Introduction aux fonctions vectorielles

A real-valued function assigns one real number to each element in its domain.

A vector-valued function, or vector function, also has a domain of real numbers, but its range consists of vectors.

It is written as r of t, where t is the independent variable and often represents time. For each value of t in the domain, the function assigns a unique vector in space.

In three dimensions, the vector r of t is defined by three component functions: f(t), g(t), and h(t), where f, g, and h are real-valued functions.

These component functions give the coordinates of the vector along the three axes. As t changes, the coordinates change. So the vector changes, and its tip traces a path in space called a space curve.

Vector-valued functions are very useful for describing motion. For example, consider a satellite orbiting Earth. At each moment, the satellite has a position in space. The three component functions give its location along the coordinate axes. Together, they form a vector function that describes the satellite's orbital path.