LFU:online

A bird's eye view on the role and the use of modern differential geometric notions for applications in the physical sciences shall be obtained. A certain ability to perform concrete and self contained computations shall be developed by means of several case studies.

Differentiable manifolds; Tangent bundle and Cotangent bundle; pull back and push forward; exterior derivative; Lie product of vector fields; Integral theorem of Stokes for differential forms; Riemannian metric; Affine Connection and covariant derivative; symplectic structur of the cotangent bundle; Examples taken from physics: equation of continuity and the flow of charge, d'Alembert's formula as a corollary to the theorem of Stokes, quasistatic work and heat in thermodynamics,  constrained mechanical systems, Maxwells equations.

Four lecture units of 45 minutes will be supplemented by two units with the students presenting their homeworks. Thus 5 blocks of themes will emerge. Thereby a continuous participation shall be guaranteed, necessary for a successfull learning process.

50 of 100 credit points can be achieved through home work presentation. Another 50 points can be obtained through the final written test at the last lecture session. For achieving a positive grade a total of at least 50 points has to be obtained.

1) Klaus Jänich, Vektoranalysis, Springer, 1993

2) Martin Schottenloher, Geometrie und Symmetrie in der Physik, Vieweg 1995

3) Harley Flanders, Differential Forms with Applications to the Physical Sciences, Dover 1989

4) Chris Isham, Modern Differential Geometry for Physicists, World Scientific, 1989

The regular lecture date will be agreed on at a first informal meeting on 11. 3. 2016 at 12:15h in HS G.