During 2016 and 2017, Tobias Holzmann attended the class of Prof. Dr. Clements Brand at the Montanuniversität Leoben. During the discourse, different topics in the field of numerical mathematics were investigated. Tobias Holzmann published a summary of the lecture given by Prof. Dr. Clements Brand after the class, which is presented here. The document further contains additional work such as a matrix construction, the Gray Scott model analysis, and other numerical topics. The document is written in German.