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====== Math 527 Outline of topics for final exam ======

Think of the final exams as 2/3 (exam1 + exam2 + exam3 + systems of equations). That's about right to fit in the allotted two hours. There will be around eight problems chosen from this outline of topics.

  * 1st order equations
    * separable
    * exact
    * 1st order linear
  * 2nd and higher-order equations
    * homogeneous constant coefficient ($y=e^{\lambda t}$ is your friend)
    * judicious guessing
    * variation of parameters
    * power series
  * Laplace transforms
    * definitions, properties, and transforms & inverses of simple functions
    * s-translation, t-translation
    * Heaviside and Dirac delta functions
    * convolution
  * Systems of equations
    * matrices, vectors, $Ax=b$ problems, and determinants
    * the eigenvalue problem, how it arises from the ODE $x' = Ax$ 
    * how to solve systems of ODEs with 
      * real eigenvalues, distinct
      * real eigenvalues, repeated
      * complex eigenvalues (solutions expressed in both complex and real-valued forms)
    * phase portraits

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