FALL SEMESTER 2013
The University of Iowa
The College of Liberal Arts and Sciences
Department of Mathematics
ORDINARY DIFFERENTIAL EQUATIONS I: MATH:6600(22M:213)
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 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 during
Spring semester 2014.
ASSIGNMENTS/HOMEWORK
 hmwk1.ps,
hmwk1.pdf due 09/06/13.
 hmwk2.ps,
hmwk2.pdf due 09/13/13.
 hmwk3.ps,
hmwk3.pdf due 09/20/13.
 hmwk4.ps,
hmwk4.pdf due 09/27/13.
 hmwk5.ps,
hmwk5.pdf due 10/04/13.
 hmwk6.ps,
hmwk6.pdf due 10/11/13.
 hmwk7.ps,
hmwk7.pdf due 10/18/13.
 hmwk8.ps,
hmwk8.pdf due 10/25/13.
 hmwk9.ps,
hmwk9.pdf due 11/01/13.
 hmwk10.ps,
hmwk10.pdf due 11/08/13.
 hmwk11.ps,
hmwk11.pdf due 11/15/13.
 hmwk12.ps,
hmwk12.pdf due 11/22/13.
 hmwk13.ps,
hmwk13.pdf due 12/11/13.
RECOMMENDED READINGS FROM THE TEXTBOOKS (AND FROM OTHER REFERENCES)
 In Sagan: 1.1, 1.2, 1.4, 1.5, 1.6, 1.7, p.40
 In Sagan: 2.1, 2.2, 2.3, 2.4, 2.6, 2.9, pp. 100102, on the first variation
 In Sagan: 7.1, 7.2, 7.3, 7.5, 7.6, on the second variation
 In Sagan: 2.11, 7.7, 7.8, 7.9, pp. 420421, on generalizations to n functions
 In Arnold: Part I (Chapters 1 and 2) on Newtonian mechanics (as light reading)
 In Arnold: 12 on variational Calculus
 In Sagan: A2.15 on Hamilton's principle
 In Arnold: 13, 17, 19, and 21 on Lagrangian mechanics and variational principles
 In Sagan: A2.16 and Arnold: 20 on Noether's theorem
 In Sagan: 2.12 and Arnold: 14 and 15 on Hamiltonian systems
 In Arnold: Chapter 7 (3236) on differential forms
 In Arnold: 37, 38, and 44 (D from p.238E) on symplectic structure and Hamiltonian systems.
Warning: 'symplectic transformation' in Arnold are called 'canonical transformation'
which may be a source of confusion since 'canonical transformations'
in the literature are sometimes defined differently and in this case
are (slightly) more general than symplectic transformations
 In Arnold: 16 on volume preservation and the Poincare recurrence Theorem
GENERAL INFORMATION
 Syllabus
 ICON
 Textbooks:

Introduction to the Calculus of Variations by Hans Sagan,
1969 edition, 449 pages, Paperback, Dover Publications,
ISBN10: 0486673669, ISBN13: 9780486673660, list price: $19.95.
Library references: Physics Library QA315 .S23 1992 and Mathematical Sciences Library QA315 .S23.
Table of contents.
The book on amazon.com.


Mathematical Methods of Classical Mechanics by Vladimir I. Arnol'd,
Translated by K. Vogtmann and A. Weinstein,
Springer, Series: Graduate Texts in Mathematics, Vol. 60,
2nd edition 1989, Corr. 4th printing (December 1, 2010), 535 pages, Softcover
ISBN10: 1441930876, ISBN13: 9781441930873, list price: $74.95.
Library references: Engineering Library QA805 .A6813 1989a, Physics Library QA805 .A6813 1989,
and Sciences Library QA805 .A6813 1989b.
The book on amazon.com.


Mathematical Aspects of Classical and Celestial Mechanics by Vladimir I. Arnol'd,
Valery V. Kozlov, Anatoly I. Neishtadt, Translated by E. Khukhro,
Springer, Series: Encyclopaedia of Mathematical Sciences, Vol. 3,
Softcover reprint of hardcover 3rd ed. 2006 edition (November 19, 2010), 531 pages,
ISBN10: 3540282467, ISBN13: 9783540282464, list price: $179.00.
Library references: Sciences Library QA805 .A67913 2006.
The book on amazon.com.
Electronic version.

COURSE TOPICS
 Variational calculus
 Lagrange's and Hamilton's mechanics
 Noether's theorem
 Divergence free ODEs (Poincare recurrence theorem)
 Reversible systems
 Perturbations
 Existence and uniqueness
 Lyapunovstability
 Differential inequalities
 Normal forms
 Unfolding of vector fields
 Invariant (stable, unstable, center) manifolds
 Canonical transformations and generating functions
 KAM (KolmogorovArnoldMoser) theory
 Poisson systems
 Variational/symplectic integrators
 Structural stability and bifurcations
 Averaging
 Homoclinic orbits
 Melnikov's method
 Boundary value problems (SturmLiouville systems)
 etc.
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.
To access the Linux network (linux.divms.uiowa.edu) from off campus, you are required to establish a VPN connection
before connecting (follow these instructions
to install the software required to establish such connections).

Selected Unix commands.
 Class directory: /group/class/m_213. Group you belong to: m_213.
 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
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.

Getting Started in the Division of Mathematical Sciences
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.
 An excellent book on Matlab:
MATLAB: An Introduction with Applications by
Amos Gilat,
Hoboken, N.J.: Wiley ; Chichester : John Wiley, 2008,
ISBN10: 0470108770, ISBN13: 9780470108772 (ENGINEERING QA297 .G48 2008)
FORTRAN
 Type "man f90" on Unix workstations for information on how to compile

A list of
Fortran tutorials,
GRADER

Rebecca Gasper ,
email: rebeccagasper@uiowa.edu, gasper.rebecca@gmail.com. 325N MLH. Phone: 3353772.
LIST OF STUDENTS
 Abdulwahid, Adnan Hashim
 Aiello, Gordon James
 Almodovar, Leyda Michelle
 Barela, Mario A
 Cai, HanQin
 Caples, Christine E
 Covello, Michael
 Dill, Benjamin Matthew
 Gerstle, Kevin Charles
 Liu, Suhui
 Murillo, Pacheco Juan Pablo
 Richmond, Nathaniel Owen
Laurent O. Jay
Department of Mathematics
14 MacLean Hall
The University of Iowa
Iowa City, IA 522421419
USA
Tel: (319)3350898
Fax: (319)3350627
Email: laurentjay@uiowa.edu