Kaisa_2012_3_photo by Veikko Somerpuro

Topics:

Smooth manifolds
Smooth mappings
Tangent vectors, tangent bundle
Cotangent bundle
Tensors
Differential forms
Integration on manifolds
De Rham cohomology
Integral curves and flows
Lie derivatives
Lie algebras and Lie groups

Prerequisites: Vector analysis, topology, linear algebra, differential equations

Ilmoittaudu
11.12.2017 klo 09:00 - 2.5.2018 klo 23:59

Viestit

Käyttäjän Ilkka O Holopainen kuva

Ilkka O Holopainen

Julkaistu, 27.4.2018 klo 10:56

There is a new version of Exercises 11.

Käyttäjän Ilkka O Holopainen kuva

Ilkka O Holopainen

Julkaistu, 15.1.2018 klo 14:02

There will be no lectures on February 20, 21, 27, and 28 (neither on March 6 and 7).

Käyttäjän Ilkka O Holopainen kuva

Ilkka O Holopainen

Julkaistu, 15.1.2018 klo 12:00

The first exercise class is on Wednesday, January 24.

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

PäivämääräAikaOpetuspaikka
Ti 16.1.2018
12:15 - 14:00
Ke 17.1.2018
12:15 - 14:00
Ti 23.1.2018
12:15 - 14:00
Ke 24.1.2018
12:15 - 14:00
Ti 30.1.2018
12:15 - 14:00
Ke 31.1.2018
12:15 - 14:00
Ti 6.2.2018
12:15 - 14:00
Ke 7.2.2018
12:15 - 14:00
Ti 13.2.2018
12:15 - 14:00
Ke 14.2.2018
12:15 - 14:00
Ti 20.2.2018
12:15 - 14:00
Ke 21.2.2018
12:15 - 14:00
Ti 27.2.2018
12:15 - 14:00
Ke 28.2.2018
12:15 - 14:00
Ti 13.3.2018
12:15 - 14:00
Ke 14.3.2018
12:15 - 14:00
Ti 20.3.2018
12:15 - 14:00
Ke 21.3.2018
12:15 - 14:00
Ti 27.3.2018
12:15 - 14:00
Ke 28.3.2018
12:15 - 14:00
Ti 10.4.2018
12:15 - 14:00
Ke 11.4.2018
12:15 - 14:00
Ti 17.4.2018
12:15 - 14:00
Ke 18.4.2018
12:15 - 14:00
Ti 24.4.2018
12:15 - 14:00
Ke 25.4.2018
12:15 - 14:00
Ke 2.5.2018
12:15 - 14:00

Muu opetus

17.01. - 28.02.2018 Ke 14.15-16.00
14.03. - 28.03.2018 Ke 14.15-16.00
11.04. - 02.05.2018 Ke 14.15-16.00
Ilkka Holopainen
Opetuskieli: englanti

Materiaalit

John M. Lee:
Introduction to smooth manifolds, Springer, 2003.

Lecture notes
Ilkka Holopainen: Johdatus differentiaaligeometriaan (in Finnish)

Lecture notes
Ilkka Holopainen and Tuomas Sahlsten: Riemannian geometry
There is a brief review on differential geometry (first 21 pages)

Tehtävät

Harjoitus 1, Exercise 1 (24.1.2018)

Harjoitus 2, Exercise 2 (31.1.2018)

Harjoitus 3, Exercise 3 (7.2.2018)

Harjoitus 4, Exercise 4 (14.2.2018)

Harjoitus 5, Exercise 5 (14.3.2018)

Harjoitus 6, Exercise 6 (21.3.2018)

Harjoitus 7, Exercise 7 (28.3.2018)

Harjoitus 8, Exercise 8 (11.4.2018)

Harjoitus 9, Exercise 9 (18.4.2018)

Harjoitus 10, Exercise 10 (25.4.2018)

Harjoitus 11, Exercise 11 (2.5.2018)

Kurssin suorittaminen

Exam and exercise classes. The exam will consists of 5 problems (evaluated as 6 pts each).
The first possible exam is on 23rd of May.

Remember to register for the exam in WebOodi at least 10 days before the exam!

You will get extra credit points by solving the home work assignments:
25% = +1p, 35% = +2p, 45% = +3p, 55% = +4p, 65% = +5p ja 75% = +6p

Kuvaus

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

Belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Topology II

Bachelor studies

Basics on smooth manifolds

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Basics on smooth manifolds and mappings between manifolds, tangent and cotangent space, tensors, differential forms. Stokes theorem.

Lee: Introduction to smooth manifolds.

Lectures and exercise classes

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later