====== 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
