User Tools

Site Tools


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
gibson/teaching/spring-2015/math527/finaloutline.txt · Last modified: 2015/05/07 09:38 by gibson