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Unformatted text preview: 286-E1, Spring 2010Final Exam Checklist11First Order ODEsDirection 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)Eulers approximation method (2.4)2Higher Order ODEsExistence and uniqueness of solutions, form of solutions...y=yc+yp(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)3Systems of ODEsRewriting 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 - eigenvalues/vectors and fundamental matrix (5....
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This note was uploaded on 10/05/2010 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08