# PřF:M7300 Global analysis - Course Information

## M7300 Global analysis

**Faculty of Science**

autumn 2021

**Extent and Intensity**- 4/2/2. 10 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- Mag. Katharina Neusser, Ph.D. (lecturer)
**Guaranteed by**- prof. RNDr. Jan Slovák, DrSc.

Department of Mathematics and Statistics – Departments – Faculty of Science

Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science **Timetable**- Mon 12:00–13:50 M6,01011, Wed 10:00–11:50 M6,01011
- Timetable of Seminar Groups:

*K. Neusser* **Prerequisites**- Elementary differential and integral calculus
**Course Enrolment Limitations**- The course is offered to students of any study field.
**Course objectives**- The goals involve the geometric differential and integral calculus. Lie group and algebras will represent useful tools, including their representation. Selected applications will focus at concepts of Riemannian and symplectic geometries, optimal control, analytical mechanics and some further equations of mathematical physics.
**Learning outcomes**- The students will master the vector fields and exterior forms and the general Stokes theorem with applications in vector calculus. Furthe, they will actively learn basic elements of Lie theory involving the exponential mapping, adjoint representation, covering phenomena, and differential calculus for functions valued in Lie groups. They will be able to exploit the knowledge in analysis based on Riemannian and symplectic geometries, optimal control, and analytical mechanics.
**Syllabus**- Vector fields and exterior forms on R^n a submanifolds of R^n,
- general Stokes theorem and its cosequences
- geometric theory of 1st oreder PDE (differencial ideals, Frobeniova theorem).
- Lie groups and subgroups, relations to Lie algebras (exponencial mapping, adjoint representation, coverings),
- Calculus for functions valued in Lie groups, basic concepts of representation theory, homogeneous spaces.
- Basics of Riemannian and symplecitc geometries.
- Applications in optimal control, analytical mechanics.

**Literature**- AGRICOLA, Ilka and Thomas FRIEDRICH.
*Global analysis : differential forms in analysis, geometry and physics*. Translated by Andreas Nestke. Providence, Rhode Island: American Mathematical Society, 2002, xiii, 343. ISBN 0821829513. info - JOST, Jürgen.
*Riemannian geometry and geometric analysis*. 5th ed. Berlin: Springer, 2008, xiii, 583. ISBN 9783540773405. info

*recommended literature*- AGRICOLA, Ilka and Thomas FRIEDRICH.
**Teaching methods**- Standard lectures and seminars, independent study
**Assessment methods**- standard oral exam
**Language of instruction**- English
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (autumn 2021, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2021/M7300