MATH251_FA2010_exam_1_guide - 7 Exact equations...

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MATH 251 FALL SEMESTER 2010 Exam I study guide Exam Date/Time : Monday, September 27, 8:15 to 9:30 pm Format : 100 points in 14 questions (9 x multiple-choice, and 5 x partial- credit / short-answer) Location : 121 Sparks (sections 1, 2, 7, 10); 102 Forum (sections 3, 4, 5, 9); 108 Forum (sections 6, 8, 11, 12) 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 compound interest problems 6. Autonomous equations: equilibrium solutions, stability classification (including semistable equilibrium solutions)
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Unformatted text preview: 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 Theorem, structure of the general solution of a second order linear equation, and the superposition principle 10. Reduction of order 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 solutions....
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