1.1.1. Introduction

Try these first

1. 1.

   What is the basic formula for the Laplace Transform?

   Hint

   Remember, it transforms a function of time into the s-domain.

2. 2.

   Find the Laplace Transform of the function f(t) = t.

   Hint

   Use basic transform rules.

3. 3.

   What does the Laplace Transform convert?

   • A. Algebraic equations to differential equations
   • B. Differential equations to algebraic equations
   • C. Trigonometric functions to exponential functions

   Hint

   Think about the role of the transform.

4. 4.

   True or False: The Laplace Transform can only handle first derivatives.

   • True
   • False

   Hint

   Recall the formulas we've discussed.

5. 5.

   Given f(t) = e^{at}, find L{f'(t)} and verify the result.

   Hint

   Start with knowing F(s) and differentiate.

6. 6.

   Using initial conditions f(0)=1 and f'(0)=0, find L{f''(t)} for a general function.

   Hint

   Plug the initial values into the general formula for the second derivative.