The exam is psuedocomprehensive, in particular:

  • The exam is written to be similar in length to the previous examse.
  • Roughly 60% of the exam will be Chapter 9 - Systems of Differential Equations.
  • Roughly 20% of the exam will be over the Phase Plane - Section 5.4
  • Roughly 20% of the exam will be over Second Order Equations - Sections 4.2, 4.3, 4.9.
  • Roughly 10% of the exam will be over Separable Equations - Section 2.2
  • Roughly 10% of the exam falls into multiple categories.
  • The following information will be given.

Expectations.

  • You will be asked to determine eigenvalues and eigenvectors for 2x2 matrices.
  • You will be asked to find general solutions and fundamental matrices for homogeneous 2x2 systems.
  • You will be asked to find a particular solution and/or a general solution to nonhomogeneous 2x2 systems.
    • There is a Variation of Parameters question.
  • You will be asked to find the solutions to initial value problems.
  • Be prepared to sketch and/or identify phase planes.  Additionally, understand nullclines and equilibrium solutions.