7.9. Key Points to Remember

Try these first

1. 1.

   What is the Laplace Transform of sin(at)?

   Hint

   Recall the basic Laplace Transform results.

2. 2.

   Define piecewise continuous function.

   Hint

   Think about functions with breaks in the graph.

3. 3.

   What does multiplying a function by t in the Laplace Transform do?

   • It increases the order of the polynomial
   • It shifts the function vertically
   • It differentiates the Transform

   Hint

   Think about the relationship between time-domain functions and their transforms.

4. 4.

   True or False: The function must be continuous to use the multiplication by tn property?

   • True
   • False

   Hint

   Consider the continuity requirements we've discussed.

5. 5.

   Derive L{t·cos(at)} using the multiplication by tn property.

   Hint

   Don't forget the alternating sign!

6. 6.

   Explain in detail the steps necessary to differentiate L{e^(st)sin(at)} in the s-domain.

   Hint

   Refer back to the basic derivatives of exponentials.