MATH251_SP2011_exam_1_guide

MATH251_SP2011_exam_1_guide - 8. Second order homogeneous...

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MATH 251 SPRING SEMESTER 2011 Exam I study guide Exam Date/Time : Thursday, February 17, 6:30 to 7:45 pm Format : 100 points in 14 questions (8 x multiple-choice, and 6 x partial- credit / short-answer) Location : 102 Forum (sections 2, 7, 9); 105 Forum (sections 3, 4, 5, 6); 108 Forum (sections 1, 8, 11, 12); 111 Forum (section 10) Topics to study 1. Classifications 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 problems 6. Autonomous equations: equilibrium solutions, stability classification (including semistable equilibrium solutions) 7. Exact equations: verification of; and solving them
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Unformatted text preview: 8. Second order homogeneous linear equations with constant coefficients 9. Linear independence, Fundamental solutions, Wronskian, Abels Theorem, structure of the general solution of a second order linear equation, and the superposition principle 10. Reduction of order 11. Second order nonhomogeneous linear equations: Method of Undetermined Coefficients Comments : Students should know basic integration techniques; partial differentiation and integration; the three types of equilibrium solutions; solving linear homogeneous equations using the characteristic equation; and the general long-term behavior of different types of functions and solutions....
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