The University of Iowa
The College of Liberal Arts and Sciences
FALL 2024
NONLINEAR DYNAMICS WITH NUMERICAL METHODS: MATH:5600, Section 0001
Course meeting time and place: 1:302:20PM MWF, 221 MLH
Department of Mathematics
Course ICON site: To access the course site, log into
Iowa Courses Online (ICON)
using your Hawk ID and password.
Course Home:
The College of Liberal Arts and Sciences (CLAS) is the home of this course,
and CLAS governs the policies and procedures for its courses.
Graduate students, however, must adhere to the academic deadlines set
by the Graduate College.
Instructor:
 Laurent O. Jay
 Office location: 225L MLH
 Student dropin hours: 11:30AM12:30PM MWF.
I am also available by appointment if you are unable to attend my dropin hours.
 Phone: (319) 3350898
 Email: laurentjay@uiowa.edu
 DEO: Prof. Ryan Kinser, 14 MLH, Email: ryankinser@uiowa.edu
Prerequisites (for undergraduate students):
 MATH:3600 Introduction to Ordinary Differential Equations
 MATH:3770 Fundamental Properties Spaces/Funct I or
MATH:4210 Foundations of Analysis
 Some computer programming experience, preferably MATLAB, will be helpful.
Other possible programming languages are Maple, Mathematica, or Scilab.
Description of course:
Topics to be covered:
 Linear and nonlinear differential equations
 Initial value problems
 Existence, uniqueness, and maximality of solutions
 Trajectories, phase space
 Differentiability of solutions
 Derivatives with respect to initial conditions
 Lyapunov stability
 Lyapunov functions
 Gradient systems
 The flow
 Invariant sets
 Fixed points
 Periodic orbits
 Poincare maps, Floquet theory
 Limit sets and limit cycles
 Variational calculus
 Hamiltonian systems
 Local bifurcations
 The Lorenz equations
 Chaos, strange attractors, Lyapunov exponents
 Taylor series methods
 RungeKutta methods
 Butcher trees
 Local and global error estimates
 Numerical linear stability
This course plan may be modified during the semester. Such modifications
will be announced in advance during class periods and on
ICON;
the student is responsible for keeping abreast of such changes.
Learning Objectives:
This course is at a graduate level and it is assumed that
you can work along the course in an independent fashion.
This course will cover linear and nonlinear ordinary
differential equations (ODEs), numerical methods for ODEs,
and some applications. We will prove some but not all theorems
and results (some of the proofs are discussed in MATH:6600/MATH:6610).
At the end of the course the student should master essential
issues in differential equations.
Class procedures:
The majority of each class period will be lecture oriented.
I will generally hand out my own class notes on the material
covered in class. Readings may be assigned.
Standard outofclass preparation is at least six hours per week.
Textbooks:

Stability, instability and chaos by
Paul Glendinning, Cambridge University Press,
Cambridge texts in applied mathematics 11,
1994, 402 pages, ISBN13: 9780521425667, reprinted 1999.
The
textbook on amazon.com.

Dynamical Systems with Applications using Matlab by
Stephen Lynch,
ISBN13: 99783319330419, 529 pages,
Publisher: Springer; Softcover reprint of the original 2nd ed. 2014 edition (September 3, 2016).
The
textbook on amazon.com.

Dynamical Systems with Applications using Mathematica by
Stephen Lynch,
ISBN13: 9783319870892, 601 pages,
Publisher: Springer; Softcover reprint of the original 2nd ed. 2017 edition (August 14, 2018).
The
textbook on amazon.com.
We will neither follow closely, nor cover entirely the whole textbooks.
They are only intended to be a reference and a complement giving a
different view of the material.
Aside from the textbooks, class notes will be handed out based on the lectures.
Additional useful readings:

Differential Dynamical Systems by
James D. Meiss.
2017, Revised Edition,
410 pages,
Publisher: Society for Industrial and Applied Mathematics (SIAM),
Series: Mathematical Modeling and Computation,
ISBN10: 1611974631,
ISBN13: 9781611974638,
list price: $87.00 (Softcover).
Table of contents.
Preface;
Index.
Library reference (1st edition): Engineering Library QA614.8 .M45 2007.
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),
ISBN10: 1493963872,
ISBN13: 9781493963874,
list price: $69.99 (Hardcover).
Electronic version.
The
textbook on amazon.com.

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.
 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.

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

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.

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.

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.

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.

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.
Academic Honesty and Misconduct:
All students in CLAS courses are expected to abide by the
CLAS Code of Academic Honesty.
Undergraduate academic misconduct must be reported by instructors to CLAS according to
these procedures.
Graduate academic misconduct must be reported to the Graduate College
according to Section F of the
Graduate College Manual.
Student Collaboration on homework:
The homework for this course is designed to help you master your knowledge
related to the topics covered during lecture. As such, you may discuss on the
homework problems with others or use online resources. However, please be
aware that to master the skills needed for this class, practice is
required and that to do well on the examinations you will need to work many
of these problems multiple times without help. Be sure to test your
knowledge by doing much of the homework on your own.
Students are allowed to partially collaborate with others on homework
through discussion for the most difficult problems. However, each student must turn
in their own homework and it must not be a copy of someone else homework.
Students are responsible for understanding this policy; if you have questions,
ask for clarification. Word per word copies will not be tolerated. In extreme cases
students may be requested to stop any kind of collaboration with other students.
Student Complaints:
Students with a complaint about a grade or a related matter should first discuss the situation with the instructor and/or the course supervisor (if applicable), and finally with the Director or Chair of the school, department, or program offering the course.
Undergraduate students should contact
CLAS Undergraduate Programs
for support when the matter is not resolved at the previous level. Graduate students should contact the CLAS
Associate Dean for Graduate Education and Outreach and Engagement when additional support is needed.
Drop Deadline for this Course:
You may drop an individual course before the deadline; after this deadline you will need collegiate approval. You can look up the drop deadline for this course here.
When you drop a course, a "W" will appear on your transcript. The mark of "W" is a neutral mark that does not affect your GPA.
Directions for adding or dropping a course and other registration changes can be found on the
Registrar's website. Undergraduate students can find policies on dropping and withdrawing
here.
Graduate students should adhere to the
academic deadlines and policies set by the Graduate College.
Grading System and the Use of +/:
In assigning grades, the plus/minus grading system will be used.
The A+ grade will be used only in extraordinary situations.
Final grades will be awarded based on the following ranges:
A+ 
A 
A 
B+ 
B 
B 
C+ 
C 
C 
D+ 
D 
D 
F 
100 % to 96.15 % 
< 96.15 % to 88.46 % 
< 88.46 % to 80.77 % 
< 80.77 % to 73.08 % 
< 73.08 % to 65.38 % 
< 65.38 % to 57.69 % 
< 57.69 % to 50.0 % 
< 50.0 % to 42.31 % 
< 42.31 % to 34.62 % 
< 34.62 % to 26.92 % 
< 26.92 % to 19.23 % 
< 19.23 % to 11.54 % 
< 11.54 % to 0.0 % 
Course Grades:
The final grade will be based as follows:
 There will be 2 tests during the semester,
with each test to account for 25% of the course grade.
 Midterm Exam 1: Thursday October 17: 6:308:30PM in room 221 MLH.
 Midterm Exam 2: Thursday November 21: 6:308:30PM in room 221 MLH.
 Homework assignments and quizzes will account for 20% of the course grade. Late
homework will be accepted only by special permission of the instructor.
Your worst 2 homework scores will not be counted.
For example if we have 12 homeworks, we will count only your best 10 homework scores
out of 12 homeworks. Only a portion of each homework assignment may be graded, based
on the availability of assistance from a grader for the course.
 The final examination will account for 30% of the course grade and
it will be comprehensive.
The 2 tests and final examination are open books and open notes examinations.
Smartphones/computers are not allowed.
Homework:
Will be assigned approximately weekly.
Presentation of your results is very important.
Scratch paper will not be accepted.
Do not expect good grades if your solution to a problem
is poorly communicated. Like for everything, if you cannot
explain something in great details, you certainly have not
fully understood it. The importance of doing homework cannot
be overemphasized, most of human people learn by doing, not
only by watching and/or listening. Late homework may not be
accepted, you need to request permission first or to provide a
reasonable justification. Late homework is not accepted once
a correction is given. Use of symbolic mathematical software
to solve problems is not allowed.
Linux computer accounts:
Linux computer accounts are available on the Linux network in MLH
(computer lab rooms B5).
To access your Linux computer account remotely.
you can use FastX, a graphical Linux virtual desktop environment
remotely accessible in your web browser.
As long as you have an active Hawk ID and you login at least once in the past year,
your CLAS Linux account will remain active. If you fail to use your account in a year,
you will receive three notices, and then your CLAS Linux account will be deleted.
Also, once your Hawk ID becomes inactive, your CLAS Linux account will be deleted.
Date and Time of the Final Exam:
The final examination date and time will be announced by the Registrar generally by the fifth week of classes and it will be announced on the course ICON site once it is known.
Do not plan your end of the semester travel plans until the final exam schedule is made public. It is your responsibility to know the date, time, and place of the final exam. According to Registrar's final exam policy, students have a maximum of two weeks after the announced final exam schedule to request a change if an exam conflict exists or if a student has more than two exams in one day (see the policy here).
Communication: UI Email:
Students are responsible for all official correspondences sent to their UI email address (uiowa.edu) and must use this address for any communication with instructors or staff in the UI community.
Note on dropin hours:
This is not a private lesson to repeat what was covered in class
for students missing classes without a valid justification.
Helper:
Ying Liu,
office: 325C MLH, mailbox is in 15 MLH (MacLean Hall),
email: yingliu1@uiowa.edu.
College of Liberal Arts and Sciences (CLAS) Course Policies:

Attendance and Absences:
Your responsibilities to this class and to your education as a
wholeinclude attendance and participation, check in particular
the
CLAS policies related to student attendance and absences.
You are also expected to be honest and
honorable in your fulfillment of assignments and in testtaking situations
(the College's policy on plagiarism and cheating is online in the
College's Student Academic Handbook).
You have a responsibility to the rest of the classand to the instructorto help
create a classroom environment where all may learn. At the most basic level,
this means that you will respect the other members of the class and the instructor,
and treat them with the courtesy you hope to receive in turn.
Smart phones, cell phones, and pagers must be on silent mode during lecture and they
are not allowed in class during exams. If you do bring a
phone or pager to an exam, you may leave it in the front of the class during
the exam. If a student is found to have a phone or pager during an
exam, the phone or pager will be taken from the student and procedures
for cheating will be followed.
Students with mandatory religious obligations or UI authorized activities must discuss their absences with me as soon as possible. Religious obligations must be communicated within the first three weeks of classes.

Exam Policies
University Policies