17. Laplace Transforms & Applications

Try these first

1. 1.

   What is the first step in using Laplace Transforms for a set of linear differential equations?

   Hint

   Consider what a Laplace Transform does.

2. 2.

   Define the Inverse Laplace Transform.

   Hint

   Think about reversing the transformation.

3. 3.

   What does the Laplace Transform do?

   • Converts algebraic equations to differential equations
   • Converts differential equations to algebraic equations
   • It has no real application

   Hint

   Think about how it simplifies the problem.

4. 4.

   True or False: The Inverse Laplace Transform is used to go from the s-domain back to the time domain.

   • True
   • False

   Hint

   Recall the definition of Inverse transformations.

5. 5.

   A system of equations is represented as dx/dt = 4x - 2y, dy/dt = x + 5y with initial conditions x(0)=2 and y(0)=3. Use Laplace Transforms to solve this system.

   Hint

   Transform, isolate variables, and then invert.

6. 6.

   Show how initial conditions affect the solution of a given set of differential equations, using an example where one initial condition is missing.

   Hint

   Consider the necessity of constraints for unique solutions.