Mathematics 2

Objectives

This course is divided into two parts:
- the first part focuses on differential systems (EDO / SDO) and linear partial differential equations (PDE); the student will have to become familiar with these objects which are at the heart of the modeling of mechanical systems.
- the second part deals with the modeling of random phenomena: the objective is to allow the student to carry out basic calculations on univariate and bivariate random variables, to put into practice the tools of statistics, and to estimate laws of probability.

Description

Part 1:
- 1st and 2nd order ODE, linear ODS, representation of solutions, critical points, stability, phase portrait
- 1st and 2nd order linear PDEs (parabolic, hyperbolic, elliptic)
- Problems in unbounded domains: FT method, feature method, complex potential method
- Problems in bounded domains: boundary conditions, method of separation of variables

 

Part 2 :
- Elements of calculation of probabilities
- Random variables
- Couple of random variables
- Calculation of probability law by transformation of v.a.
- Elements of statistics
- Adjustment of probability laws

Targeted skills

Part 1 ODS and PDE:

- To know how to solve an equation or a linear differential system with constant coefficients by applying the methods of separation of the variables, of the integrating factor, of diagonalization (characteristic equation).

- know how to analyze a 2x2 nonlinear differential system (balance, stability, isoclines, collar, focus ...).

- be able to use a numerical solver to solve a nonlinear ODE

- recognize the nature of a second order linear PDE (elliptic, hyperbolic, elliptic) and apply basic methods of resolution (Fourier transform, characteristics, separation of variables).

 

Part 2: Probability and Statistics

- knowing how to model a random phenomenon: probabilized space, discrete / continuous variable, probability law, mutlivariate variables, joined law, moments ...

- know how to use statistical tools to characterize random data

- know how to adjust a probability law and apply the adequacy tests

Pre-requisites

Mathematics 1

Session 1 ou session unique - Contrôle des connaissances

Session 2 - Contrôle des connaissances