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====== About the Math 527 Final Exam ====== The final exam takes place Wed 12/16 8:00am-10:0am in Horton 4. You must take the final exam at the scheduled time. No early exams or make-up exams will be offered. The final exam is cumulative, including all topics covered in the course **except power series**. Think of the final exam as 2/3 (exam1 + exam2 + exam3 + systems of ODEs). The outline of topics is as follows * 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 * Laplace transforms * definitions, properties, and transforms & inverses of simple functions * s-translation, t-translation * Heaviside and Dirac delta functions * 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
