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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 (SNB)

1b. The Unit Step Function - Products (SNB)

2. Laplace Transform Definition (SNB)

3. Properties of Laplace Transform (SNB)

4. Transform of Unit Step Functions (SNB)

5. Transform of Periodic Functions (SNB)

6. Transforms of Integrals (SNB)

7. Inverse of the Laplace Transform (SNB)

8. Using Inverse Laplace to Solve DEs (SNB)

9. Integro-Differential Equations and Systems of DEs (SNB)

10. Applications of Laplace Transform (SNB)

• Comments, Questions?

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From the math blog...

6. Laplace Transforms of Integrals

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

1. If G(s) = {g(t)}, then

2. For the general integral, if

is the value of the integral when t = 0, then:

 

EXAMPLES

Use the above information and the Table of Laplace Transforms to find the Laplace transforms of the following integrals:

(a)

Answer

(b)

Answer

(c)

Answer

(d)

Answer