Question

reasonable chance of getting good scores on the exams. References: Lectures 8.1 and 8.2. Sections 9.1, 9.2, and 9.3 in the textbook. You can make free use of the table of Laplace Transforms on Page 500 but you must justify any other formulas for Laplace transforms. When we speak of "the" inverse Laplace transform of a function F(s) we mean the unique continuous function / : [0,00) → R (if there is one!) whose Laplace transforn is F(s) (for sufficiently large s). (1) Assume n is a positive integer throughout this problem. (a) Find "the" inverse Laplace transform of s-n. (Hint: It is basically right there on the table on Page 500.) (b) Use the result of the previous part, the convolution property of the Laplace transform, and the uniqueness of (continuous) inverse Laplace transforms to describe the n-fold convolution product 1'n of the constant function 1 with itself. (c) Verify your formula for 1*m directly from the definition of the convolution product by using induction on n and a calculation like: ert (I")(T) 1dr

Answer 1

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