**Author: **Youssef F. Rashed, Dept. of Structural Engineering, Cairo University, Giza Egypt

**Summary:**

In this tutorial we will introduce the reader to how the direct integral forms for a partial differential equation can be derived. We will start from the well-known form for the integration by parts rule and then we will generalize it to demonstrate how Green's second identity works. Therefore the main objectives of this tutorial are:

- To review the philosophy behind the integration by part rule.
- To generalize the integration by parts formulae to the form of Green's second identity for multi- dimensional system.
- To review the rules of indicial notation.
- To derive the integral equation formulation for Laplace equation.
- To extend the above formulation to Poisson's equation.
- To give an overview of the different possible research areas in the BEM.