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Unformatted text preview: Name: Student ID: Section: Instructor: Steven McKay Math 334 (Ordinary Differential Equations) Exam 3 June 13,14 2006 Instructions: • For questions which require a written answer, show all your work. Full credit will be given only if the necessary work is shown justifying your answer. • Simplify your answers. • Calculators are not allowed. • Should you have need for more space than is allocated to answer a question, use the back of the page the problem is on and indicate this fact. • Please do not talk about the test with other students until after the last day to take the exam. For Instructor use only. # Possible Earned MC 24 9 12 10a 4 10b 4 11 12 12 12 13 12 14 12 15a 4 15b 4 Total 100 Elementary Laplace Transforms f ( t ) = L 1 { F ( s ) } F ( s ) = L{ f ( t ) } 1. 1 1 s , s > 2. e at 1 s a , s > a 3. t n , n = positive integer n ! s n +1 , s > 4. sin at a s 2 + a 2 , s > 5. cos at s s 2 + a 2 , s > 6. sinh at a s 2 a 2 , s >  a  7. cosh at s s 2 a 2 , s >  a  8. e at sin bt b ( s a ) 2 + b 2 , s > a 9. e at cos bt s a ( s a ) 2 + b 2 , s > a 10. t n e at , n = positive integer n ! ( s a ) n +1 , s > a 11. u c ( t ) e cs s , s > 12. u c ( t ) f ( t c ) e cs F ( s ) 13. e ct f ( t ) F ( s c ) 14....
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 Fall '08
 DALLON
 Differential Equations, Equations, ORDINARY DIFFERENTIAL EQUATIONS, Technological singularity, Frobenius method

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