The First Step to the Direct Integral Forms

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: 1. To review the philosophy behind the integration by part rule. 2. To generalize the integration by parts formulae to the form of Green’s second identity for multidimensional system. 3. To review the rules of indicial notation. 4. To derive the integral equation formulation for Laplace equation. 5. To extend the above formulation to Poisson’s equation. 6. To give an overview of the different possible research areas in the BEM.