MathBio: Midterm 2, Wednesday, April 2

Our second midterm will be Wednesday April 2.  The test will cover topics from Chapters 3 and 4.

More details will be posted soon, but the main theme is:

Qualitative Analysis of two-dimensional systems in both discrete and continuous time.

A non-exhaustive list of topics includes:

  • Biological Modeling concepts
    • Age-structured models (e.g., Juvenile-Adult)
    • Epidemic models (SIS, SIR, SIRS)
    • Multi-species models (Predator-Prey, Niche Competition, Host-Parasitoid)
  • Linear Algebra concepts
    • Writing dynamical systems as Matrix-Vector equations
    • Eigenvalues and Eigenvectors
  • Analysis of linear 2d discrete-time systems
    • The Jury Conditions for Stability
    • Computing Stable Age Structures
  • Analysis of nonlinear 2d discrete time systems
    • Finding equilibria
    • Computing the Jacobian and evaluating at the equilibria to determine stability
  • Analysis of linear continuous-time systems
    • The Trace-Determinant Plane
    • The three forms of general solutions when the eigenvales are 1) real and distinct; 2) real and repeated; 3) complex.
  • Analysis of nonlinear continuous-time systems
    • Finding equilibria
    • Using nullclines to sketch flow in the phase portrait
    • Computing the Jacobian and evaluating at the equilibria to classify type

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s