Global Analysis 1 (WS 16/17)

Global Analysis I is the first course in a series of courses on the analysis on manifolds. Global analysis combines (and therefore the course teaches) methods from geometry, topology and partial differential equations to study global behavior of (partial) differential operators. Furthermore, the methods are heavily used in modern theoretical physics.

In this course we will cover:
  • Manifolds
  • Vector fields and dynamical systems
  • Vector bundles, tensor bundles and tensor fields
  • Differential forms, Integration of differential forms, and Stokes' Theorem
  • de Rham Cohomology and Hodge theory

Examination Information

Dates:
  • First Exam: 22.02.2017, 9:00 - 11:00, Großer Hörsaal
  • Klausureinsicht: Samstag, 11.3.2017, 9:00-11:00, SR 0.011.
  • You can review your corrected exam on Saturday, 11.3.2017, 9:00-11:00, SR 0.011.
  • Second Exam: 27.03.2017, 9:00 - 11:00, Seminar Room 0.011
Additional Information:
  • Bring a document of identification containing a photo to the exam.
  • You have 2 hours (120 minutes) to answer the questions.
  • There are 10 questions, each with a maximum of 10 points.
  • You can reach a maximum of 80 points.
  • 41 points suffice to pass the exam.
Sample Exam: Here

Exercise Sheets

Material

Prerequisites

Real Analysis and Linear Algebra. Basic knowledge of differential topology and functional analysis is helpful but not mandatory.

Persons

Dates

  • Lecture:

    • Monday 8-10 Zeichensaal
    • Wednesday 12-14 Zeichensaal
  • Exercise classes:

    • 1. Monday 10-12 N0.007
    • 2. Wednesday 16-18 Zeichensaal

    The exercise classes start in the second lecture week.

    The exercise sheets will be handed out during each Monday lecture. You have to hand in your solutions on Monday, too. You have one week to work on your solutions.

Language

If necessary, the lecture will be held in English. You can hand in your solutions to the exercise sheets in German and English.

Admittance to examination

Successful participation in Recitation class (50% of homework assignments, oral presentation of homework).

Literature

  • Abraham, Marsden, Ratiu: Manifolds, tensor analysis, and applications, Springer
  • Bott, Tu: Differential forms in algebraic topology
  • Guillemin, Pollack: Differential Topology
  • Chern, S.S.; Chen, W.H.; Lam, K.S.: Lectures on differential geometry, 1999.
  • Jänich K.: Vektoranalysis. Spinger, 1992.
  • Milnor, J.W.: Topology from a differential viewpoint. Princeton, 1997.
  • Bröcker T., Jänich K.: Einführung in die Differentialtopologie, Springer, 1973.
  • O'Neill B., Semi-Riemannian Geometry, Academic Press, 1983.

Basis