Minimum+Things+to+Know+for+the+Exam

Minimum+Things+to+Know+for+the+Exam - matrix and the state...

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125:305 Numerical Modeling in Biomedical Systems Fall, 2010 Dr. Shoane Minimum Things to Know for the Exam 1) Know how to find the damping ratio and undamped natural frequency given a 2 nd -order differential equation. 2) Know the exact form of the equations for the 2 nd -order step response for the underdamped, critically-damped, and overdamped conditions. 3) Know how to use Cramer’s rule to obtain the solution of a matrix equation of the form Ax=B, where B is the forcing vector. 4) Know how to draw the standard form simulation diagram given a higher- order differential equation; and how to make adjustments if the output must be put in the state equation form, y=Cx+Du. 5) Know how to use the Cayley-Hamilton technique to find the state transition
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Unformatted text preview: matrix and the state equation output y. 6) Know how to obtain the resolvent matrix of a set of state equations. 7) Remember the rules given in the Sakai Lecture Notes entitled Summary of Laplace Transform Properties Useful for This Course. Know how to apply these for the forward as well as inverse Laplace transform. 8) Know how to derive the numerical equations for x A (n+1) for Explicit, Implicit, and Trapezoidal Integration. 9) Know how to explain the different steps in the Runge-Kutta integration algorithm given the programming code for this technique. 10) Know how to obtain the Newton-Raphson numerical equation for solving for the root of a given function. 1...
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