6.9. Summary

Try these first

1. 1.

   Define the Laplace Transform in mathematical terms.

   Hint

   Consider the definition and basic parameters.

2. 2.

   What does it mean for a function to have exponential order?

   Hint

   Think about how the function behaves as t increases.

3. 3.

   What is the Laplace Transform of an integral represented as?

   • F(s)/s
   • sF(s)
   • s^2F(s)

   Hint

   Remember how integration relates to the Laplace Transform.

4. 4.

   True or False: Fubini's Theorem is not needed to evaluate the Laplace Transform of integrals.

   • True
   • False

   Hint

   Consider when you have multiple integrals involved.

5. 5.

   Using properties of Laplace Transforms, derive the Laplace Transform of the integral L{∫t^2 dτ} from 0 to t.

   Hint

   Consider how derivatives relate to integrals.

6. 6.

   Formulate an integro-differential equation that utilizes the theorem of Laplace Transforms.

   Hint

   Remember the linear properties of Laplace Transform.