/hanche/75045info.html

75045 Dynamical systems 1998

Course information
 
Lecturer:
Harald Hanche-Olsen <hanche@math.ntnu.no>
Lectures
Under the link above you will find a brief overview of the lectures, and links to further information of interest.
Exercises
There is no allocated time for exercises, but I give some exercises anyway.
Literature:
Lawrence Perko, Differential equations and dynamical systems Second edition, Springer-Verlag 1996 (ISBN 0-387-94778-7) or First edition, Springer-Verlag 1991 (ISBN 0-387-96443-1)
Note on Fractals and chaos (in Norwegian).
Reading list
This year's exam (as PostScript files)
The problems, in Norwegian and in English.
A suggested solution (in English only -- preliminary draft, not even proofread, and likely full of errors).
For the curious, a Maple worksheet containing some direction field plots for the systems in problems 3-5.
Last year's exam (as PostScript files)
The problems and suggested solutions (in Norwegian).
Support literature:
M. W. Hirsch & S. Smale: Differential equations, dynamical systems and linear algebra, Academic Press 1974. More mathematically stringent than Perko.
D. W. Jordan & P. Smith: Non-linear ordinary differential equations, Oxford University Press 1977. Possibly easier reading than Perko or Hirsch & Smale.
V. I. Arnold, Ordinary Differential equations, MIT Press 1980. More thorough than Perko, but doesn't go as far.
Other literature for those who want to dig deeper:
V. I. Arnold, Geometric methods in the theory of ordinary differential equations, Springer-Verlag 1983.
J. Guckenheimer & P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer-Verlag 1983.
Subjects (not necessarily in the order lectured):
Fractals, attractors, and chaos
LInear systems of ordinary differential equations
Higher order differential equations
Discrete dynamical systems and iteration processes
The contraction principle
Existence and uniqueness of solutions
Geometry in phase space
Nonlinear differential equations and systems
Stability concepts
Equilibrium and Liapunov theory
Limit cycles and periodic solutions
Poincaré-Bendixson theory
Examples and applications
Timeplan
  Mandag Tirsdag Onsdag Torsdag Fredag
08:15-09:00          
09:15-10:00          
10:15-11:00         Forelesning
(S5)
11:15-12:00        
12:15-13:00 Forelesning
(K5) 		       
13:15-14:00        
14:15-15:00          
15:15-16:00          
Første forelesning er mandag 19. januar.
Harald Hanche-Olsen
1998-05-19 16:11:34 UTC