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286finalexamchecklist - 286-E1 Spring 2010 Final Exam...

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286-E1, Spring 2010 Final Exam Checklist 1 1 First Order ODEs Direction fields and solution curves, existence and uniqueness of solutions to first order ODEs (1.3) Methods for solving first order ODEs - separable, linear, exact, and substitution tricks (1.4, 1.5, 1.6) Equilibria, phase and bifurcation diagrams for autonomous equations (2.2) Euler’s approximation method (2.4) 2 Higher Order ODEs Existence and uniqueness of solutions, form of solutions... y = y c + y p (3.2) Solving homogeneous equations with constant coefficients - via roots of the characteristic polynomial (3.3) Solving nonhomogeneous equations - guessing a particular solution/undetermined coefficients (3.5) Application of 2nd order ODEs to oscillations - under/overdamped, natural frequencies, resonance (3.4, 3.6) 3 Systems of ODEs Rewriting higher order systems as first order systems - in matrix-vector notation (4.1, 5.1) Solving constant coefficient homogeneous systems - eigenvalues/vectors and fundamental matrix (5.2, 5.4) Solving constant coefficient homogeneous systems - matrix exponentials (5.5)
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