Advanced Level - Tutorials


After finishing the base tutorials, the advanced tutorials deal with the introduction of basic mechanisms and the methodology of using generic software components to create an application. Most of the tutorials deal with discrete mathematical structures. It is important to state, that due to the limited resolution of computational data structures we can not deal with real numbers. We have to restrict ourselves to the discrete representation, e.g. the double data type. Already known parts of mathematics are transfered to the finite structure of a computer.

This means that some values such as \pi or \mathrm{e} can not be specified exactly but inevitably induce some discretization error.

For higher structures such as functions in space and time the discrete nature of the computer has twofold implications. On the one hand, we have to discretize space or time, which is ususaly called mesh generation. On the other hand, we have to discretize the well known differential and integral operations into their discrete counterparts such as algebraic equations and sum operations.

To quote Wikipedia:

"Numerical differentiation is a technique of numerical analysis to produce an estimate of the derivative of a mathematical function or function subroutine using values from the function and perhaps other knowledge about the function."

"In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. "

 

The required source files for this section can be obtained in the download area.

In the given package, a basic kernel for the GSSE can be found. It is not complete nor up to date. For real applications we are using several other mechanisms. This package was compiled to ease the start with the GSSE. Therefore only three directories are in this package: