1.1 Complex Numbers The goal of this chapter is to introduce complex numbers. We define what is the algebraic form of a complex number: z = a+ib, where a and b are real numbers. From the algebraic form, we distinguish the real part Re, the imaginary part Im of a complex number. In a second time we will de ne the modulus and the argument of a complex number. These definitions allow us to define the trigonometric form. Using Euler formula, the modulus and the argument, we define exponential form.
1.2 Vectors In this chapter, we study vectors in 2d and 3d. We start this chapter by specifying what we mean by direction. Because we observe that a large part of students in L0 make the confusion between direction of vector and the sense of vector. After this, we define properly what is a vector. We define the sum of vectors and the multiplication by a real number. We study orthogonality by introducing the scalar product. We deal also with collinearity. To make the calculation easiest we introduce the concept of coordinates. Using coordinates we de ne easily the scalar product, vector product and the mixed product. To end the chapter we show how to calculate distance, area and volume.
1.3 Sequences This chapter is divided in two part. In the rst part we give some basic and general de nitions. We de ne explicit sequences, sequences de ned by induction. We study variations of sequences, limits, Sandwich Theorem, convergence and divergence. We introduce the concept of induction. In the second part, we study arithmetic and geometric sequences (arithmetic and geometric progressions).

Introduce the basics of mathematics