ORDINARY DIFFERENTIAL EQUATIONS I-22M:214
SPRING SEMESTER 2010
This course is a continuation of 22M:213 (Ordinary Differential
Equations I). Though the course is mostly about the theory of ordinary
differential equations (ODEs), we may 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.
hmwk1.pdf due 02/05/10.
hmwk2.pdf due 02/12/10.
hmwk3.pdf due 02/24/10.
hmwk4.pdf due 03/03/10.
hmwk5.pdf due 03/12/10.
hmwk6.pdf due 04/02/10.
hmwk7.pdf due 04/16/10.
hmwk8.pdf due 04/23/10.
hmwk9.pdf due 04/30/10.
hmwk10.pdf due 05/07/10.
RECOMMENDED READINGS FROM THE TEXTBOOKS (AND FROM OTHER REFERENCES)
- Perturbation methods: Verhulst: 9.1,9.2,9.3
- Differential and integral inequalities: Verhulst: 1.3
- Normal forms: Verhulst: 13.2; Wiggins: 19.1 (also Meiss: 8.5; Glendinning: 4.1)
- Unfolding vector fields: Wiggins: 20.3, 20.4AD (also Meiss: 8.3; Perko: 4.3; Glendinning: 10.1)
- Stable, unstable, and center manifolds: Verhulst: 3.3, 13.4;
Wiggins: 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
- Canonical transformations and generating functions: Gelfand: 19; Wiggins: 13.7C, 14.4; Arnold 47A, 48
- Hamilton-Jacobi PDE, etc.: Gelfand: 23; Wiggins: 13.8; Arnold 46D, 47B
- Integrable Hamiltonian systems: Verhulst: 15.7; Wiggins: 14.5, 14.6; Arnold: 15C, 49, 50 (also Meiss: 9.12)
- KAM theory: Verhulst: 15.7; Wiggins: 14.7; Arnold: Appendix 8 (also Meiss: 9.13)
- Poisson systems: Arnold: 43; (Meiss: 9.4);
Electronic version of chapter VII
(look at pp.254-293) of
Geometric numerical integration: structure-preserving algorithms
for ordinary differential equations
by E. Hairer, Ch. Lubich, and G. Wanner.
- Textbooks (recommended):
Nonlinear Differential Equations and Dynamical Systems (second Edition) by Ferdinand Verhulst,
Springer, Series: Universitext, 303 pages, Softcover, Corr. 2nd printing, 1996,
ISBN-10: 3540609342, ISBN-13: 978-3540609346, list price: $49.95.
Library reference: Physics Library QA372 .V48513 1996.
Table of contents.
The book on amazon.com.
Introduction to Applied Nonlinear Dynamical Systems and Chaos by
Springer, Series: Texts in Applied Mathematics, Vol. 2, 2nd edition,
2003, 808 pages, Hardcover,
ISBN-10: 0387001778, ISBN-13: 978-0387001777, list price: $109.00.
of contents. Library reference: Mathematical Sciences Library QA614.8 .W54 2003.
The book on amazon.com.
Differential Equations: Theory and Applications by Davis Betounes,
Springer, 2nd edition, 2010, 620 pages, Hardcover,
ISBN-10: 1441911626, ISBN-13: 978-1441911629, list price: $79.95. Library reference: Engineering Library QA371.5.D37 B47 2010.
The book on amazon.com.
- Existence and uniqueness (covered in 22M:213)
- Lyapunov-stability (covered in 22M:213)
- Variational calculus (covered in 22M:213)
- Lagrange's and Hamilton's mechanics (covered in 22M:213)
- Noether's theorem (covered in 22M:213)
- Divergence free ODEs (Poincare recurrence theorem) (covered in 22M:213)
- Reversible systems (covered in 22M:213)
- Perturbations (covered in 22M:214)
- Differential inequalities (covered in 22M:214)
- Normal forms (covered in 22M:214)
- Unfolding of vector fields (covered in 22M:214)
- Invariant (stable, unstable, center) manifolds (covered in 22M:214)
- Canonical transformations and generating functions (covered in 22M:214)
- KAM (Kolmogorov-Arnold-Moser) theory (covered in 22M:214)
- Poisson systems (covered in 22M:214)
- Variational/symplectic integrators
- Structural stability and bifurcations
- 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/m_214. Group you belong to: m_214.
- If you do not know your password go to 303A MLH.
To change your Mathematical Sciences password here is the
online password change tool.
- 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
e-mail: email@example.com. B20J MLH. Phone: 335-3650.
LIST OF STUDENTS
- Diedrichs, Danilo Roberto
- Ellingwood, Nathan David
- Gasper, Rebecca Elizabeth
- Goertzen, Corissa Marie
- Mills, Andrew Thomas
- Mooney, Christopher Park
- Padberg, Mary Therese Zeithaml
- Rhomberg, Patrick Seton
- Usova, Ekaterina
- Yong, Kamuela E
- Yu, Lu
Laurent O. Jay
Department of Mathematics
14 MacLean Hall
The University of Iowa
Iowa City, IA 52242-1419