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.

ASSIGNMENTS/HOMEWORK

1. hmwk1.ps, hmwk1.pdf due 02/05/10.
2. hmwk2.ps, hmwk2.pdf due 02/12/10.
3. hmwk3.ps, hmwk3.pdf due 02/24/10.
4. hmwk4.ps, hmwk4.pdf due 03/03/10.
5. hmwk5.ps, hmwk5.pdf due 03/12/10.
6. hmwk6.ps, hmwk6.pdf due 04/02/10.
7. hmwk7.ps, hmwk7.pdf due 04/16/10.
8. hmwk8.ps, hmwk8.pdf due 04/23/10.
9. hmwk9.ps, hmwk9.pdf due 04/30/10.
10. hmwk10.ps, 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.

GENERAL INFORMATION

• Syllabus
• ICON
• 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. Erratum. The book on amazon.com.
  • Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins, 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. Table of contents. Library reference: Mathematical Sciences Library QA614.8 .W54 2003. The book on amazon.com. Electronic version.
  • 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. Electronic version.

COURSE TOPICS

• 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
• Averaging
• Homoclinic orbits
• Melnikov's method
• Boundary value problems (Sturm-Liouville systems)
• etc.

MATLAB

• 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 Tutorial, 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
• MATLAB 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 html)
• 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

FORTRAN

• Type "man f90" on Linux terminals for information on how to compile.
• A list of Fortran tutorials, Fortran 90 for the Fortran 77 programmer, Fortran 90 for Fortran 77 programmers.

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 Information form.
• 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 home directory.

GRADER

• Beven Kair, e-mail: bkair@math.uiowa.edu. B20J MLH. Phone: 335-3650.