# Math 230 - Chapter 7 Study Guide

1. Use the definition of the Laplace transform to find a transform. Show work!. Look at problems 7.1.19-36.
2. Use the table of Laplace transforms to find the transform. Three parts.
3. Find the inverse transform. Three parts. Look at problems 7.2.1-30.
4. Use the coverup method to find the inverse transform with partial fractions. Show work! Look at problems 7.2.21-24.
5. Solve the initial value problem using the Laplace transform. Two parts. Look at problems 7.2.31-40.
6. Use the convolution theorem to evaluate the transform. Do not evaluate the integral before transforming. Two parts. Look at problems 7.4.19-30.
7. Use the transform of a convolution to find the inverse transform. Sort of look at 7.4.31-34.
8. Write the piecewise function using the unit step function. Look at problems 7.3.55-60.
9. Use the Laplace transform to solve the integral equation. Look at problems 7.4.37-44.
10. Solve the initial value problem using the Laplace transform. Two parts. Look at problems 7.3.63-70 and 7.5.1-12.
11. Find the Laplace transform for the periodic function. Look at problems 7.4.49-54.
12. Use the unit step function to write the function shown in the graphs. Three parts. Look at problems 7.3.49-54 except it isn't matching.

## Notes

• A table of key Laplace transforms is provided with the test.
• Not every transform from the back of the book is in the table, so you may have to apply some of the transformation formulas rather than using the transform directly from the table. As an example, formula 17, L{tneat}, wouldn't be there because formulas 3, L{tn}, and 52, L{eatf(t)}, are there.
• You may not have your own notecards on this test.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 8 9 9 6 14 8 6 5 6 14 6 9 100