# Algebra and Analysis

• Cours (CM) 20h
• Cours intégrés (CI) 64h
• Travaux dirigés (TD) -
• Travaux pratiques (TP) -
• Travail étudiant (TE) -

Langue de l'enseignement : Anglais

## Description du contenu de l'enseignement

1 Functions

This part is composed of 5 chapters. In the first chapter we define the domain of a function. After this we study polynomial function particularly affine function and second order polynomial functions. In this chapter also, we deal with equations, sign table of a function and inequalities. In the second chapter we define the concept of limit of a function at a point and in an interval. Using this limits we study continuity of a function. We study elementary function. We define convex functions and periodic functions. The third chapter is devoted to differentiability and variations of functions. In the fourth chapter, we deal with exponential function exp. The last chapter of this part will be concerned by the logarithmic function.

2 Integration

This chapter is an introduction and an initiation to elementary integration. Here we define a primitive of a function. Using this primitive one should be able to calculate the integral of a function between to real numbers. At the of the chapter we show how to calculate the area of a domain by using integrals.

3 Linear Differential Equations

Here we define a first order differential equation and what we mean by linear. After this we explore the first order homogeneous differential equations. In a second time we solve first order non homogeneous differential equations. To end this chapter we introduce second order differential equations with constant coefficients.

4 Arithmetic

In this chapter we study euclidean division, Gauss theorem and Fermat's theorem. We will deal also with diophantine equations and congruence.

5 Probabilities

In this chapter we introduce basic definitions and concepts of probabilities. After this, we study discrete probabilities. We end the chapter by defining some continuous distributions: uniform distribution, exponential law, Normal distributions etc.

6 Statistics

For statistic, we just remi nd the basic definitions: mean value, median, expectation, variance etc.