Global analysis

Course Code :1600WETGLA
Study domain:Mathematics
Academic year:2019-2020
Semester:1st semester
Sequentiality:Min 8/20: Calculus, Multivariate Calculus, Linear Algebra and Geometry, Differential geometry, Differential equations and dynamical systems
Contact hours:30
Study load (hours):84
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)Lieven Le Bruyn
Sandor Hajdu

3. Course contents *

Global analysis aims to extend your knowledge of multivariate calculus and differential equations to more general geometric objects than standard n-dimensional real space, so called differential manifolds. We introduce tangent vectors and differentials on such manifolds en globalise these local information in special new manifolds, vector bundles such as the tangent-bundle and cotangent-bundle. We introducte vectorfields as sections of the tangentbundle and differential forms as sections of exterior products of the cotangent-bundle. We define oriented manifolds as well as manfifold with a boundary, which will allow us to integrate certain differential forms. This will culminate in the proof of Stokes' theorem.