Laplace Transform Overview
56 min 12 Examples
- Overview of the Definition of the Laplace Transform
- Find the Laplace Transform by definition (Examples #1-5)
- Table of Basic Laplace Transforms
- Use the table to find the Laplace Transform (Examples #1-7)
Inverse Laplace Transforms
1 hr 16 min 10 Examples
- Overview of the Basic Laplace Transforms and the Importance of Linearity
- Find the given inverse Laplace Transform (Examples #1-5)
- Find the given inverse Laplace Transform using Partial Fractions (Examples #6, 7, & 10)
- Find the given inverse Laplace Transform using Completing the Square (Examples #8-9)
Initial Value Problems with Laplace Transforms
1 hr 3 Examples
- Overview of the Transform of a Derivative and Steps for using Laplace Transforms to Solve ODEs
- Use Laplace Transforms to solve the IVP (Examples #1-3)
Translation Theorems of Laplace Transforms
43 min 6 Examples
- Overview of the First Translation Theorem with Two Examples
- Use the First Translation Theorem to set up an IVP (Example)
- Overview of Heaviside Functions with Example
- Overview of the Second Translation Theorem with Example
- Find the Laplace Transform using the Second Shift Theorem (Four Examples)
- Find the Inverse of the Second Translation Theorem (Three Examples)
Chapter Test
1 hr 37 min 7 Practice Problems
- Find the Laplace transform by definition (Problem #1)
- Use the table of Laplace transform (Problem #2a-d)
- Find the inverse Laplace transform (Problem #3a-d)
- Use the Laplace Transform to solve the IVP (Problem #4)
- Use the translation theorem to find F(s) (Problems #5-6)
- Solve the IVP using the second translation theorem (Problem #7)
