1b-2009-exam_3_review - Second-Order Dierential Equations-...

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Math 1B — Exam #3 Review Sheet Fall Program for Freshmen 2009 Fred Bourgoin The exam will cover chapters 9 and 17. You are responsible for all of the material presented in lecture and/or included in homework assignments #10–14. First-Order Differential Equations - Understand what direction fields are. I will not ask you to draw one. - Use Euler’s method to approximation the value of a solution at a point. - Solve separable equations. - Find orthogonal trajectories. - Solve mixing problems. - Know the natural-growth and logistic models for population growth. - Solve any population growth problems modeled by a separable equation. - Solve linear equations using the integrating factor. - There will be no predator-prey problem on the exam. Suggested review exercises: #1, 2b, 3–21 on pp. 615-6
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Unformatted text preview: Second-Order Dierential Equations- Solve homogeneous second-order linear dierential equations with constant coe-cients.- Solve nonhomogeneous such equations using both methods (undetermined coecients and variation of parameters).- Solve simple harmonic motion problems. (Memorize the dierential equation.) Be able to nd the spring constant.- Solve damped-vibrations problems. (Memorize the dierential equation.) Know the three cases: overdamping, underdamping, and critical damping.- Solve a rst-order linear dierential equation using power series. Be able to nd the recurrence relation and write the solution in terms of c only. Suggested review exercises: #114, 18 on p. 1138...
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