12.2. Definition

Try these first

1. 1.

   What is L⁻¹{1/s}?

   Hint

   Consider what function remains constant over time.

2. 2.

   What does L⁻¹{1/s²} yield?

   Hint

   This represents linear growth over time.

3. 3.

   What is the inverse of L{f(t)} = F(s)?

   • f(t)
   • F(s)
   • L⁻¹{F(s)}

   Hint

   Think about what the operation denotes.

4. 4.

   True or False: The Inverse Laplace Transform only works for polynomial F(s).

   • True
   • False

   Hint

   Remember other function types learned in class.

5. 5.

   Find L⁻¹{(s + 2)/(s² + 3s + 2)}. Demonstrate utilizing partial fractions.

   Hint

   Start with the quadratic denominator.

6. 6.

   Apply the Convolution Theorem for two functions: f(t)=t and g(t)=e^(-2t). What is the resulting function?

   Hint

   Utilize the convolution integral format and integrate accordingly.