Assessments in this class are designed to be formative, meaning that their purpose is to give you feedback on your learning. Towards that end, you will be expected to correct any mistakes that you make on quizzes or the evening exam. These corrections contribute substantially towards your quiz and evening and exam grades.
In Class Quizzes |
Quiz 3: Thursday, November 5th.
You may bring notes (front and back of a sheet of paper, handwritten) to this quiz.
- For a planar nonlinear dynamical system
- identify the fixed points
- linearize about them
- use trace/determinant to classify their stability
- for saddles, use eigenvalues and eigenvectors to sketch behavior near the fixed points
- place the linear info on a global phase portrait
- identify limit cycles in systems given in polar coordinates, or argue that such cycles do or do not exist
- identify bifurcations of fixed points and of limit cycles in phase portraits or using analytic criteria
- find a Poincare map at the level of 8.7.1, 8.7.2 or 8.7.9, find an associated periodic orbit, P(y) = y, and use a Floquet multiplier to assess its stability.
- Answer short answer questions about bifurcations in 2D, or other 2D phenomena
Quiz 2: Thursday, October 15th.
- For a planar nonlinear dynamical system
- identify the fixed points,
- linearize about them,
- use the trace and determinant of the Jacobian to identify the stability of the fixed points,
- find a conserved quantity or argue that one does not exist,
- if appropriate, use eigenvalues and eigenvectors to sketch behavior near the fixed points,
- place the linear information on a global phase portrait,
- use nullclines or other vector field information to piece together a global picture.
- 6.3.1 to 6.3.6, 6.3.9, 6.3.10, 6.3.14, 6.3.16, 6.4.1-6.4.6, 6.5.1 to 6.5.6, 6.5.9, 6.5.11, 6.5.12, 6.5.13, 6.5.19, 6.5.20, 6.8.1 to 6.8.8
- Answer true/false or short answer questions about planar dynamical systems, including
- information about conservative systems
- facts based on using index theory
- the difference between hyperbolic and nonhyperbolic fixed points
- vocabulary including homoclinic and heteroclinic orbits, stable, unstable, and center manifolds
Quiz 1: Thursday, September 24th.
- Nondimensionalize a dynamical system
(See 3.5.7, 3.5.8, 3.7.3a, 3.7.4b, 3.7.5a, 3.7.8b) - Sketch a bifurcation diagram for the system
(See 2.2.7, 3.4.9, 3.7.4, 3.7.5, 3.7.7, 3.7.8) - Classify any bifurcations that occur
- Discuss the implications of your analysis for the model
All quizzes are followed by a quiz rewrite assignment. Your final grade on the quiz will be the sum of your initial quiz grade and your score on the rewrite (up to 50% of points lost).
Example: An 80% on the initial quiz, with a perfect rewrite, would become a 90% as your quiz score.
Exams |
Exam 2: Final activity during final exam period