• Instructor: Rafail Abramov
• Office: 1223 SEO
• Office Hours: MWF 11 am at Math Learning Center, or make an appointment.
• Phone: (312) 413 7945
• E-mail: abramov@uic.edu

Textbook: "Ordinary Differential Equations and Dynamical Systems" by G. Teschl, available online for free

Exams

• First midterm exam: Wednesday October 3, 2018, in class.
• Second midterm exam: Friday November 9, 2018, in class.
• Final exam: TBA.

Tentative syllabus:

• Introduction (Chapter 1). Classification of differential equations. First-order autonomous equations, conditions for existence of solutions, non-uniqueness. Qualitative analysis of first-order equations.
• Basic theorems (Chapter 2). Contraction mapping, Picard iterations, existence and uniqueness. Gronwall's inequality, dependence on initial conditions. Regular perturbation theory. Extensibility of solutions. Peano existence theorem.
• Linear equations (Chapter 3). Matrix exponential, Jordan normal form. Linear autonomous systems, Duhamel's formula. General time-dependent and periodic linear systems, Floquet theory.
• Dynamical systems (Chapter 6). Flows, orbits, invariant sets. Poincare maps, stability of fixed points.
• Planar dynamical systems (Chapter 7). Examples. Poincare-Bendixson theorem.
• Higher-dimensional systems (Chapter 8). Attracting sets. Hamiltonian systems, complete integrability.
• Local behavior near fixed points (Chapter 9). Stable and unstable manifolds.

Homework:

• Homework #1: Problems 1.8, 1.11, 1.13, 1.27, 1.33. Due Friday September 14.
• Homework #2: Problems 2.6 (i,ii), 2.8, 2.10. Due Wednesday October 3.
• Homework #3: Problems 3.16, 3.30, 3.43. Due Friday October 26.
• Homework #4: Problems 6.5, 6.9, 6.19. Due Friday November 9.

Final score: 20% homework, 20% first midterm, 20% second midterm, 40% final exam.

Tentative final grade cut-offs: ≥85% - A, ≥70% - B, ≥55% - C, ≥40% - D, <40% - F.

Academic dishonesty: Those caught cheating will receive the grade of "F". I will also file a complaint with the Dean of Students.

I will be continuously updating this webpage as the course progresses. Please watch this webpage, although I will try to announce any further changes by e-mail.