MATH251_SP2010_exam_1_guide

MATH251_SP2010_exam_1_guide - Theorem, structure of the...

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MATH 251 SPRING SEMESTER 2010 Exam I study guide Exam Date/Time : Thursday, February 25, 6:30 to 7:45 pm Format : 100 points in 14 questions (9 x multiple-choice, and 5 x partial- credit / short-answer) Location : 108 Forum (sections 4, 5, 8, 9); 105 Forum (sections 3, 7, 10, 11); 111 Forum (sections 1, 2, 6) Topics to study 1. Classification of differential equations 2. First order linear equations 3. Separable equations 4. Existence and Uniqueness Theorems (of 1st and 2nd order linear equations only) 5. Solution-mixing and air-resistance problems 6. Autonomous equations: equilibrium solutions, stability classification (including semistable equilibrium solutions) 7. Exact equations: verification of; and solving them 8. Second order homogeneous linear equations with constant coefficients 9. Linear independence, Fundamental solutions, Wronskian; Abel’s
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Unformatted text preview: Theorem, structure of the general solution of a second order linear equation 10. Reduction of order 11. Nonhomogeneous equations: method of Undetermined Coefficients 12. Mechanical vibrations: damped and undamped free vibrations, damping classification, natural frequency/period, quasi-frequency/period, undamped forced vibration and resonance 13. Higher order homogeneous linear equations with constant coefficients Comments : Students should know basic integration techniques; partial differentiation and integration; the three types of equilibrium solutions; over-, under-, and critical damping; solving linear homogeneous equations using the characteristic equation; and the general long-term behavior of different types of solutions....
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