12.7. Summary

Try these first

1. 1.

   Find the inverse Laplace transform of F(s) = 1/s.

   Hint

   Recall basic pairs of transforms.

2. 2.

   What is L^{-1}{1/s^2}?

   Hint

   This is one of the standard inverses.

3. 3.

   What is the primary purpose of the Inverse Laplace Transform?

   • To convert time-domain functions to frequency domain.
   • To convert frequency domain functions back to time domain.
   • To solve algebraic equations.

   Hint

   Think about the purpose of Laplace transforms and their inverses.

4. 4.

   True or False: The Partial Fraction Method can be used for any Laplace transform.

   • True
   • False

   Hint

   Recall the conditions required for using this technique.

5. 5.

   Derive the inverse Laplace transform using the complex inversion formula for F(s) = (1/(s^2 + 4)). State your final result in terms of a function.

   Hint

   Consider how to evaluate the contour integral.

6. 6.

   Using the Convolution Theorem, find L^{-1}{(s+3)/(s^2 + 3s + 2)}. Show results in a detailed step.

   Hint

   Starting with partial fractions is the key step.