# Math 230 - Chapter 7 Study Guide

1. You are given the result of an indefinite integral for the Laplace transform. Identify any restrictions on s so the integral converges, find the Laplace transform, identify the original function, and find the Laplace transform if the function is periodic. For example, if the original function was $$f(t) = \cos 3t$$, then you would be given $$\frac{e^{-st}}{s^2+9}\left(3 \sin 3t - s \cos 3t \right )$$
2. Rewrite the piece-wise function using the unit step function. Then find the Laplace transform for the function.
3. Solve the initial value problems using Laplace transforms. 3 parts.
4. Use Laplace transforms to solve the system of differential equations.
5. Solve the initial value problems as far as Y(s) =. Do not use partial fractions or attempt to find the inverse Laplace transform. 3 parts.
6. The Y(s) from solving a differential equation is given. Use it to find the solution y(t). 4 parts.

## Notes

• You may need to bring scratch paper for extra work, although most of the problems shouldn't require more space than is given.
• You may not use Maxima during the exam.
• Make sure you can find a partial fraction decomposition for cases more complicated than what can be found with the cover-up method.
• You may also need to know integration by parts.

## Points per problem

 # Pts 1 2 3 4 5 6 Total 16 8 24 10 18 24 100