Chapter 4: The Laplace Transform

1. Chapter 4: The Laplace Transform Introduction The Laplace transform studied in this chapter is an invaluable tool in solving problems such as these ( section 4.4 )

2. 4.1 Definition of the Laplace Transform Leads to Function of two variables Function of one variable Improper integral

3. Note: • L[f(t)] is a function of s • Improper integral functions in t functions in s Example 1: Using Definition 4.1 4.1 Definition of the Laplace Transform Definition 4.1 Laplace Transform

4. Example 2: Using Definition 4.1 Example 3: Using Definition 4.1 Example 4: Using Definition 4.1 4.1 Definition of the Laplace Transform

5. 4.1 Definition of the Laplace Transform L[..] is a Linear Transform Example :

6. 4.1 Definition of the Laplace Transform Theorem 4.1 Transforms of Some Basic Functions HW

7. 4.1 Definition of the Laplace Transform Example 5: Piecewise defined function

8. 4.1 Definition of the Laplace Transform Definition 4.2 Exponential Order

9. 4.1 Definition of the Laplace Transform Theorem 4.2 Sufficient Condition for Existence

10. 4.1 Definition of the Laplace Transform 39) One definition of the gamma function is given by the improper integral 40) Use Problem 39 to find the Laplace transform of HW

11. Matlab and Mathematica