Description

1.1 Complex Numbers
The goal of this chapter is to introduce complex numbers. We
de ne 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 de nitions allow us to de ne
the trigonometric form. Using Euler formula, the modulus and the
argument, we de ne exponential form.

1.2 Vectors
In this chapter, we study vectors in 2d and 3d. We start this chap-
ter 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 de ne
properly what is a vector. We de ne the sum of vectors and the
multiplication by a real number. We study orthogonality by intro-
ducing 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 prod-
uct 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, se-
quences de ned by induction. We study variations of sequences,
limits, Sandwich Theorem, convergence and divergence. We intro-
duce the concept of induction.
In the second part, we study arithmetic and geometric se-
quences (arithmetic and geometric progressions).