The objective of this course is to equip students with a systematic and widely applicable framework for analyzing physical or technical systems through their dimensional structure. Participants will learn how to use dimensional analysis to reduce complex problems, derive scaling laws, identify governing variables, and construct dimensionless representations that reveal the essential physics. By the end of the course, students will be able to apply dimensional reasoning as a powerful tool for modeling, interpretation, and cross-disciplinary problem solving in engineering, physics, and the natural sciences.

Dimensional Analysis is a powerful and very broadly applicable method in science and engineering. Despite its elementary appearance, it can provide deep insight into the structure of physical laws, reveals essential scaling relationships, and allows complex systems to be reduced to a small set of fundamental, dimensionless parameters. The central idea is that all physical laws can be rewritten in terms of a small number of dimensionless groups. This allows complex problems to be reduced to their core, often exposing the governing mechanisms at a glance. In practice, it means fewer experiments, clearer models, and deeper intuition.

This short course introduces dimensional analysis as a unifying language across the sciences. You will learn how to transition in a structured way from dimensional variables to dimensionless representations , which capture the essence of a problem and often reveal similarities between systems. This perspective allows one to identify which effects matter, which can be neglected, and how results obtained in one context can be transferred to another.

Dimensional analysis plays a key role across disciplines:

• In physics, dimensional arguments can yield nontrivial predictions, guide model construction, and provide consistency checks for theoretical results.
• In engineering and applied sciences, dimensional analysis reduces experimental effort, organizes data ef"ciently, and supports the design of scalable systems.
• In thermo-fluid dynamics in particular, dimensionless numbers such as the Reynolds or Biot number characterize operating regimes and enable scaling from laboratory models to full-scale systems.

Monday to Thursday morning and afternoon; Friday morning.

Specific times to be provided after acceptance. 

• Munich City Tour
• Traditional Bavarian Dinner (students pay on their own)
• Christmas Market Tour
• BMW Museum or BMW Factory Group Visit
• Deutsches Museum Tour
• Local Brewery Tour
• Art Museum Visit
• Medical Museum Visit
• Lab or Research Facility Visit