home page |
## teaching in 2006/2007 |

## Reading course semigroup theory |

**First series of exercises** here.

**Second series of exercises (with a correction in 1.)(e))** here.

Previous meetings:

31 May: Theme: nonlinear perturbation. Chapter III: p. 182 through Example 3.5. Also: Chapter 3 and Chapter 5 through Section 5.1 of the thesis "The FitzHugh-Nagumo equation on an Unbounded Domain" by Gerard Houtman. Maint point: compare both methods.

24 May: Theme: sun dual semigroups and application to delay equations. Chapter II: 2.5, 2.6, Chapter IV: Section 6 through Lemma 6.5 (not all details required).

10 May: Theme: perturbation theory. Chapter III: 1.1-1.3 (not the part in the smaller font after 1.3 on pp. 159-160), 1.7-1.12, 2.1-2.4, 2.7 en 2.10 (both without proof), 2.11-2.12.

26 April: Theme: delay differential equations, Chapter II: 3.29, 4.22-4.25, 4.28 and Chapter IV: 1.17-1.19, 2.8, 3.12 (without proof).

10 April: Chapter IV: 1.1-1.4, 1.6, 1.8-1.9, 1.11, 1.13-1.14, 2.1-2.3, 2.5, 3.1-3.3, 3.6 (notations here are those from IV.1.17: m_{a} is algebraic multiplicity, m_{g} is geometric multiplicity, k is order of pole).

29 March: Chapter II: 3.28 (why is this more difficult for a Lebesgue space L^p(R^n) instead of C_0?), 4.1-4.6, 4.8-4.11.

15 March: Chapter II: 1.10-1.11, 2.2-2.3, 2.9-2.11, 3.1-3.9.

Sander Hille and I organize a reading course on the theory of semigroups of operators during the Spring 2007 semester. We will use the book `One-parameter semigroups for linear evolution equations' by K.-J. Engel and R. Nagel, Springer-Verlag, 2000, ISBN 0-387-98463-1.

The course covers the basics of the theory of semigroups of operators and some special topics (e.g., analytic semigroups, positive semigroups, eventually compact semigroups, perturbation theory) and applications. We will meet biweekly to discuss the reading material and there may be presentations and lectures.

Some knowledge of functional analysis (on the level of the mastermath course Functional Analysis) is prerequisite. It is possible to obtain EC by active participation and handing in exercises that will be assigned.

Place: Snellius building, University of Leiden, Niels Bohrweg 1, Leiden. Here are directions to the "Snellius" building, in which the Mathematical Institute is located.

## Analyse 4 - Complexe analyse |

Derde keer bonushuiswerk: opgaven 17.13, 18.6(ii), 20.7(i) en 21.13 uit Priestly.

Tweede keer: opgaven 11.3(ii), 14.4, 14.7(i) en 15.11(i) uit Priestley, donderdag 12 april.

Eerste keer: opgaven 8.10(ii), 9.4(iii) en 10.5(ii) uit Priestley, maandag 12 maart 2007.

Het programma en de opgavenlijst voor het huiswerk en werkcollege staan hier.

## Linear Algebra 1 Fall 2006 |

Linear algebra 1 for physics and astronomy. Students and colleagues can find more information on the according blackboard pages. The program with general information and the list of exercises is also available here.