General Information
Scheduled Lectures
TuTh 2:25–4:15
(x-hour) F 4:35–5:25 (used occasionally for catchup)
Kemeny 006
Instructor
Professor Dimitris Giannakis
Office: 337 Kemeny Hall
Office Hours: Wednesday 4:00–5:00 (email for confirmation)
Prerequisites
MATH 22 and MATH 23, or instructor approval.
List of topics
- One- and two-dimensional maps.
- Linearization, stable and unstable manifolds.
- Attractors, chaotic behavior of maps.
- Linear and nonlinear continuous-time systems.
- Limit sets, periodic orbits.
- Chaos in differential equations, Lyapunov exponents.
Textbooks
Required:
- Alligood, Sauer, Yorke. Chaos: An Introduction to Dynamical Systems. Springer.
Recommended:
- Strogatz. Nonlinear Dynamics and Chaos. CRC Press.
- Hirsch, Smale, Devaney. Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press.
Teaching Methods
The course will follow the standard lecture-style teaching, complemented with computer simulations and visualizations. We will discuss a variety of models from physics, biology, chemistry, and engineering, but no prior background in these application areas is required. Students are expected to attend and participate in the course lectures, study lecture notes and textbook material, and complete homework assignments. Lectures will be held in person. Office hours and X hour will be held either in person or via Zoom.
Learning objectives
The primary learning objectives for the course are as follows.
- Master mathematical techniques, including methods based on ODE and linear algebra, to solve problems in dynamical systems.
- Identify applications in physics, biology, chemistry, engineering, and other fields where dynamical systems are useful.
- Analyze unfamiliar problems and craft solutions.
- Develop skills to write detailed solutions using appropriate mathematical language.
Assessment and grading
Grading will based on the following components:
- Weekly homework assignments (30\%).
- Midterm (30\%).
- Final (40\%).
Homework
The goal of the homework assignments is to reinforce concepts and skills, while challenging students to extend what they have learned to other types of problems. The homework assignments will include problems to measure quantitative (calculation-style) and qualitative (proof-style) understanding of the material. Because it is important for students to have this experience, instructors will not solve assigned homework problems during office hours before the due date. We will of course answer questions you may have in approaching problems that give you difficulty. Homework assignments will be nominally issued every Thursday and will be due on Thursday of the following week. We will use Gradescope for homework submission and grading. Please submit assignments as a \emph{single PDF}. Each weekly assignment will carry the same number of total points. The lowest assignment score will be dropped. If students are unable to return assignments for reasons such as religious observance, medical issues, etc., they should notify the instructor in advance or as soon as reasonably possible. Otherwise, assignments which are not turned in on time will receive no marks.
Exams
The midterm will be tentatively held on Thursday, April 28. The final exam will be cumulative, and will be conducted at a time and location determined by the Registrar during the finals period (Friday June 3 to Tuesday June 7). Neither the midterm nor the final examination will be given early, unless there are extenuating circumstances.
Academic integrity
We will strictly enforce Dartmouth's Academic Honor Principle. Violations of the Academic Honor Principle will be referred to the the Committee on Standards. In particular, please be aware of rules regarding plagiarism and collusion.
- On exams: Giving and/or receiving assistance during an examination violates the Academic Honor Principle.
- On homework: Collaboration is both permitted and encouraged, but it is a violation of the honor code for someone to provide the answers for you.
Failure to review and understand the Academic Honor Principle will not be considered a mitigating excuse if a violation occurs.
COVID policies
Students are expected to attend class in person unless they have made alternative arrangements due to illness, medical reasons, or the need to isolate due to COVID-19. For the health and safety of our class community, please: do not attend class when you are sick, nor when you have been instructed by Student Health Services to stay home.
In accordance with current College policy, all members of the Dartmouth community are required to wear a suitable face covering when indoors, regardless of vaccination status. This includes classrooms and other course-related locations, such as labs, studios, and office hours.
Disabilities
Students with learning, physical, or psychiatric disabilities enrolled in this course who may need disability-related academic adjustments and services should consult the Student Accessibility Services (SAS) office in Carson Hall 125. Students are also encouraged to make an office appointment to see the instructor before the end of the second week of the term. All discussions will remain confidential, although the SAS office may be consulted to discuss appropriate implementation of any accommodation requested. At such a meeting please provide your instructor with a copy of a disability registration form, which lists the accommodations recommended for the student by SAS within the Academic Skills Center.Religious observances and athletic participation
Students may wish to take part in religious observances and athletic activities that occur during the term. If you have such an event that conflicts with your participation in the course, please meet with the instructor before the end of the second week of the term to discuss appropriate accommodations.