SPRING 2018
The University of Iowa
The College of Liberal Arts and Sciences
Department of Mathematics
ORDINARY DIFFERENTIAL EQUATIONS II: MATH:6610, Section 0001
12:30PM1:20PM MWF in 113 MLH
ANNOUNCEMENTS
This course is a continuation of MATH:6600
(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.
RECOMMENDED READINGS FROM THE TEXTBOOKS (AND FROM OTHER REFERENCES)
 Meiss: 9.6 on Poincare invariant
 Meiss: 9.2 on volumepreserving flows
 Meiss: 8.5 on normal forms
 Glendinning: 4.1 on Poincare's linearization theorem
 Meiss: 8.3 on unfolding vector fields
 Glendinning: 10.1 on unfolding degenerate singularities
 Meiss: chapter 5 on invariant manifolds
 Glendinning: 4.2 and 4.6 on the stable manifold theorem
 Glendinning: 8.1 on center manifolds
 Meiss: 9.4 on Poisson dynamics
 Meiss: 9.12, 9.13 on integrabiLIty and nearly integrable dynamics
 Meiss: 6.4 on symmetries and reversors
GENERAL INFORMATION
 Syllabus.
 ICON.
Homework assignments can be found there.
 Textbook:
Additional useful readings:

Introduction to the Calculus of Variations by Hans Sagan,
1969 edition, 449 pages, Paperback, Dover Publications,
ISBN10: 0486673669, ISBN13: 9780486673660, list price: $21.95.
Library references: Physics Library QA315 .S23 1992 and Mathematical Sciences Library QA315 .S23.
The book on amazon.com.

Calculus of Variations by I. M. Gelfand and
S. V. Fomin, October 2000, 240 pages, Paperback, Dover Publications,
ISBN10: 0486414485, ISBN13: 9780486414485, list price: $11.95.
Library reference: Mathematical Sciences Library QA315 .G417.
The book on amazon.com.

The Calculus of Variations
by B. van Brunt, SpringerVerlag, New York, Universitext, 2004, 291 pages,
ISBN: 9780387402475 (Print), 9780387216973 (Online).

Differential Dynamical Systems, Revised Edition by
James D. Meiss.
2017,
410 pages,
Society for Industrial and Applied Mathematics (SIAM),
Series: Mathematical Modeling and Computation,
ISBN13: 9781611974638, list price: $87.00 (Softcover).
Table of contents.
Preface;
Index.
Library reference (1st edition): Engineering Library QA614.8 .M45 2007.

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: 9780387001777, list price: $109.00.
Library reference: Mathematical Sciences Library QA614.8 .W54 2003.
Electronic version.

Differential Equations and Dynamical Systems (Hardcover) by Lawrence Perko,
Springer, Series: Texts in Applied Mathematics, Vol. 7, 3rd edition,
2001, 568 pages, ISBN: 0387951164.
Library reference: Mathematical Sciences Library QA372 .P47 1991.

An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition by
R. Clark Robinson,
American Mathematical Society; 2 edition, December 7, 2012,
Pure and Applied Undergraduate Texts,
733 pages, ISBN: 9780821891353, Library reference: Engineering Library QA614.8 .R65 2012.
Errata on the book by the author.

Dynamical Systems with Applications using Matlab by
Stephen Lynch,
Birkhauser, Boston, 2004, 450 pages, ISBN 0817643214,
Library reference: Engineering Library QA614.8 .L97 2004.

Nonlinear dynamics and chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity), 2nd Edition by
Steven H. Strogatz, Westview Press, 2014, ISBN13: 9780813349107,
Library reference: Engineering Library Q172.5.C45 S767 2015.

Chaos: an introduction to dynamical systems by
Kathleen T. Alligood, Tim D. Sauer, James A. Yorke,
Springer, New York, Textbooks in mathematical sciences,
1997, 603 pages, ISBN: 0387946772,
Library reference: Mathematical Sciences Library QA614.8 .A44 1997.

Solving ordinary differential equations I. Nonstiff problems
by E. Hairer, S. P. Norsett, and Gerhard Wanner, Springer, Berlin,
Springer Series in Computational Mathematics, vol. 8,
Second Revised Edition, 1993, 528 pages, ISBN: 9783540566700.
Library reference: Mathematical Sciences Library QA372 .H16 1993 v.1.

Solving ordinary differential equations II.
Stiff and differentialalgebraic problems
by E. Hairer and G. Wanner, Springer, Berlin,
Springer Series in Computational Mathematics, vol. 14,
Second Revised Edition, 1996, 614 pages, ISBN: 9783540604525.
Library reference: Mathematical Sciences Library QA372 .H16 1993 v.2.

Geometric numerical integration: structurepreserving algorithms
for ordinary differential equations
by E. Hairer, Ch. Lubich, and G. Wanner, Springer, Berlin,
Springer Series in Computational Mathematics, vol. 31,
Second Revised Edition, 2006, 644 pages, ISBN: 9783540306634.
Library reference: Mathematical Sciences Library QA299.3 .H35 2006.
 Ordinary Differential Equations and Dynamical Systems
by Gerald Teschl,
American Mathematical Society, Providence, Series: Graduate Studies in Mathematics,
vol. 140, 2012,
356 pages, Softcover, ISBN10: 0821883283, ISBN13: 9780821883280, list price: $64.00.
Electronic version and
erratum.

Nonlinear Differential Equations and Dynamical Systems (second Edition) by Ferdinand Verhulst,
Springer, Series: Universitext, 303 pages, Softcover, Corr. 2nd printing, 1996,
ISBN10: 3540609342, ISBN13: 9783540609346, list price: $49.95.
Library reference: Physics Library QA372 .V48513 1996.
The book on amazon.com.

Ordinary Differential Equations by Vladimir I. Arnol'd (Author), R. Cooke (Translator),
Springer, 272 pages, Softcover, 3rd edition, 1992,
ISBN13: 9783540345633, list price: $64.95.
The book on amazon.com.

Principles of Differential Equations by Nelson G. Markley,
WileyInterscience, Hoboken, N.J., Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts,
2004, 352 pages, Hardcover, ISBN: 0471649562.
Table of contents.
Library reference: Mathematical Sciences Library QA371 .M264 2004.

The Theory of Differential Equations: Classical and Qualitative by Walter G. Kelley and Allan C. Peterson,
Springer, Series: Universitext, Vol. 278, 424 pages, Softcover, 2nd edition, 2010,
ISBN10: 1441957820, ISBN13: 9781441957825, list price: $69.95.
The book on amazon.com.

Ordinary Differential Equations: Basics and Beyond,
by David G. Schaeffer and John W. Cain.
Publisher: Springer; 1st ed. 2016 edition (November 12, 2016),
542 pages,
Series: Texts in Applied Mathematics (Book 65),
ISBN13: 9781493963874,
list price: $69.99 (Hardcover).
Electronic version.
The
textbook on amazon.com.

Differential Equations: Theory and Applications by Davis Betounes,
Springer, 2nd edition, 2010, 620 pages, Hardcover,
ISBN10: 1441911626, ISBN13: 9781441911629, list price: $79.95. Library reference: Engineering Library QA371.5.D37 B47 2010.
The book on amazon.com.
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
 CLAS Linux Support.

Linux computer accounts are available on the Linux network in MLH
(computer lab rooms B5 and 301). Set up a
CLAS Linux Account here
by just entering your hawkid and passphrase.

You can find
local online Linux Help
for questions/problems you may have about Linux.

Selected Unix commands.
 If you have problems with your Linux account go to 303A MLH.
 These accounts expire, see the
account expiration policy. If there is anything in this directory
that you would like to save, you must archive it to your own home directory.
REMOTE ACCESS TO YOUR LINUX COMPUTER ACCOUNT
 To access your Linux computer account remotely.
you can use FastX, a graphical Linux virtual desktop environment
remotely accessible in your web browser:
 Login with your Hawkid username/password
 Click "Start a new session" (make sure your popup blocker doesn't block)
 Click "Bookmarks"
 Click "starxfce4 or startkde" depending on which desktop you want to
 Click "Start"
More details can be found
here.
You can make your browser window larger and then click in the lower left
hand corner, the box of nine dots that make a square, then click on the
arrow head with arrows on both ends to "maximize" the Linux desktop.
 https://virtualdesktop.uiowa.edu, another Windows virtual desktop
where you can access MATLAB in a Windows environment with your web browser (does not seem to work if your machine is a Linux machine).
GRADER
No grader.
CURRENT LIST OF STUDENTS
 Adams, Christopher
 Hagen, Pake
 Merwine, Brice
 Pensoneault, Andrew
 Shen, Yanqing
 Singh, Himanshu
 Tiema, Violet
 Zou, Qing
 Park, Jeungeun (auditing)
 Tanner, Gregory (auditing)
Laurent O. Jay
Department of Mathematics
14 MacLean Hall
The University of Iowa
Iowa City, IA 522421419
USA
Tel: (319)3350898
Email: laurentjay@uiowa.edu