DOI
https://doi.org/10.1002/cae.21607

Summary
The course on the combined finite element method and mathematical optimization with flip teaching approach is presented in the article. The list of course topics and assignments, the teaching approach, and the example of benchmark problem and programming assignment are introduced. The weaknesses of the current curriculum and approach to teaching two distinct courses is discussed as a motivation to apply the proposed approach. In this course, the “flipped teaching” term is used by the means that the course material is provided in the order reverse to the traditional approach. That is, the students are given the software modules and then they perform the analysis of how these modules relate to the mathematical methods. The course assignments included 1D structural analysis, assembly of element matrices, solving problems with rectangular elements, and others. The authors provide the summarized feedback from the students’ survey. In general, students agree that they enjoyed the course and learned useful engineering skills.

Relevance for Complex Systems Knowledge
The authors mention that conventional strategy for teaching finite element method is to analyze separate cases in class and leave programming assignments to be performed at home. In addition, mathematical optimization course is usually offered as a separate course. The authors suggest that a course which combines mathematical optimization and finite element method would help students to solve real-life problems and apply knowledge of both fields which were taught in this course. This course also requires knowledge in the field of physics, mechanics, mathematics, numerical analysis. The suggested flipped teaching strategy, projects related to realistic problems and oral presentation of the results also help students to develop programming, teaching skills and critical thinking to assess feasibility of the results.

Point of Strength
The article presents how flipped teaching can be applied to teach finite element method and mathematical optimization, included developing programming skills.