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 |

Credits: | 3 |

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 |

At the start of this course the student should have acquired the following competences:

an active knowledge of

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

The students have a solid background in elementary analysis and linear algebra. They know the basics of classical differential geometry (curves and surfaces in three dimensional Euclidian space).

- The students can work with differentiable manifolds, and with the calculus that can be defined on such spaces.

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.

Class contact teachingLectures

ExaminationWritten examination without oral presentation Closed book

Continuous assessment(Interim) tests Participation in classroom activities

Continuous assessment

The course notes can be downloaded from blackboard for free.

A few related books (for your information):

J.M. Lee, Introduction to smooth manifolds, Springer, 2006.

L.W. Tu, An introduction to manifolds, Springer, 2007.

lieven.lebruyn@uantwerpen.be