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]
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
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.
Funktionaalianalyysin peruskurssi, luentomoniste.
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.