ECTS
6 credits
Training Structure
College of Sciences
Time of year
Spring
Description
This course is intended for first-year PCSI students. It provides an introduction to linear algebra and the solution of linear differential systems (matrix calculus, solving linear systems, eigenvalues and diagonalization, and solving linear differential systems).
Objectives
- Matrices: operations, powers, properties, calculations. Special matrices. The vector space of matrices. The concept of a vector subspace. The spaceR^n viewed as the space of column matrices.
- Linear systems and the pivot method. Solution space.
- Determinants in 2 and 3 dimensions - Invertible matrices - Application to linear systems.
- Bases ofRn - coordinates. Intuitive concept of dimension. Change of basis - transition matrix.
- Linear applications fromRp toRn. Matrices relative to a basis. Basis change formula.
- Elementary diagonalization (the exercises and examples will be limited to 2×2 and 3×3 matrices).
- Application of diagonalization to the solution of linear differential equations.
- (Optional: Matrix Exponential. Introduction to Nonlinear Differential Systems.)
Class Hours
- Mathematical Tools 3 - CMLecture27 hours
- Mathematical Tools 3 - TutorialTutorials27 hours
Mandatory Prerequisites
Requiredprerequisites*: High school mathematics curriculum + Mathematical Tools 1 course.
Recommended prerequisites*: High school advanced mathematics course. It is also strongly recommended that students have taken the Calculus course in Semester 1 or—at a minimum—have a basic understanding of polynomials and complex numbers.
Knowledge Assessment
1 ongoing assessment (written) + 1 final exam (written).
Additional Information
Content Manager: laurent.guieu@umontpellier.fr