IBEMA is a project for the improvement of the teaching quality of the Catalan Universities, funded by AGAUR. It began on September 1, 2008, and it is to be finished by the end of July 2009.

The project also uses resources from the Facultat de Matemàtiques i Estadística and from the Departament de Matemàtica Aplicada II, both of the Universitat Politècnica de Catalunya.

The acronym IBEMA is formed with initial letters of "Interfaces to Banks of Exercises of Mathematics for Auto-learning".

On September 9, 2008, a test was administered to the students enrolled for the first time in the five-year Mathematics program of the Universitat Politècnica de Catalunya (UPC).

To properly understand Stokes' theorem, it is useful to recall a few basic notations and results from calculus.

These notations and results refer to the gradient of a function, to the curl and divergence of a vector field, and to a few fundamental relations among them.

Contents

• Gradient
• Curl
• Divergence

In this chapter the learner will find the basic facts about line, surface and volume integrals that we will need.

Contents

• Line Integrals

• Surface Integrals

• Volume Integrals

• Summary