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* Declaration of self reliance
I hereby declare that I have written this thesis independently in accordance with § 35 para. 7 RaPO (Framework Examination Regulations for Universities of Applied Sciences in Bavaria, BayRS 2210-4-1-4-1-WFK), have not submitted it elsewhere for examination purposes, have not used any sources or aids other than those indicated, and have marked all direct and indirect quotations as such.
* Task desciption
Topic 5: Numerical integration methods
The aim of this task is to implement three variants of numerical approaches for calculating integrals
in a software module.
A function for the rectangle method, the trapezoid method, and the Simpson method should be designed and coded in a reusable module.
When defining the interface of the C functions, pay attention to reusability.
The task also includes developing a sample application to test the three variants. Select two examples of mathematical functions whose integrals are to be determined, with corresponding integration boundaries, and compare the three methods in terms of their precision. Test the limitations of the methods. Substantiate your results.
Explain the mathematical relationships underlying the methods in your paper. A graphical representation will help to illustrate the understanding of the relationships.
Optimize the source code as far as possible for performance-optimized use on an embedded controller.
The result of the task is a project that can be compiled with MS Studio, which enables the software module to be tested (suitable test cases, etc.) using a command line application, plus the documentation specified below.
Scope of relevant task-specific documentation
- Graphical representation of the software design and compact description of the key relationships (1 page)
- Theoretical explanation of the relationships (mathematical, algorithmic, etc.) that need to be taken into account here (2 pages)
- Documentation of the reference examples used for testing, with graphical representation and explanation of method limitations (2 pages)
* Graphical representation of the software design
#+BIND: org-latex-images-centered nil
#+ATTR_LATEX: \textwidth :float nil
[[./graphical-representation-white.drawio.png]]