# Mathématics (06POBMAT)

**Coefficient :**2.5**Hourly Volume:**66h (including 36h supervised)- CTD : 36h supervised (and 6h unsupervised)
- Out-of-schedule personal work : 24h

### AATs Lists

## Description

- algebra: linear applications, reduction of endomorphisms
- analysis
- Functions of several variables
- level lines and surfaces
- limits, continuity, partial derivation
- Taylor formulae, differential
- extrema

- Curvilinear and surface integrals

- Functions of several variables

## Learning Outcomes AAv (AAv)

AAv1 [heures: 18,B1,B2,B3] (diagonalization) : At the end of this course, students will be able to diagonalize a square matrix and geometrically interpret the characteristic elements (eigenvalues, eigenvectors, eigensubspaces). They will be able to apply this to situations such as solving a system of recurrent sequences, calculating the power of a matrix or solving a linear differential system with constant coefficients.

AAv2 [heures: 15, B2,B3] : At the end of this course, each student will be able to prove the continuity or non-continuity of a function of 2 or 3 variables, calculate partial first and second derivatives, particularly in situations involving the composition of functions and changes of variables.

AAv3 [heures: 18, B2,B3] : At the end of this course, each student will be able to search for and classify critical points (and possible extrema) independently according to the sign of the Hessian determinant. He/she will be able to suggest avenues in the case not determined by the classification.

AAv4 [heures: 15, B2,B3] : At the end of this course, in relation to physics situations such as the study of vibrating strings or the evolution of the temperature of a bar, each student will be able to solve elementary differential equations (linear 1st and 2nd order), to apply or propose a change of variable in order to return to the simple case, and to specify solutions verifying boundary conditions.

## Assessment methods

One long continuous assessment (coefficient 1) and the average of several short continuous assessments (coefficient 3).

## Key Words

Functions of several variables, partial derivatives, extrema, simple and multiple integrals, curvilinear and surface integrals.

## Prerequisites

Mathematics S5O content

## Resources

All analysis books for first and second year preparatory classes.