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Paper, print media and biomaterials  # Mathematics - 3FMA1003

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• #### Number of hours

• Lectures : 0
• Tutorials : 27.0
• Laboratory works : 0
• Projects : 0
• Internship : 0
• Written tests : 1.5
ECTS : 25.0
• Officials : Jean-Claude ROUX

### Goals

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
Contact Jean-Claude ROUX

Content

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

Tests

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.

The material can be made up 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 - Apprentice->Semester 5

Sécurité-Environnement

Bibliography

All books of high-school final year can be a help for students. Other possibilities are the books in mathematics of the two years of Superior Education for example.

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Date of update July 24, 2020