Resum: The Jet Transport, also known as differential algebra or automatic differentiation, is a numerical technique that allows us to compute the Taylor approximation of any function without computing its derivatives. Usually, it is used to compute the derivatives of the function when it cannot be computed explicitly or its computation is difficult. The value obtained is exact up to round off errors. The method does not introduce any error. For that reason this technique has been implemented successfully in several applications as a substitute of the classical numerical differentiation.

In this talk we will introduce the jet transport and the basis needed to implement it. First we will talk about the polynomial algebra as a substitute of the floating point arithmetic. Then we will show how the technique can be applied to compute the differential of the flow map associated to a vector field, which is equivalent to the computation of the variational equations. 

We will end the presentation introducing some details on the interaction of the Jet Transport with the Newton's method.