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4. Laplace Transforms of the Unit Step Function

We saw some of the following properties in the Table of Laplace Transforms.

1.

2.

3. Time Displacement Theorem:

If then

[You can see what the left hand side of this expression means in the section Products Involving Unit Step Functions.]

EXAMPLES

Sketch the following functions and obtain their Laplace transforms:

(a)

Assume the constants a, b, and A are positive, with a < b.

Answer

(b)

Assume the constants a and b are positive, with a < b.

Answer

(c)

Answer

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Chapter Contents

• Laplace Transforms
• 1a. The Unit Step Function - Definition
• 1b. The Unit Step Function - Products
• 2. Laplace Transform Definition
• Table of Laplace Transformations
• 3. Properties of Laplace Transform
• 4. Transform of Unit Step Functions
• 5. Transform of Periodic Functions
• 6. Transforms of Integrals
• 7. Inverse of the Laplace Transform
• 8. Using Inverse Laplace to Solve DEs
• 9. Integro-Differential Equations and Systems of DEs
• 10. Applications of Laplace Transform

Following are the original SNB files (.tex or .rap) used in making this chapter. For more information, go to SNB info.

SNB files

1a. The Unit Step Function - Definition

1b. The Unit Step Function - Products

2. Laplace Transform Definition

3. Properties of Laplace Transform

4. Transform of Unit Step Functions

5. Transform of Periodic Functions

6. Transforms of Integrals

7. Inverse of the Laplace Transform

8. Using Inverse Laplace to Solve DEs

9. Integro-Differential Equations and Systems of DEs

10. Applications of Laplace Transform

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