MATH251_SP2011_exam_2_guide

MATH251_SP2011_exam_2_guide - 6. Differential equations...

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MATH 251 SPRING SEMESTER 2011 Exam II study guide Exam Date/Time : Monday, April 4, 6:30 to 7:45 pm Format : 100 points in 12 questions covering sections 3.7 through 9.3. Location : 010 Sparks (sections 1, 3, 12); 121 Sparks (sections 4, 5, 6, 10); 112 Kern (sections 2, 7, 9); 100 Life Sci (sections 8, 11) A table of Laplace transforms (a copy of table 6.2.1 from the textbook) will be provided during the exam. Topics to study 1. Mechanical vibrations: damped and undamped free vibrations, damping classification, natural frequency/period, quasi-frequency/period, undamped forced vibration and resonance 2. Higher order homogeneous linear equations with constant coefficients 3. Definition (by an integral) and properties of the Laplace transform. 4. Solving initial value problems using the Laplace transform method. 5. Step functions, writing a piecewise continuous function in terms of step functions; Laplace transforms of step and piecewise continuous functions.
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Unformatted text preview: 6. Differential equations with piecewise continuous and/or impulsive forcing functions. 7. Writing an n-th order linear equation into an n x n system. 8. The Eigenvalues/vectors method of solving 2 x 2 systems of homogeneous linear equations 9. Phase portrait: type and stability of a critical point. 10. Nonlinear system: finding critical points, type and stability of its critical points Note: The predator-prey equations are not covered on this exam. Comments : Students should understand how damping affects the behavior of a mass-spring system; how to solve differential equations using the Laplace transform; how translations work with the Laplace transform, and to transform piecewise continuous functions; solving systems of linear equations using Eigenvalues and Eigenvectors; the type and stability classifications of critical points (know the 6 types and 3 stabilities); and how to linearize a nonlinear system about one of its critical points....
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