MATH 243
Dynamical Systems I

Instructor: Roberto De Leo.     Term: Fall 2024.

Stephen Smale
Henri Poincaré
When & Where: M-W 9:40am-11am, ASB-B room 201 (lounge)

Office: Annex 3, Room 226

Office Hours: will fix soon, in the meantime email me anytime and we will arrange for a zoom meeting time.

HU Email: roberto DOT deleo AT howard DOT edu

Preferred Email: roberto AT deleo DOT info

Canvas address: https://canvas.howard.edu/courses/49779/

Textbooks

Other Suggested Sources

Outline

This class is an elementary introduction to Dynamical Systems.

Topics to be covered (in bold the topics we already covered)

  1. Discrete Dynamical Systems
  2. Chaos in Discrete Dynamical Systems
  3. Fractals
  4. Chaotic Attractors
  5. Continuous Dynamical Systems
  6. Periodic orbits and limit sets
  7. Chaos in Continuous Dynamical Systems
  8. Stable Manifolds and Crises
  9. Bifurcations
  10. Cascades

Grades policy

Grades will be evaluated on the following bases:
  1. Homework: 40%;
  2. Midterms: 2x15%;
  3. Project: 30%.
Based on the total, you will get the following letter: A (90-100%), B (80-89%), C (70-79%), D (60-69%), F (0-59%).

Collaboration

Especially with online classes, teamwork is very important and will give you the occasion to interact with your classmates. You are encouraged in general to work with study partners and also to collaborate on homework. On the other side, you must write your solutions yourself, in your own words, and you must list all collaborators and outside sources of information.
It is a serious violation of academic integrity to copy an answer without attribution.

Academic Code of Student Conduct

(please see Howard University handbook) No copying, unauthorized use of calculators, books, or other materials, or changing of answers or other academic dishonesty will be tolerated. Cheating will not be tolerated. Anyone caught cheating will receive an F for the course and may be expelled from the university.

Grievance Procedure

If you have any problems with the policies or rules of this course, discuss your concerns with your instructor. If you are still unable to come to a satisfactory arrangement, you may contact the Director of Undergraduate Studies, Dr. Jill McGowan, and, if still unsatisfied, the Chair of the Department, Dr. Bourama Toni.

Americans with Disabilities Act

Howard University is committed to providing an educational environment that is accessible to all students. In accordance with this policy, students in need of accommodations due to a disability should contact the Office of the Dean for Special Student Services (202-238-2420, bwilliams@howard.edu) for verification and determination of reasonable accommodations as soon as possible after admission and at the beginning of each semester as needed.

Statement on Sex and Gender-Based Discrimination, Harassment and Violence

Howard's Policy Prohibiting Sex and Gender-Based Discrimination, Sexual Misconduct and Retaliation (aka, the Title IX Policy) prohibits discrimination, harassment, and violence based on sex, gender, gender expression, gender identity, sexual orientation, pregnancy, or marital status. With the exception of certain employees designated as confidential, note that all Howard University employees University - including all faculty members - are required to report any information they receive regarding known or suspected prohibited conduct under the Title IX Policy to the Title IX Office (TitleIX@howard.edu or 202-806-2550), regardless of how they learn of it. For confidential support and assistance, you may contact the Interpersonal Violence Prevention Program (202-836-1401) or the University Counseling Service (202-806-7540). To learn more about your rights, resources, and options for reporting and/or seeking confidential support services (including additional confidential resources, both on and off campus), visit titleix.howard.edu.