# TMA4165

# Differential Equations and Dynamical Systems

# Spring 2013

**Did you like this course?**

** Do you like working with differential equations? **

Then a natural next step is to take ** TMA4305 Partial Differential Equations.**

For **stochastic differential equations** try **MA8109 Stochastic processes in systems theory**

(PhD course fall 2013 - ok for 4th year students)

## Messages

- Problem set and solution sketch for the exam.

**Good luck**on the exam Thursday!

**Final curriculum**available - see 'General information' in left menu.- Not covered this year and in 2012:
- Index at infinity
- Bifurcations
- Fractals
- Discrete dynamical systems and chaos

- New this year and 2012:
- Much more extensive and general discussion of existence, uniqueness, and continuous dependence results.
- More emphasis on linear theory, the fundamental matrix, and stability results
- Invariant domains, LaSalle's principle

**Other messages:****All summary slides**are posted under 'General information' in the left menu.**Exam problems**for Lectures 25.4. and 30.4.: 2012: 1,5,7; 2010:2a,3,4; 2011:3a; 2009:2a,2b**Excursion week 12 and 14:**The lecture notes for these weeks are posted in the left menu under 'General infomation'.

(There will be exam poblems from this part of the curriculum.)- A
**simpler proof**of continuous dependence on the data in scanned lecture note of 21.1. ('General information' in left menu). - Copies of chp. 6 of the
**Birkhoff & Rota**book can be bought at the math. department office (7th floor SB2).

** Homework:**

- 23.4.: Read the proofs of sections 11.2 and 11.3 of Jordan-Smith
- 05.3.: Read the note of Hanche-Olsen p. 23-24
- 28.2.: Read Birkhoff & Rota page 6.13.
- 21.2.: Read Birkhoff & Rota chp. 6.5.
- 29.1.: Read Jordan-Smith chapters 2.5 and 2.6.
- 24.1.: Read the following lecture note.
- 17.1.: Read chapter 1 in Jordan-Smith.

<schedule> <daytitles>Mon|Tue|Wed|Thu|Fri</daytitles> <timeslots>08:15-09:00|09:15-10:00|10:15-11:00|11:15-12:00|12:15-13:00|13:15-14:00|14:15-15:00|15:15-16:00|16:15-17:00|17:15-18:00</timeslots>

<entry day:Tu start:2 end:3 color:blue>Lecture R3</entry> <entry day:Th start:2 end:3 color:blue>Lecture F2</entry> <entry day:Mo start:9 end:9 color:lightgrey>Exercises R10</entry> </schedule>