ORDINARY DIFFERENTIAL EQUATIONS I-22M:213
FALL SEMESTER 2007
This course is a natural continuation of 22M:142 (nonlinear
dynamics with numerical methods).
Though the course is mostly about the theory of ordinary
differential equations (ODEs), we will consider this
theory in conjunction with some theoretical and practical
aspects of numerical methods for ODEs.
If you have a high interest in a specific topic related to ODEs,
please let me know. If a majority of students taking the class
is interested in the topic then I may cover it during
Spring semester 2008.
hmwk1.pdf due 09/10/07.
hmwk2.pdf due 09/17/07.
hmwk3.pdf due 09/24/07.
hmwk4.pdf due 10/08/07.
hmwk5.pdf due 10/17/07.
hmwk6.pdf due 10/26/07.
hmwk7.pdf due 11/09/07.
hmwk8.pdf due 11/16/07.
hmwk9.pdf due 11/26/07.
hmwk10.pdf due 12/03/07.
READINGS FROM THE TEXTBOOK (AND FROM OTHER REFERENCES)
- 1.1, 1.2
- Chapter 2
- Introduction of Chapter 7, 7.1, 7.2, 7.3, 7.4
- From [HNW,1993] you can read section II.2 if you wish
- Introduction of Chapter 3, 3.1, 3.2, 3.4 (and 3.5 if you are adventurous!)
- Introduction of Chapter 18, 18.1, 18.3, and 18.5
- Section 2.7 and 2.12 from Perko's book
- Introduction of Chapter 5, 5.1
- Introduction of Chapter 13, 13.1, 13.2, 13.3, 13.5, 13.7AB
- Introduction of Chapter 14, 14.1, 14.2, 14.3
- Introduction of Chapter 16, 16.1, 16.2
- Variational calculus
- Lagrange's and Hamilton's mechanics
- Noether's theorem
- Divergence free ODEs (Poincare recurrence theorem)
- Reversible systems
- Invariant (stable, unstable, center) manifolds
- Poisson systems
- Variational/symplectic integrators
- Differential inequalities
- KAM (Kolmogorov-Arnold-Moser) theory
- Normal forms
- Structural stability
- Homoclinic orbits
- Melnikov's method
- Boundary value problems (Sturm-Liouville systems)
- Free electronic textbook Numerical Computing with MATLAB
by Cleve Moler
himself!, the founder of Matlab.
- Matlab Help is available directly from the Help menu of the Matlab window.
- A Very Elementary
MATLAB Tutorials from Other Universities,
MATLAB & Simulink Tutorials,
MATLAB Homework Helper,
all presented by Mathworks, Inc., producers of Matlab.
Crash Course in MATLAB by Tobin Driscoll, University of Delaware.
Some Matlab tutorials from Edward Neuman
Matlab tutorial - University of New Hampshire
Matlab tutorial - University of British Columbia
Matlab tutorial - University of Florida
Online Reference Documentation provides direct hypertext links to
specific MATLAB function descriptions (from the Math Dept, University of Florida).
- Matlab Primer (ps)
(for an earlier version of Matlab)
- Matlab 5 introduction
(ps, see also
- MATLAB Guide by D. J. Higham and N. J. Higham,
SIAM, Philadelphia, 2005 (ENGINEERING QA297 .H5217 2005)
Introduction to Engineering Programming: in C, MATLAB and JAVA
by Mark A. Austin.
- Matlab for first order ODEs
- Matlab for higher order ODEs and systems of ODEs
- Matlab for PDEs
LINUX COMPUTER ACCOUNTS
Linux computer accounts will be made available on the Linux network in MLH
(computer lab rooms B5 and 301).
You can also use the NoMachine
NX Client Windows software to
access your Linux computer account remotely.
Selected Unix commands.
- Class directory: /group/class/m213. Group you belong to: m213.
- If you do not know your password go to 303A MLH.
- Accounts for students who are not majoring in Computer Science,
Mathematics, or Statistics and Actuarial Science
will be deleted after the term has ended!
Note the expiration date at the top of your Unix Account
- The directory for this class will be removed before the
beginning of the next term! If there is anything in this directory
that you would like to save, you must archive it to your own
LIST OF 13 STUDENTS
- Abiva, Jeannine Therese
- Alexander, Simone Volon
- Correa, Alvaro
- Drube, Paul Harlan
- Kair, Beven Michael
- Kozak, Christopher L
- Meyers, Anna Lynn
- Mohr, Darin Griffin
- Nam, Sang Yop
- Price, Candice
- Reinkoester, Jeremiah N
- Small, Scott Joseph
- Wolf, Roseanne Marie
Laurent O. Jay
Department of Mathematics
14 MacLean Hall
The University of Iowa
Iowa City, IA 52242-1419