 dimensions 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 base. Change of basis formula.
- 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 prerequisites
Necessary prerequisites*: High school mathematics curriculum + UE Mathematical tools 1.
Recommended prerequisites*: High school mathematics option. It is also highly recommended to have taken the Calculus UE in semester 1 or - at the very least - to have basic knowledge of polynomials and complex numbers.
Knowledge control
1 continuous assessment (written) + 1 final examination (written).
Further information
Content manager: laurent.guieu@umontpellier.fr