Differential Forms

What it is about

You learn the foundations and tools of differential forms on smooth manifolds: construction, exterior product, exterior derivative, integration and Stokes’ theorem. In the end you can differentiate, integrate and apply differential forms in contexts of geometry, topology, analysis and physics.

What you will be able to do

• Understand differential forms on smooth manifolds
• Be able to apply exterior product and exterior derivative
• Master integration and differentiation of differential forms
• Apply Stokes’ theorem
• Establish connections to vector analysis, topology, geometry and physics
• Comprehend the basics of De Rham cohomology and Hodge duality

What the module consists of

• VorlesungConveying theory and formal proofs
• ÜbungsblätterIndependent work for preparation
• TutoriumDiscussion and review of exercises

Teaching method

• Lectures at the blackboardMathematical proofs are presented step by step
• Exercise sheets to work on at homeStrengthening and application of the material
• Tutorial for solution discussionClarification of problems and deepening