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Introduction to differential geometry, fall 2015

 

Teacher: Ilkka Holopainen 

Scope: 10 cr

Type: Advanced studies

Teaching: Weeks 36-42 and 44-50, Wednesday 10-12 and Thursday 10-12 in room C123. First lecture on Wednesday, September 2.

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

News

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Teaching schedule

Weeks 36-42 and 44-50, Wednesday 10-12 and Thursday 10-12 in room C123.

First lecture on Wednesday, September 2.

Last lecture on Thursday, December 3.

Exams

The course can be passed by an exam. First possibilities are on December 10 or December 21.

Course material

John M. Lee: Introduction to smooth manifolds, Springer, 2003.
I. Holopainen: Johdatus differentiaaligeometriaan, (in Finnish).

Registration


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Exercises

Assignments and solutions


Exercise classes

GroupDayTimeRoomInstructor
1.Monday 10-12 B321 Elefterios Soultanis

You will get extra credit points by solving the home work exercises:

25% = +1p, 35% = +2p, 45% = +3p, 55% = +4p, 65% = +5p ja 75% = +6p.

Course feedback

Course feedback can be given at any point during the course. Click here.

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