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  1. Hint 3: Use the sifting property of the delta function, which allows you to pull the function e i!t out of the integral while inserting the value of t at which the delta function has non-zero value.

  2. ANSWERS TO PRACTICE PROBLEMS CHAPTER 6 AND 7 I. Laplace Transform 1. (a) Using the double angle trigonometric identity, the function f t can be rewritten as f t = 1 2 sin 4t . Thus L{f t }= 2 s2 16 (b) Using the half angle trigonometric identity, the function f t can be rewritten as f t = 1 2 1 cos 6t . Thus L{f t }= 1

  3. Answer. \ (2t^ {2}-2t+1-e^ {-2t}\) Exercise \ (\PageIndex {6.1.14}\) Find the Laplace transform of \ (te^ {-t}\) (Hint: integrate by parts).

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  5. † Know how to use all of the Laplace transform formulas developed in Section 3.1 to be able to compute the Laplace transform of elementary functions. † Know how to use partial fraction decompositions to be able to compute the inverse Laplace transform of any proper rational function. The key recursion algorithms for computing

  6. MAT 275 CHAPTER 6, 7 PRACTICE PROBLEMS (Material from earlier sections are on previous reviews) Given Laplace Transform Table: 6.3. Step Functions 1. Find the Laplace transform of the following functions. (a) ( ( )= +3 7 ) (b) ( )=2 3 (c) ( )={1, 0≤ <2 2−4 +4, ≥2

  7. 6 Ιουν 2018 · Dirac Delta Function – In this section we introduce the Dirac Delta function and derive the Laplace transform of the Dirac Delta function.

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