Pagora rubrique Formation 2022

Mathematics - 3FME1003

  • Number of hours

    • Lectures -
    • Projects -
    • Tutorials 21.0
    • Internship -
    • Laboratory works -

    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)

Aniss ZIAD

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

Evaluation : 30% of Written exam and 70% of Written exam (1,5h)

Resit : Written exam (1,5h)

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.

Calendar

The course exists in the following branches:

Additional Information

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

You can find this course among all other courses.

Environmental security

Déroulement de l’enseignement en salle de cours standard.
Sécurité : RAS
Environnement : RAS

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).