Solving Initial Value Problems with the Laplace Transform
Reference: Logan, A First Course in Differential Equations, 3rd ed., §3.2 "Solving Initial Value Problems with the Laplace Transform", pp. 147-159
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §3.2 “Solving Initial Value Problems with the Laplace Transform”, pp. 147-159 |
| Read this week | Week 8 of the quarter: pages 147 to 159 |
The reading is Logan §3.2, pages 147 to 159. Have your copy open.
Objectives
After working through this material you can:
- Transform a differential equation into the s-domain using the derivative rule
- Solve the resulting algebraic equation for the transform of the unknown
- Invert the transform using a table and partial fraction decomposition
- Use the method on problems with discontinuous forcing where other methods are harder
Prerequisite Check
The method assumes you are comfortable with:
- The Laplace transform and its derivative rule
- Partial fraction decomposition
- Solving constant-coefficient equations
Status
The Logan reading, the learning targets, and the prerequisites are above. Worked examples and a leveled practice set are still in progress.