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Tutorial 6. Laplace transform and Euler method The Laplace transform F(s) of a function f(t) is defined as: ?{f(t)} = F(s) = ??? f(t)e??? dt Using this definition derive F(s) for each of the following functions: 1. f(t) = t² 2. f(t) = t²e?³? Using tables of Laplace transforms, find F(s) for each of the following functions: 3. f(t) = cos(5t) 4. f(t) = cos(5t)e²? 5. f(t) = sin(2t) 6. f(t) = sin(5t)e??? Using tables of Laplace transforms, find f(t) for the following functions: 7. F(s) = 1 / (s² + 9) 8. F(s) = (5s + 1) / (s² - s - 12) 9. F(s) = 1 / (s² + 6s + 13) 10. F(s) = (s + 7) / (s² + 2s + 5)

          Tutorial 6. Laplace transform and Euler method

The Laplace transform F(s) of a function f(t) is defined as:

?{f(t)} = F(s) = ??? f(t)e??? dt

Using this definition derive F(s) for each of the following functions:

1. f(t) = t²
2. f(t) = t²e?³?

Using tables of Laplace transforms, find F(s) for each of the following functions:

3. f(t) = cos(5t)
4. f(t) = cos(5t)e²?
5. f(t) = sin(2t)
6. f(t) = sin(5t)e???

Using tables of Laplace transforms, find f(t) for the following functions:

7. F(s) = 1 / (s² + 9)
8. F(s) = (5s + 1) / (s² - s - 12)
9. F(s) = 1 / (s² + 6s + 13)
10. F(s) = (s + 7) / (s² + 2s + 5)

Tutorial 6. Laplace transform and Euler method

The Laplace transform F(s) of a function f(t) is defined as:

?f(t) = F(s) = ??? f(t)e??? dt

Using this definition derive F(s) for each of the following functions:

1. f(t) = t²
2. f(t) = t²e?³?

Using tables of Laplace transforms, find F(s) for each of the following functions:

3. f(t) = cos(5t)
4. f(t) = cos(5t)e²?
5. f(t) = sin(2t)
6. f(t) = sin(5t)e???

Using tables of Laplace transforms, find f(t) for the following functions:

7. F(s) = 1 / (s² + 9)
8. F(s) = (5s + 1) / (s² - s - 12)
9. F(s) = 1 / (s² + 6s + 13)
10. F(s) = (s + 7) / (s² + 2s + 5)

Added by Allen M.

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