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Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 31.1.2018 at 14:22

Results for the final exam on 10.1.2018 have been linked to the page Results/Tulokset (please login to read this page).

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 17.1.2018 at 14:57

I have linked model solutions for the 1. partial exam from 27.10.2017 to the "Tehtävät"-part (I seem to have forgotten to do this earlier).

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 9.1.2018 at 15:54

The results from the course have now been linked to the page Results/Tulokset. Please note that you will have to log in to view the page.

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 9.1.2018 at 11:53

Model solutions to the 2. partial exam from 18.12.2017 have been added to the "Tehtävät"-part. Results from the course will be linked in a moment.

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 15.12.2017 at 16:59

Model solutions to the 2. partial exams from 2010 and 2008 have been linked to the course page (two different pdf-files).

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 14.12.2017 at 21:13

REMINDER: the 2. partial exam of Functional Analysis is on Monday 18.12. from 12-15 o'clock in room D123. Topics of the exam: chapters 5-9, but excluding the part "Sobolev spaces" (pp. 101-114 in the Finnish course notes).
Older partial exams (2010 and 2008), as well as a couple of final exams, have been linked to the course pages. Related model answers will be linked on Friday 15.12 (as well as for Exercises 13).
The next final exam (for the whole course) is on Wed 10.1.2018. Note that you need to register in WebOodi for final exams (at latest 10 days before the date)!

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 11.12.2017 at 20:12

A misprint has been corrected in the definition in Exercise 13:2, where the duality c_0^* = \ell^1 refers to the identification from Exercise 12:3.

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 8.12.2017 at 19:24

Exercises 13 for Wed 13.12 have been added. This is the last exercise.

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 2.12.2017 at 20:30

Solutions to Exercises 11 have been added (including an second proof of problem 11:5 that does not use the Baire theorem).

Hans-Olav Tylli's picture

Hans-Olav Tylli

Published, 1.12.2017 at 15:26

Exercises 12 for Thursday 7.12 (14-16 o'clock, room C123) have been added. Note the change of day (because of Independence day 6.12 on Wednesday).

Pages

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Mon 4.9.2017
10:15 - 12:00
Tue 5.9.2017
12:15 - 14:00
Mon 11.9.2017
10:15 - 12:00
Tue 12.9.2017
12:15 - 14:00
Mon 18.9.2017
10:15 - 12:00
Tue 19.9.2017
12:15 - 14:00
Mon 25.9.2017
10:15 - 12:00
Tue 26.9.2017
12:15 - 14:00
Mon 2.10.2017
10:15 - 12:00
Tue 3.10.2017
12:15 - 14:00
Mon 9.10.2017
10:15 - 12:00
Tue 10.10.2017
12:15 - 14:00
Mon 16.10.2017
10:15 - 12:00
Tue 17.10.2017
12:15 - 14:00
Mon 30.10.2017
10:15 - 12:00
Tue 31.10.2017
12:15 - 14:00
Mon 6.11.2017
10:15 - 12:00
Tue 7.11.2017
12:15 - 14:00
Mon 13.11.2017
10:15 - 12:00
Tue 14.11.2017
12:15 - 14:00
Mon 20.11.2017
10:15 - 12:00
Tue 21.11.2017
12:15 - 14:00
Mon 27.11.2017
10:15 - 12:00
Tue 28.11.2017
12:15 - 14:00
Mon 4.12.2017
10:15 - 12:00
Tue 5.12.2017
12:15 - 14:00
Mon 11.12.2017
10:15 - 12:00
Tue 12.12.2017
12:15 - 14:00

Other teaching

06.09. - 18.10.2017 Wed 14.15-16.00
01.11. - 29.11.2017 Wed 14.15-16.00
07.12.2017 Thu 14.15-16.00
13.12.2017 Wed 14.15-16.00
Hans-Olav Tylli
Teaching language: English

Material

The course will follow the course notes "Funktonaalianalyysin peruskurssi" (latest version 2012) by Kari Astala, Petteri Piiroinen & Hans-Olav Tylli. A current version for the Autumn 2017 will also be uploaded during the course (including notes indicating topics not covered this year during the lectures).

The following books contain related material (as well as much more), that can be used to compare with the course notes:

Bollobas: Linear Analysis (Cambridge Mathematical Textbooks)
Werner: Funktionalanalysis (Springer-Lehrbuch) [in German]
Rudin: Real and Complex Analysis (Tata McGraw-Hill) [chapters 3-5 used as material for this course]

Tasks

Exercises 1 Laskuharjoitus 1

Improved hint for 1:4

Exercises 2 Laskuharjoitus 2

Exercises 3 Laskuharjoitus 3

Exercises 4 Laskuharjoitus 4

Exercises 5 Laskuharjoitus 5

Exercises 6 Laskuharjoitus 6

Partial exams 2010/2008/1998

Partial exam 2010 model solutions

Partial exam 2008 model solutions

Exercises 7 Laskuharjoitus 7

Exercises 8 Laskuharjoitus 8

Exercises 9 Laskuharjoitus 9

Exercises 10 Laskuharjoitus 10

Exercises 11 Laskuharjoitus 11

Exercises 12 Laskuharjoitus 12

Exercises 13 (last) Laskuharjoitus 13 (viimeinen)

2. partial exams 2010/2008

2. partial exam 2010 model answer

2. partial exam 2008 models

2. partial exam 18.12.2017 model answers

1. partial exam 27.10.2017 model answers

Description

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.

Analysis I&II, Linear algebra I&II, Topology I

Elements of measure theory and complex analysis

Elements of linear functional analysis including Banach and Hilbert spaces and linear operators between them, three basic principles, and applications to differential equations.

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

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

Introduction to linear functional analysis including Banach and Hilbert spaces and linear operators between them; topology of normed spaces; examples of Banach spaces including sequence and function spaces; three basic principles; Fourier-series; Sobolev spaces; applications to differential equations.

Required:

Funktionaalianalyysin peruskurssi, luentomoniste.

Recommended:

Rynne, B., Youngson, M., Linear Functional Analysis, Springer Undergraduate Mathematics Series, London, 2000. (Introduction to the topic)
Friedman, A., Foundations of Modern Analysis, Dover 1982. Conway, J. A Course in Functional Analysis. Springer, 1990. (Introduction to the topic) Werner, D., Funktionalanalysis, Springer Lehrbuch 1990. (In German)

Lectures and exercise classes

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

Exam, other methods will be described later.