Portal de Periódicos da CAPES

Derivation

2018; Springer International Publishing; Linguagem: Inglês

10.1007/978-3-319-69242-5_5

2510-1307

Cyril Fleurant, Sandrine Bodin-Fleurant,

German Literature and Culture Studies

In the phenomena studied in geography and Earth science, we are often interested in variations, in growth. We are familiar with the notion of the slope of a line. How can this notion be adapted for a curve? The slope will not be constant; each point on the curve will be associated with a given slope (valid only locally); we thus define a new function, the derived function. The free software used for the calculations is Xcas. This chapter introduces the notion of slope (gradient) and derivative for a curve at one point and the derivative function. It shows how to use the basic derivative formulas but also to use free software for the computation of the derivative calculation. It shows how to calculate the equation of a tangent line and to use differentiation to find the variation of a function. Some basics on partial derivative, second derivative, and concavity are also given.