## The natural scalar (or dot) product: a numerical combination of vectors

The scalar or dot product of two vectors in real space is a real number that takes into account the direction, sense and magnitude of both vectors. 1.The natural scalar product

## The derivative of a function: definition and geometric interpretation

The derivative of a function is its instantaneous variation, i.e. the slope of the tangent to the graphical representation of the function at that point. 1. General idea: an instantaneous variation We

## Linear transformations of the plane: determinant, bases and inversion

The linear transformations of the Euclidean plane are the invertible linear applications, i.e. of non-zero determinant. They allow us to move from one basis of the plane to another, and

## The bases of the Euclidean plane: vectors and coordinates

The representation of the Euclidean plane as the Cartesian product $$\mathbb R^2$$ allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This

## Vector rotations of the plane: the analytical approach

The vector rotations of the plane (i.e. centred in the origin), are derived analytically (by coordinates) as linear applications of determinant $$1$$, which makes it possible to characterise them integrally