• ECTS

    5 credits

  • Component

    Faculty of Science

Description

This course is an introduction to linear algebra (formalized in S2) based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The EU also introduces the basic language of polynomials.

Read more

Objectives

Geometry of the plane and space :

  • Points, vectors, translation by a vector, linear combinations, collinearity, independence, bases, landmarks and coordinates, change of landmark, barycenters
  • Lines and planes (without coordinates then with), relative positions, intersections, equations
  • Classical linear and affine transformations: homotheties, translations, symmetries, projections of the plane and space
  • Introduction to Euclidean geometry: dot product, orthogonality, distance, vector product, orthonormal bases and reference points, orthogonal projections, distance of a point from a line/plane.

Linear algebra in R², R³ and Rn:

  • Points and vectors of Rn, affine subspaces and vector subspaces of Rn, parametric expression and equations, sev generated by a family of vectors, sea generated by a point and a sev.
  • Linear systems and pivot method: systems, solution sets, matrix of a system, staggered and reduced staggered systems, elementary operations, pivot method
  • Matrix calculation: operation on matrices, matrices of elementary operations on rows
  • Linear applications of R², R³ and Rn
  • Inversibility of a matrix and Gauss-Jordan method

Polynomials with real coefficients :

  • Definitions of a polynomial and a polynomial function, links
  • Coefficients, degree, roots, operations
  • Factoring and euclidean division of polynomials
  • Multiplicity of roots, link to the derivative, Taylor formula for polynomials
Read more

Necessary pre-requisites

High school mathematics program (including plane and space geometry, and solving equations), at least first year specialization and final year specialization in mathematics or complementary mathematics option.

 

Recommended prerequisites*:

High school mathematics program (including plane and space geometry, and solving equations), ideally with a mathematics major or even an expert mathematics option.

Read more

Additional information

Hourly volumes* :

            CM : 24 h

            TD : 25,5 h

            TP : 0

            Land : 0

 

Read more