# Math 230 - Chapter 7 Study Guide

- 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 \( \frac{e^{-st}}{s^2+9}\left(3 \sin 3t - s \cos 3t \right ) \)
- Rewrite the piece-wise function using the unit step function. Then find the Laplace transform for the function.
- Solve the initial value problems using Laplace transforms. 3 parts.
- Use Laplace transforms to solve the system of differential equations.
- 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.
- 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

# |
1 |
2 |
3 |
4 |
5 |
6 |
Total |

Pts |
16 |
8 |
24 |
10 |
18 |
24 |
100 |