The Laplace Transform: Definition and Properties
Reference: Logan, A First Course in Differential Equations, 3rd ed., §3.1 "The Laplace Transform: Definition and Properties", pp. 138-146
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §3.1 “The Laplace Transform: Definition and Properties”, pp. 138-146 |
| Read this week | Week 7 of the quarter: pages 138 to 146 |
Bring your copy of Logan to this topic. The section and pages above are the exact reading for this skill.
Objectives
By the end of this section you should be able to:
- State the definition of the Laplace transform as an improper integral
- Use linearity and compute the transform of one, t, and the exponential e to the a t
- Apply the shift and step properties
- Identify when a function has a transform, using piecewise continuity and exponential order
Prerequisite Check
Before this section, make sure you are comfortable with:
- Improper integrals over an infinite interval
- Integration by parts
- Properties of the exponential function
Status
Below are the exact Logan reading with page numbers, the week it falls in the quarter, the learning targets, and what to review first. The full worked examples and the leveled practice set for this section are being written and will appear here.