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# HW1 - ECE 302 Homework#1 Due 1/21 http/www.ece.purdue.edu...

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Unformatted text preview: ECE 302, Homework #1, Due 1/21 http://www.ece.purdue.edu/ ∼ chihw/ECE302 09S.html Review of Calculus: Question 1: Compute the values of the following integrals, given the condition that λ > 0. Z ∞ 1 1 x 2 dx Z ∞ λe- λx dx Question 2: Compute the expressions of the following indefinite integrals. Z ye- y 2 2 x 2 dy Z Z xe yz dzdx Question 3: Compute the values of the following integrals. Hint: It can be solved by inspection. Z 10- 10 ye- 2 | y | dy Z 20- 20 x 3 e- x 2 10 dx Question 4: Compute the values of the following integrals. Hint: Use the integration by part formula. Z ∞ z . 5 e- . 5 z dz Z ∞ z 2 . 5 e- . 5 z dz Question 5: Compute the bilateral Laplace transform of the following functions. f ( x ) = ( . 5 e- . 5 x if x ≥ otherwise g ( x ) = ( 1 / 3 if x ∈ [0 , 3] otherwise Hint: The bilateral Laplace transform of any function f ( x ) is defined as L f ( s ) = Z ∞-∞ e- sx f ( x ) dx....
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HW1 - ECE 302 Homework#1 Due 1/21 http/www.ece.purdue.edu...

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