## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 1)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, t^{3} - \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{18}{s^{4}} - e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 2)

Use a table of Laplace transformations to find the following.

$L\left\{2 \, \cos\left(3 \, t\right) - 2 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{2 \, s}{s^{2} + 9} - \frac{2 \, e^{\left(-s\right)}}{s}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 3)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, \cos\left(3 \, t\right) + 2 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, s}{s^{2} + 9} + 2 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 4)

Use a table of Laplace transformations to find the following.

$L\left\{2 \, \sin\left(2 \, t\right) - 3 \, u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{3 \, e^{\left(-3 \, s\right)}}{s} + \frac{4}{s^{2} + 4}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 5)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, \delta\left(t - 2\right) - 3 \, \sin\left(2 \, t\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{6}{s^{2} + 4} - 2 \, e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 6)

Use a table of Laplace transformations to find the following.

$L\left\{4 \, \cos\left(2 \, t\right) - 2 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4 \, s}{s^{2} + 4} - 2 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 7)

Use a table of Laplace transformations to find the following.

$L\left\{4 \, \cos\left(3 \, t\right) + 4 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4 \, s}{s^{2} + 9} + 4 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 8)

Use a table of Laplace transformations to find the following.

$L\left\{4 \, \sin\left(3 \, t\right) + u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{e^{\left(-3 \, s\right)}}{s} + \frac{12}{s^{2} + 9}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 9)

Use a table of Laplace transformations to find the following.

$L\left\{2 \, \sin\left(2 \, t\right) + 2 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{2 \, e^{\left(-s\right)}}{s} + \frac{4}{s^{2} + 4}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 10)

Use a table of Laplace transformations to find the following.

$L\left\{2 \, t^{2} - u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{e^{\left(-3 \, s\right)}}{s} + \frac{4}{s^{3}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 11)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, t^{2} - u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{e^{\left(-s\right)}}{s} - \frac{4}{s^{3}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 12)

Use a table of Laplace transformations to find the following.

$L\left\{-3 \, t^{3} - 4 \, u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, e^{\left(-2 \, s\right)}}{s} - \frac{18}{s^{4}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 13)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, t^{2} - 3 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{8}{s^{3}} - 3 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 14)

Use a table of Laplace transformations to find the following.

$L\left\{-t^{3} + u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{e^{\left(-2 \, s\right)}}{s} - \frac{6}{s^{4}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 15)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, \cos\left(2 \, t\right) - 3 \, \delta\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{3 \, s}{s^{2} + 4} - 3 \, e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 16)

Use a table of Laplace transformations to find the following.

$L\left\{-3 \, t^{3} - 4 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{18}{s^{4}} - 4 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 17)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, t^{3} - 4 \, u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, e^{\left(-2 \, s\right)}}{s} - \frac{12}{s^{4}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 18)

Use a table of Laplace transformations to find the following.

$L\left\{2 \, \cos\left(2 \, t\right) + 2 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{2 \, s}{s^{2} + 4} + 2 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 19)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, \sin\left(2 \, t\right) + 3 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{3 \, e^{\left(-s\right)}}{s} - \frac{8}{s^{2} + 4}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 20)

Use a table of Laplace transformations to find the following.

$L\left\{-3 \, t^{2} + 4 \, u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4 \, e^{\left(-3 \, s\right)}}{s} - \frac{6}{s^{3}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 21)

Use a table of Laplace transformations to find the following.

$L\left\{-\sin\left(2 \, t\right) - 3 \, u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{3 \, e^{\left(-3 \, s\right)}}{s} - \frac{2}{s^{2} + 4}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 22)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, \sin\left(3 \, t\right) - u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{e^{\left(-3 \, s\right)}}{s} - \frac{6}{s^{2} + 9}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 23)

Use a table of Laplace transformations to find the following.

$L\left\{-\sin\left(2 \, t\right) - 2 \, u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{2 \, e^{\left(-3 \, s\right)}}{s} - \frac{2}{s^{2} + 4}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 24)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, t^{2} - 3 \, u\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{3 \, e^{\left(-3 \, s\right)}}{s} - \frac{8}{s^{3}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 25)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, t^{3} + 3 \, u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{3 \, e^{\left(-2 \, s\right)}}{s} - \frac{24}{s^{4}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 26)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, \cos\left(3 \, t\right) - 3 \, u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{3 \, s}{s^{2} + 9} - \frac{3 \, e^{\left(-2 \, s\right)}}{s}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 27)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, t^{3} + 2 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{24}{s^{4}} + 2 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 28)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, \cos\left(3 \, t\right) + 2 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, s}{s^{2} + 9} + 2 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 29)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, t^{3} - u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{e^{\left(-2 \, s\right)}}{s} + \frac{18}{s^{4}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 30)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, \cos\left(2 \, t\right) - 3 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, s}{s^{2} + 4} - 3 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 31)

Use a table of Laplace transformations to find the following.

$L\left\{\delta\left(t - 3\right) - 3 \, \sin\left(2 \, t\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{6}{s^{2} + 4} + e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 32)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, \sin\left(3 \, t\right) + 4 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4 \, e^{\left(-s\right)}}{s} + \frac{9}{s^{2} + 9}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 33)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, \sin\left(3 \, t\right) + 4 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4 \, e^{\left(-s\right)}}{s} - \frac{6}{s^{2} + 9}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 34)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, \delta\left(t - 3\right) + 4 \, \sin\left(3 \, t\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{12}{s^{2} + 9} - 2 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 35)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, \cos\left(3 \, t\right) + 4 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, s}{s^{2} + 9} + 4 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 36)

Use a table of Laplace transformations to find the following.

$L\left\{\delta\left(t - 2\right) + 2 \, \sin\left(2 \, t\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4}{s^{2} + 4} + e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 37)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, t^{3} + 2 \, \delta\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{18}{s^{4}} + 2 \, e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 38)

Use a table of Laplace transformations to find the following.

$L\left\{-t^{3} - 3 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{6}{s^{4}} - 3 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 39)

Use a table of Laplace transformations to find the following.

$L\left\{\cos\left(2 \, t\right) + 2 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{s}{s^{2} + 4} + \frac{2 \, e^{\left(-s\right)}}{s}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 40)

Use a table of Laplace transformations to find the following.

$L\left\{-2 \, t^{3} - \delta\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{12}{s^{4}} - e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 41)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, \cos\left(3 \, t\right) + \delta\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{4 \, s}{s^{2} + 9} + e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 42)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, t^{2} + 3 \, \delta\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{8}{s^{3}} + 3 \, e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 43)

Use a table of Laplace transformations to find the following.

$L\left\{-3 \, \cos\left(3 \, t\right) - 3 \, u\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{3 \, s}{s^{2} + 9} - \frac{3 \, e^{\left(-2 \, s\right)}}{s}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 44)

Use a table of Laplace transformations to find the following.

$L\left\{-\cos\left(2 \, t\right) - \delta\left(t - 2\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{s}{s^{2} + 4} - e^{\left(-2 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 45)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, t^{2} - 3 \, u\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{3 \, e^{\left(-s\right)}}{s} + \frac{6}{s^{3}}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 46)

Use a table of Laplace transformations to find the following.

$L\left\{-4 \, t^{2} - 2 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{8}{s^{3}} - 2 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 47)

Use a table of Laplace transformations to find the following.

$L\left\{2 \, t^{2} - 2 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{4}{s^{3}} - 2 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 48)

Use a table of Laplace transformations to find the following.

$L\left\{-3 \, t^{3} + 4 \, \delta\left(t - 3\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{18}{s^{4}} + 4 \, e^{\left(-3 \, s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 49)

Use a table of Laplace transformations to find the following.

$L\left\{-\cos\left(3 \, t\right) - 2 \, \delta\left(t - 1\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$-\frac{s}{s^{2} + 9} - 2 \, e^{\left(-s\right)}$

## D1 - Laplace transform. Compute the Laplace transform of a function from the definition. (ver. 50)

Use a table of Laplace transformations to find the following.

$L\left\{3 \, \delta\left(t - 2\right) + \sin\left(2 \, t\right)\right\}$

Then verify this result by using the integral definition of a Laplace transform. (You may use a table of integrals.)

$\frac{2}{s^{2} + 4} + 3 \, e^{\left(-2 \, s\right)}$