mid1 - Sample problems for exam #1 in Math 421(1) The exam...

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Unformatted text preview: Sample problems for exam #1 in Math 421(1) The exam will cover Laplace transform and Sections 5.4, 5.5, 6.1. On the exam, you will be expected to show all the steps. A bare asnwer is not sufficient. The exam will be shorter than this set of problems! Some of the solutions for problems 1–7 and 12–16 can be found at http://www.math.rutgers.edu/ ∼ greenfie/mill courses/math421/rev1 ans.html These problems are the same as in Section 2 of the course taught by Prof. Greenfield. The rest of the porblems are different. The answers will be posted. 1. Find the inverse Laplace transform of se- s s 2- 1- s 2 ( s + 2) 2 2. Compute the convolution f ( t ) = ( H ( t ) t 2 ) * ( H ( t ) cos( t )) and its Laplace transform. 3. Use the Laplace transform to solve the initial value problem y 00 +2 y- 3 y = H ( t- 2)( t- 1) with y (0) = 1 and y (0) =- 1. 4. Consider the function f ( t ) = ( < t < 1 t 1 < t < 3 1 3 < t a) Sketch f ( t )....
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This note was uploaded on 01/12/2010 for the course MATH 421 taught by Professor Nataliakomarova during the Winter '07 term at San Jose State University .

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mid1 - Sample problems for exam #1 in Math 421(1) The exam...

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