Math 5260 Dynamical Systems
Fall 2019 Syllabus



Course Description

Dynamical Systems is currently one of the most active and rapidly growing areas of mathematics. Dynamical systems is the study of systems that evolve over time. They are broadly classified as either continuous time (differential equations) or discrete time (iteration of maps). This course covers both continuous and discrete dynamical systems. We focus on nonlinear dynamical systems. Because nonlinear systems are typically too complicated to allow analytic (formula) solutions, we concentrate on qualitative descriptions of solutions. For example, we study the long-term behaviors of solutions. There is a surprising amount of complexity present in the ``orbits'' of relatively simple differential equations and maps. Our goal will be to understand some of these ``simple'' systems, and in the process, understand what is meant by mathematical chaos.

The material is mostly covered in Chapters 1-10, 15-17 of Devaney and Chapters 1-9 of the Strogatz text. Not all sections of all chapters will be covered. Some supplemental material, not included in the text, will occasionally be presented in lecture.

Course Prerequisites

Differential Equations with Linear Algebra (Math 3280) or equivalent or permission of the instructor.

Grading (Topics are subject to change)

Test 1 Mon. Oct. 7 5-6:30 Devaney Ch's 1-10 16%
Test 2 Mon. Nov. 18 5-6:30 Selected topics from Strogatz Ch's 1-9 and Devaney Ch15-17 19%
HW/Quizzes/Labs Weekly ... 45%
Final HW Set Due Wed. Dec 11 at 3pm Cumulative 20%
Total 100%

General policy statement

Lectures, material in the text, homework sets, labs, and tests are all intended to complement each other. No one is a replacement for any of the others. You are, in general, expected to learn material which is covered via any of these sources.

Homework Sets and Ground Rules

Homework/labs will be turned in roughly every week or two. All work should be neatly written, well-organized, and complete.

For regular homework sets, you are encouraged to exchange ideas with each other, but each person should write up his/her solutions completely in his/her own words. It is never appropriate to give a written version of a problem/proof to another classmate, except to have the classmate read and evaluate your work with you present. It is OK to verbally explain your ideas to another classmate, as long as the classmate then writes up his/her work on his/her own. One person copying a classmate's solution(s) is expressly forbidden and will result in both students receiving zeroes for that complete homework set and facing academic disciplinary action. Copying from textbooks or online resources is also expressly forbidden and will result in zero for that assignment. ANY WORK YOU HAND IN SHOULD CLEARLY STATE ANY WORK THAT WAS NOT COMPLETELY YOUR OWN: PEOPLE WHO CONTRIBUTED TO THE WORK, WEBSITES, SOLUTIONS MANUALS, TEXTBOOKS, AND ANY OTHER REFERENCES THAT WERE USED SHOULD BE LISTED. THE SPECIFIC PROBLEM(S) FOR WHICH OUTSIDE REFERENCES WERE USED SHOULD ALSO BE STATED CLEARLY. You need not explicitly reference material taken from either textbook. See the links for Academic Integrity and the Student Conduct Code below.

It is often instructive to read the problems at the end of each section and think about how you would solve them, even if you don't actually attempt to solve them.

Late homework will be accepted, but unless you make specific prior arrangements with me, points will be taken off. GRACE DAYS: all students will be allowed 5 grace days for the course. No point will be deducted for these grace days. Grace days can be distributed between any number of assignments, from all 5 days for a single course, to one grace day for 5 different assignments. After grace days have been used, points will be deducted for late work. Deduction schedule: 10% off per day late. Weekends count as one day. (For example, one week late will be 50% off.) Work more than one week late will count 50%.

Assignments will be posted on the course homepage at http://www.d.umn.edu/~bpeckham/5260/F2019/Math5260F2019.html

Computer Lab Policy

Labs will be assigned as part of homework sets. Some time to do labs will be provided during regularly scheduled times. Other time must be arranged on your own. You are encouraged to any formal labs in the course with a lab partner. When you do, you may turn in one lab writeup for the pair. It is expected, however, that both partners participate in all parts of the lab. For example, it is unacceptable for one person to do the computer part of a lab and another to do the writeup. In particular, both partners should have proofread the final version before handing the lab in. You should not have the same lab partner for more than two labs.

Computational expectations. Most labs for discrete dynamical systems will be performed with spreadsheets or software from the Boston University Dynamics Website (requires JAVA) or other sites. Labs for continuous dynamical systems (differential equations) will use either software linked to the course homepage, or Mathematica. No computer programming will be required, but writing your own programs to do your own investigations, or to duplicate tasks performed by the course software, is encouraged. Use of the ``Manipulate'' command in Mathematica could be especially productive!

Missed Exams or Quizzes

Missed quizzes or exams will be assigned a zero score unless you provide a valid written, signed (by a Doctor, for example) excuse for your absence; unless it is not possible to do so, you must provide verbal notice ahead of time to your instructor for an absence. Arrangements for a makeup should be made as soon as you know you will miss. Do not wait for the next class. You can leave the instructor a message 24 hours a day by phone or email. Oversleeping, poor preparation, slight colds, and cold weather are not valid excuses.

Student Learning Outcomes

By the end of the course, students should be able to

Broader Course Goals

More broadly, students should develop problem-solving and investigation strategies, and they should develop expertise in numerical techniques, analytical techniques, and scientific vizualization, and be able to apply these to problems outside of dynamical systems.

General UMD Policies

See the following link for a description of UMD policies: Policies. In particular, see the following links:
Learning Disabilities.
Instructor and Student Responsibilities.
Student Conduct Code.
Academic Integrity.

Other References



This page is maintained by Bruce Peckham (bpeckham@d.umn.edu) and was last modified on Wednesday, 25-Sep-2019 13:37:01 CDT.