# Math 230 - Chapter 7 Study Guide

1. Find the Laplace transform of the expression. (10 parts).
2. Find the inverse Laplace transform of the expression. (6 parts).
3. Rewrite the piece-wise function using the unit step function.
4. Find the Laplace transform for the periodic function. You will need to be able to find the equation from the graph.
5. Solve the equations. May be initial value problems, integral equations, or integrodifferential equations. (6 parts).
6. Use Laplace transforms to solve the system of differential equations.

## Notes

• You may need to bring scratch paper for extra work, although most of the problems shouldn't require more space than is given.
• Problems 1-3 must be worked without a computer or a formula sheet.
• Problems 4-6 should use Maxima to assist with algebra and calculus, but you should show the steps for the differential equations portion. Show work where necessary.
• You may use a formula sheet with the common Laplace transforms on it for problems 4-6.

## Points per problem

 # Pts 1 2 3 4 5 6 Total 30 24 4 6 30 6 100