Applied Introduction to Differential Geometry

What it is about

You receive an application-oriented introduction to the fundamentals of differential geometry. By the end you can recognise manifolds and vector bundles and compute with simple geometric objects (Lie derivatives, exterior derivatives, integration of differential forms) as well as apply Lie groups to describe symmetries in physical systems.

What you will be able to do

• Understand the basic concepts of differential geometry (manifolds, vector bundles)
• Handle vector fields, flows and the Frobenius theorem
• Apply Lie groups and Lie algebras as well as their actions
• Compute tensor equations and Lie derivatives
• Use and integrate differential forms and exterior derivative
• Apply Stokes' theorem
• Recognise fundamental applications in Hamiltonian mechanics, fluid mechanics and electromagnetism

What the module consists of

• VorlesungIntroduction of concepts with mathematical rigor; focus on applications and examples
• ÜbungDeepening of lecture content through problem sets and practical tasks

Teaching method

• Vorlesungen mit Definitionen, Theoremen und BeweisenConveying the theoretical foundations; some theorems are stated without proof
• Begleitende Übungssitzungen mit ÜbungsblätternDeepening and self-checking of what has been learned through practical tasks