Mathematische Grundlagen der Ingenieurinformatik

Mathematics is one of the foundations of engineering. Due to the significant importance of the physical behavior of engineering structures, calculus has traditionally been at the center of the mathematical education of engineers; it is used for the mathematical formulation of physical problems. This formulation has greatly contributed to the systematization of engineering and the mastery of engineering works. Before the introduction of computers into engineering, it was challenging to determine numerical solutions for the mathematical formulations of physical engineering problems with irregular geometries, varying material properties, diverse influences, and complex manufacturing processes. The enhancement of human cognitive abilities by computers, with a factor of 10 in terms of computing speed, storage capacity, and communication speed today, has opened entirely new possibilities for solving mathematically formulated physical problems. New fields of science, such as Computational Mechanics, and widely adopted new calculation methods, such as the Finite Element Method, have emerged. Alongside the introduction of computers, the character of engineering has profoundly changed. While the core of competitiveness used to lie primarily in the use of better materials, the development of new construction methods, and the design of new engineering systems, organization and management now have a comparably significant influence on success. Some reasons for these changes include a holistic view of the market, product, economy, and society, the importance of organization and management in global competition, and the increased complexity of the environment, technology, and the interactions among those involved in planning and production in engineering.