MATH251_SP2010_exam_2_guide

MATH251_SP2010_exam_2_guide - n-th order linear equation...

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MATH 251 SPRING SEMESTER 2010 Exam II study guide Exam Date/Time : Wednesday, April 7, 6:30 to 7:45 pm Format : 100 points in 10 questions covering chapters 6, 7, and 9. Location : 105 Forum (sections 4, 5, 8, 9); 112 Kern (sections 1, 2, 6); 010 Sparks (sections 3, 7, 11); 119 Osmond (section 10) 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. Definition (by an integral) and properties of the Laplace transform. 2. Solving initial value problems using the Laplace transform method. 3. Step functions, writing a piecewise continuous function in terms of step functions; Laplace transforms of step and piecewise continuous functions. 4. Differential equations with piecewise continuous and/or impulsive forcing functions. 5. Writing an
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Unformatted text preview: n-th order linear equation into an n x n system. 6. The Eigenvalues/vectors method of solving 2 x 2 systems of homogeneous linear equations 7. Phase portrait: type and stability of a critical point. 8. 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 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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