# Mathematics (05AOBMAT)

**Coefficient :**4**Hourly Volume:**123h (including 63h supervised)- CTD : 63h supervised (and 10.5h unsupervised)
- Out-of-schedule personal work : 49.5h

### AATs Lists

## Description

- Algebra:
- Vector space and subspace, basis and dimension. Scaling table.
- Operations on matrices, cofactors, inversion and square matrix polynomial
- Change of basis and transition matrix
- Determinants

- Analysis :
- Integration tools, integration by parts, change of variables, decomposition into simple elements, linearisation.
- Differential equations: Linear - order 1, variation of the constant, linear with coefficients - order 2, change of variables or unknown.
- Multiple integrals: Fubini's theorem, calculating volume, moments of inertia and centre of gravity

- Probability:
- Notion of event, tribe, probability, independence
- Discrete or continuous simple random variable

## Learning Outcomes AAv (AAv)

AAv1 [heures: 27,B2,B3] ( Integral calculus): The student masters the basics of integral calculus: (primitive search, simple definite integrals and multiple integrals).

AAV2 [heures: 27,B2,B3] ( Differential equations ). At the end of this course, students will know the methods for solving differential equations.

AAv3 [heures: 27,B2,B3] (vector spaces) : At the end of this course, students will be able to apply the concepts relating to vector spaces (vector subspaces, free family, generatrix, base) and will be able to identify a vector space.

AAv4 [heures: 21,B2,B3] (linear applications) : At the end of this course, students will be able to recognise or show that an application is linear and to determine its kernel and image. In finite dimension, students will be able to explain the matrix of a linear application in a basis.

AAv5 [heures: 21,B1,B2,B3] (matrices) : At the end of this course, students will have mastered matrix calculus (sum, product, inverse, determinant) and will be able to recognise a linear algebra problem in a concrete situation.

## Assessment methods

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

## Key Words

## Prerequisites

## Resources

Mathématiques DEUG A AZOULAI et AVIGNANT