Pagora rubrique Formation 2022

Mathematics - 3FME1003

  • Number of hours

    • Lectures -
    • Projects -
    • Tutorials 21.0
    • Internship -
    • Laboratory works -
    • Written tests 1.5

    ECTS

    ECTS 25.0

Goal(s)

Learning outcomes :

  • To do sums and matrix products
  • To calculate the determinant of a matrix
  • To invert a matrix in order to solve equation systems
  • To calculate the eigenvalues of a matrix
  • To determine subspaces associated with specific eigenvalues and to diagonalize matrices
  • To solve a linear differential equation of first order (an initial condition to find a constant) and second order (two initial conditions to find two constants) to determine all solution functions, over one or more intervals, n times derivable over this or these intervals
  • To decompose a rational fraction into simple elements and calculate eigenvalues and subspaces based on complex numbers, polynomials, and trigonometric functions
  • To know the relationship between integrals and primitives and integration methods (Immediate method, Integration by variable change, Integration by parts, Integration of trigonometric functions, Integration of rational functions)
  • To understand scientific or technical articles that would use mathematics as a descriptive language

Responsible(s)

Jean-Claude ROUX

Content(s)

The aim is to review and deepen the 6 fundamental chapters that must constitute the basic training of a Pagora engineer so that he can easily understand any scientific or technical article that would use mathematics as a language of description.

All 6 chapters are chosen so as to later understand the mathematics 2 course which uses the Laplace and Fourrier transform. A physical problem is often described by a differential equation. Taking the Laplace transform is equivalent to obtaining a rational fraction of polynomials. Searching for polynomial roots is thus based on complex numbers. The 6 chapters are therefore the following: study of complex numbers, polynomials, rational fractions with their decomposition into simple elements, study of integrals and primitives, recall of linear algebra (eigenvalues, subspaces), linear differential equations of order 1 and 2. We strive to show the links between all its chapters.

Targeted skills: resource teaching to develop solutions and pilot a system

Prerequisites

Mathematics knowledge of high-school final year, knowledge of Superior Education in mathematics are obviously a plus

Test

A positioning assignment at the beginning of the year: DSStart (see subject sheet: Mathematics Test 3FMT3065)
If the grade obtained on this assignment is greater than or equal to 10/20, the student is exempt from taking the module. The note will be kept as a note of the subject.

A supervised assignment at the end of the module: DSFinal

All documents are allowed for homework.

Possibility of catchable session in September.

  • Pour les étudiants ayant une note supérieure ou égale à 10/20 au test de rentrée, et qui sont donc dispensés de suivre les cours de cette matière, la note de la matière est par défaut égale à la note du test de rentrée :
    Note=DSRentrée
  • Cependant, la possibilité est laissée aux étudiants ayant une note supérieure ou égale à 10/20 au test de rentrée, et qui sont donc dispensés de suivre les cours de cette matière, de venir passer l'examen final. La note gardée est alors la meilleure des deux notes :
    Note=max(DSRentrée, DSFinal)
  • Pour les étudiants ayant une note strictement inférieure à 10/20 au test de rentrée, et qui ont donc obligation de suivre les cours de la matière, la note finale est égale à la note du DS de fin de module (qu'elle soit meilleure ou non par rapport au test de rentrée) :
    Note=DSFinal

Calendar

The course exists in the following branches:

  • Curriculum - Pagora Engineer - Student - Semester 5
see the course schedule for 2022-2023

Additional Information

Course ID : 3FME1003
Course language(s): FR

You can find this course among all other courses.

Bibliography

Un polycopié est distribué. Il peut être complété par des ouvrages centrés sur le programme de premier cycle (type classes préparatoires MP et PC).