5 credits

45.0 h + 20.0 h

Q2

Teacher(s)

Language

French

Main themes

The course is intended for students with an elementary background in calculus as given in the basic course of physics in BAC1.
It contains:
-an introduction to linear algebra with emphasis on the computation of solutions to systems of linear equations, matrix algebra, eigenvalues, eigenvectors and diagonalization of matrices;
-an introduction to the study of functions of several variables (partial derivatives, differentials, gradients, maxima and minima, Lagrange multipliers, multiple integrals) and systems of differential equations with a view on applications;
-an introduction to analytical geometry, in particular to the equations and properties of straight lines, conics and quadrics;
-a good deal of illustrations and applications to pharmacokinetics, chemical and enzymatic kinetics, genetics, statistics, themodynamics

Aims

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1 | The objective of this course is to introduce the students to the fundamental notions of linear algebra, calculus and analytical geometry in order to provide them with the basic mathematical tools essential for the biomedical sciences |

Content

-Linear algebra : systems of linear algebraic equations, solution procedures by Gauss-Jordan elimination, matrix algebra, rank theory, inversion, eigenvalues, eigenvectors and diagonalization of matrices; -Complex numbers and periodic functions. Introduction to the theory of systems of ordinary differential equations -Applications to pharmacokinetics and statistics, thermodynamics.

METHODS: Lectures and supervised practical works (in small groups) are organized weekly. The pracrical works, in close connexion with the lecture of the week, are not restricted to mere applications of recipes but require an active involvement of the students, who are encouraged to establish the link between theory and practice

METHODS: Lectures and supervised practical works (in small groups) are organized weekly. The pracrical works, in close connexion with the lecture of the week, are not restricted to mere applications of recipes but require an active involvement of the students, who are encouraged to establish the link between theory and practice

Teaching methods

Lectures and exercises sessions

Evaluation methods

The evaluation consists in a written examen graded on 20 points:

a theoretical part (10 points), exercises (6 points), pharmacocinetics and statistic (4 points).

a theoretical part (10 points), exercises (6 points), pharmacocinetics and statistic (4 points).

Other information

PREREQUISITE : Background in mathematics as given in the course of physics (BAC 1).

Bibliography

livre conseillé: J. Stewart, Analyse. Concepts et contextes, Volume 2, Fonctions de plusieurs variables

Teaching materials

- syllabus sur la page Moodle du cours
- énoncés d'exercices sur la page Moodle du cours
- énoncés et corrigés d'anciens examens sur la page Moodle du cours

Faculty or entity