Test3map2302 page 2 of 4 3 15 pts a if f t and g t

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Page 2 of 4 ______________________________________________________________________ 3. (15 pts.) (a) If f ( t ) and g ( t ) are piecewise continuous functions defined for t 0, what is the definition of the convolution of f with g , ( f * g )( t )?? ( f g )( t ) (b) Using only the definition of the convolution as a definite integral, not some fancy transform shenanigans, compute ( f * g )( t ) when f ( t ) = 3 t 2 and g ( t ) = 4 t . ( f g )( t ) (c) Using the Laplace transform table, compute the Laplace transform of f * g when f ( t ) = t cos( t ) and g ( t ) = exp(2 t ). [Do not attempt to simplify the algebra after computing the transform.] {( f g )( t )}( s ) ______________________________________________________________________ 4. (10 pts.) (a) Suppose that f ( t ) is defined for t > 0. What is the definition of the Laplace transform of f , { f ( t )}, in terms of a definite integral?? { f ( t )}( s ) (b) Using only the definition, not the table, compute the Laplace transform of f ( t ) 0 , if 0 < t < 4 3 , if 4 < t . { f
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TEST3MAP2302 Page 2 of 4 3 15 pts a If f t and g t are...

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