MAP 2302 Midterm: MAP 2302 FIU de Test 3 a
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Show me the all magic on the page. ________________________________________________________________: (10 pts. ) definition of the laplace transform of f, integral? (a) suppose that f(t) is defined for t > 0. Use correct notation when presenting your computations and. Remember this: "=" denotes "equals" , " " denotes "implies" , and. 0 f(t)e st dt for all s for which the integral converges. (b) using only the definition, not the table, compute the laplace transform of f(t) Observe that the improper integral converges for every real number s. ________________________________________________________________: (15 pts. ) defined for t 0, what is the definition of the convolution of f with g, (f*g)(t)? (a) if f(t) and g(t) are piecewise continuous functions ( f g )(t) 0 f(x)g(t x) dx (b) using only the definition of the convolution as a definite integral, not some fancy transform shenanigans, compute (f*g)(t) when f(t) = e2t and g(t) = e3t. ( f g )(t)
