# 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. (7 parts).
3. Rewrite the function using the unit step function and then find the Laplace transform.
4. Rewrite the function involving the unit step function as one in piecewise form without the unit step function.
5. Use the definition of the Laplace transform to find the Laplace transform.
6. Find the Laplace transform for the periodic function.
7. Solve the equations. May be initial value problems, integral equations, or integrodifferential equations. (6 parts).
8. Find the Laplace transform involving derivatives. (2 parts).
9. Find the inverse Laplace transform using partial fractions.
10. 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 1-6 must be worked without a computer.
• Problems 7-10 should use Maxima to assist with algebra and calculus, but you should show the steps for the differential equations portion. That is, do NOT use ode2, desolve, laplace, or ilt to solve the problem. It is okay to use the computer for partial fractions, derivatives, integrals, solving equations, etc.
• There are 106 points possible, but the exam is only worth 100 points. This means that you may miss up to 6 points without adversely affecting your grade.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 30 21 4 4 4 4 24 6 3 6 106