Kaisa_2012_3_photo by Veikko Somerpuro

!! distance learning from 16.03

Basic theory of one-parameter semigroups for linear evolution equations, applied to various problems in biology

This course is an introduction to one-parameter semigroups for linear evolution equations. After a gentle prelude with well known examples of semigroups, the participants will learn about generators of semigroups and their resolvents, perturbation and approximation of semigroups, the spectral theory for semigroups and generators as well as asymptotics. General theory will be complemented with examples of semigroups in biological systems and the participants will learn to use the semigroup theory to model and study the dynamics of structured populations (e.g. cell population dynamics, gut microbiota dynamics).

Lecturer: Barbara Boldin (University of Primorska)

Recommended literature: K-J. Engel, R. Nagel: One-parameter semigroups of linear evolution equations. Springer-Verlag, 2000. ISBN: 0-387-98463-1

DISTANCE LEARNING FROM 16.03.

Following the instructions of the Head of the Department of Mathematics and Statistics, we will terminate all the remaining contact teaching and continue the course online.

From Monday 16.3. on, this means the following:
Lecture notes for weeks 9, 10 and 11 will be available on the course website and you will be informed by e-mail about the corresponding passages in the book.
Weeks 12, 13 and 14 will be devoted to studying applications. Information about the literature will be posted on the course website and distributed over e-mail.
Each Tuesday 12-14 and Wednesday 12-14 the lecturer will be available on Skype for questions and discussions. You get her Skype name by e-mail.
For the tutorials, exercises will be posted on the course website and the TA will be available on Skype on Fridays 12-14.
Information about exams will be posted later.

Questions are welcome by e-mail.

Enrol
9.12.2019 at 09:00 - 29.4.2020 at 23:59

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Eva Kisdi's picture

Eva Kisdi

Published, 14.3.2020 at 15:31

Distance learning from 16.03. Detailed instructions in the course description above.

Timetable

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

DateTimeLocation
Tue 14.1.2020
12:15 - 14:00
Wed 15.1.2020
12:15 - 14:00
Fri 17.1.2020
12:15 - 14:00
Tue 21.1.2020
12:15 - 14:00
Wed 22.1.2020
12:15 - 14:00
Fri 24.1.2020
12:15 - 14:00
Tue 28.1.2020
12:15 - 14:00
Wed 29.1.2020
12:15 - 14:00
Fri 31.1.2020
12:15 - 14:00
Tue 4.2.2020
12:15 - 14:00
Wed 5.2.2020
12:15 - 14:00
Fri 7.2.2020
12:15 - 14:00
Tue 11.2.2020
12:15 - 14:00
Wed 12.2.2020
12:15 - 14:00
Fri 14.2.2020
12:15 - 14:00
Tue 18.2.2020
12:15 - 14:00
Wed 19.2.2020
12:15 - 14:00
Fri 21.2.2020
12:15 - 14:00
Tue 25.2.2020
12:15 - 14:00
Wed 26.2.2020
12:15 - 14:00
Fri 28.2.2020
12:15 - 14:00
Tue 10.3.2020
12:15 - 14:00
Wed 11.3.2020
12:15 - 14:00
Fri 13.3.2020
12:15 - 14:00
Tue 17.3.2020
12:15 - 14:00
Wed 18.3.2020
12:15 - 14:00
Fri 20.3.2020
12:15 - 14:00
Tue 24.3.2020
12:15 - 14:00
Wed 25.3.2020
12:15 - 14:00
Fri 27.3.2020
12:15 - 14:00
Tue 31.3.2020
12:15 - 14:00
Wed 1.4.2020
12:15 - 14:00
Fri 3.4.2020
12:15 - 14:00
Tue 7.4.2020
12:15 - 14:00
Wed 8.4.2020
12:15 - 14:00
Fri 17.4.2020
12:15 - 14:00
Tue 21.4.2020
12:15 - 14:00
Wed 22.4.2020
12:15 - 14:00
Fri 24.4.2020
12:15 - 14:00
Tue 28.4.2020
12:15 - 14:00
Wed 29.4.2020
12:15 - 14:00

Material

Weeks 1-11: Lecture notes (contact lecturer)

Week 12:
O. Diekmann, H.J.A.M. Heijmans, H.R. Thieme: On the stability of the cell size distribution. J. Math. Biol. (1984) 19, pp. 227-248

Week 13:
M. Gyllenberg, G.F. Webb: Age-size structure in populations with quiescence. Math. Biosci. (1987) 86, pp. 67-95

Week 14:
B. Boldin: Persistence and spread of gastro-intestinal Infections: the case of Enterotoxigenic Escherichia coli in piglets. Bull. Math. Biol. (2008) 70: pp 2077-2101

Conduct of the course

The course consists of lectures and exercise classes with an exam graded 1-5.

Description

Target group: MAST, LSI students

BSc courses on analysis, differential equations, linear algebra

BSc courses on analysis, differential equations, linear algebra

Understanding the basic theory of one-parameter semigroups for linear evolution equations and using the knowledge to study various problems in biology

2019-2020 periods III and IV (spring 2020)

This course is an introduction to one-parameter semigroups for linear evolution equations. After a gentle prelude with well known examples of semigroups, the participants will learn about generators of semigroups and their resolvents, perturbation and approximation of semigroups, the spectral theory for semigroups and generators as well as asymptotics. General theory will be complemented with examples of semigroups in biological systems and the participants will learn to use the semigroup theory to model and study the dynamics of structured populations (e.g. cell population dynamics, gut microbiota dynamics)

exam

K-J. Engel, R. Nagel: One-parameter semigroups of linear evolution equations. Springer-Verlag, 2000. ISBN: 0-387-98463-1

Lectures and exercise classes

Exam and exercises, course graded 1-5