The Laplace transform

Defined as an improper integral, with linearity, existence for functions of exponential order, table entries for exponentials and sines, and the inverse.

Notes on Diffy Qs: Differential Equations for Engineers, The Laplace transform

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4 exercises

Exercise 101

Find the Laplace transform of $4{(t+1)}^2$ .

2.5

Exercise 102

Find the inverse Laplace transform of $\frac{8}{s^3(s+2)}$ .

2.5

Exercise 103

Find the Laplace transform of $te^{-t}$ . Hint: Shifting property.

2.5

Exercise 104

Find the Laplace transform of $\sin(t)e^{-t}$ . Hint: Integrate by parts.

2.5