Analysis is a crucial pillar of our current mathematical research, with a particular focus on differential equations. This is reflected in the orientation of our course offerings for the Analysis specialization. The courses cover a broad spectrum of analytical sub-disciplines, offered in lectures and seminars, some annually and others at somewhat longer intervals, depending on demand.

• Functional analysis considers infinite-dimensional vector spaces and (mostly linear) mappings between them. The methods of linear algebra are considerably extended for this purpose, and the emergence of various convergence concepts necessitates analytical methods to a surprisingly large extent. The result is a fundamental theory that plays a similar role in advanced analysis as linear algebra does in Analysis II-III.
• The study of partial differential equations is fundamental to the natural sciences and engineering because virtually all fundamental laws of nature are formulated as partial differential equations. Fortunately, the theory is also mathematically very interesting, and the questions posed by nature will continue to drive intensive development in the field. Questions about the existence, uniqueness, stability, and regularity of (generalized) solutions are paramount.
• In contrast, the theory of ordinary differential equations offers a wealth of explicit solution methods. Here, the desired functions depend on only one variable, which simplifies many aspects.
• Because of the central role of differential equations in the natural sciences and engineering, questions of modeling are essential for the further development of the theory. We therefore regularly offer lectures on modeling aspects, for example, on continuum mechanics or topics in theoretical physics.
• Interesting mathematical fields with strong connections to ordinary and partial differential equations include differential geometry and global analysis. Here, analytical methods lead to profound insights into geometric questions.