ANNOUNCEMENTS

FINAL EXAMINATION

To be held on Tuesday, December 12, 2017, 10:00AM-12:00 PM (noon) in room 214 MLH. The final examination is comprehensive (up to the top of p.81 in the class notes before the subsection on `symplectic transformations in terms of differential 2-forms'). It will be done with open books and open notes, but calculators are NOT allowed.

This course is a natural continuation of MATH:5600 (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.

RECOMMENDED READINGS FROM THE TEXTBOOKS (AND FROM OTHER REFERENCES)

• Sagan: 1.1, 1.2, 1.4, 1.5, 1.6, 1.7, p.40
• Sagan: 2.1, 2.2, 2.3, 2.4, 2.6, 2.9, pp. 100-102, on the first variation
• Sagan: 7.1, 7.2, 7.3, 7.5, 7.6, on the second variation
• Sagan: 2.11, 7.7, 7.8, 7.9, pp. 420-421, on generalizations to n functions
• Wiggins: 13.1-4, on Lagrange's equations
• Sagan: A2.15 on Hamilton's principle
• Sagan: A2.16, on Noether's theorem
• Glendinning: 7.1-7.5: on perturbation theory
• Sagan: 2.12: on Hamiltonian systems

GENERAL INFORMATION

• Syllabus.
• ICON. Homework assignments can be found there.
• Textbook:
  • Introduction to the Calculus of Variations by Hans Sagan, 1969 edition, 449 pages, Paperback, Dover Publications, ISBN-10: 0486673669, ISBN-13: 978-0486673660, list price: $21.95. Library references: Physics Library QA315 .S23 1992 and Mathematical Sciences Library QA315 .S23. The book on amazon.com.

Additional useful readings:

• Calculus of Variations by I. M. Gelfand and S. V. Fomin, October 2000, 240 pages, Paperback, Dover Publications, ISBN-10: 0486414485, ISBN-13: 978-0486414485, list price: $11.95. Library reference: Mathematical Sciences Library QA315 .G417. The book on amazon.com.
• The Calculus of Variations by B. van Brunt, Springer-Verlag, New York, Universitext, 2004, 291 pages, ISBN: 978-0-387-40247-5 (Print), 978-0-387-21697-3 (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, ISBN-13: 978-1611974638, 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: 978-0387001777, 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: 0-387-95116-4. Library reference: Mathematical Sciences Library QA372 .P47 1991.
• Stability, instability and chaos by Paul Glendinning, Cambridge University Press, Cambridge texts in applied mathematics 11, 1994, 388 pages, ISBN: 0-521-42566-2, reprinted 1999.
• 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: 978-0821891353, 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 0-8176-4321-4, 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, ISBN-13: 978-0813349107, 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: 978-3-540-56670-0. Library reference: Mathematical Sciences Library QA372 .H16 1993 v.1.
• Solving ordinary differential equations II. Stiff and differential-algebraic problems by E. Hairer and G. Wanner, Springer, Berlin, Springer Series in Computational Mathematics, vol. 14, Second Revised Edition, 1996, 614 pages, ISBN: 978-3-540-60452-5. Library reference: Mathematical Sciences Library QA372 .H16 1993 v.2.
• Geometric numerical integration: structure-preserving 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: 978-3-540-30663-4. 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, ISBN-10: 0-8218-8328-3, ISBN-13: 978-0-8218-8328-0, 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, ISBN-10: 3540609342, ISBN-13: 978-3540609346, 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, ISBN-13: 978-3540345633, list price: $64.95. The book on amazon.com.
• Principles of Differential Equations by Nelson G. Markley, Wiley-Interscience, Hoboken, N.J., Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts, 2004, 352 pages, Hardcover, ISBN: 0-471-64956-2. 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, ISBN-10: 1441957820, ISBN-13: 978-1441957825, 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), ISBN-13: 978-1493963874, 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, 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.

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
• Lyapunov-stability
• Differential inequalities
• Normal forms
• Unfolding of vector fields
• Invariant (stable, unstable, center) manifolds
• Canonical transformations and generating functions
• KAM (Kolmogorov-Arnold-Moser) theory
• Poisson systems
• Variational/symplectic integrators
• Structural stability and bifurcations
• Averaging
• Homoclinic orbits
• Melnikov's method
• Boundary value problems (Sturm-Liouville 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 pop-up 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

• Gordon Aiello, e-mail: gordon-aiello@uiowa.edu. Office: B20J MLH. Phone: 335-3650.