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429-2009-Q1key - (0 pts 3 The Laplace transform of a...

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580.429 SBE3 2009 Quiz 1 (10 pts) Name: Section meeting time: Section meeting location: ----------------------------------------------- detach here at your option ------------------------------------------------------------ (0 pts) 1. Do you prefer to hand in HW on paper in class or to upload PDFs using WebCT? (0 pts) 2. Using a computer programming language of your choice, write a program to sum the integers from 0 through 100, leaving out any integer divisible by 7 with no remainder. You can use the back of the page if desired. Pseudocode: sum = 0 for (i = 0; i <= 100; i = i + 1) { if (i % 7 > 0) { sum = sum + i; }
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Unformatted text preview: } (0 pts) 3. The Laplace transform of a function is defined as ! f ( s ) = exp( ! st ) f ( t ) dt " # . What is the Laplace transform of f ( t ) = exp( ! at ) ? ! f ( s ) = 1 / ( s + a ) (0 pts). 4. Suppose that ! f ( s ) = 1 / ( s + 3) and ! g ( s ) = exp( ! s ) . What is the Laplace transform of C ( t ) = f ( t ! " t ) g ( " t ) d " t t # ? ! C ( s ) = exp( ! s ) / ( s + 3) (0 pts) 5. What is a solution to the ODE dy / dt = ! " y with y = 100 at t = ? y ( t ) = 100 exp( ! t ) (0 pts) 6. What are the determinant and eigenvalues of the matrix M = 2 1 2 ! " # $ % & ? det( M ) = 4 ! = 2 and 2 (degenerate)...
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