1. Chapter 6 Laplace Transform

2. Introduction To solve differential equation Convert to algebraic form
Include Initial Condition

3. Laplace Transform

6. Initial value problem

7. Shifting Theorem
Example

8. The Inverse Transformation
Example

9. Invert using Partial Fraction
Case I Distinct linear factor in the denominator

10. Case II Linear factor in the denominator, some repeat
Case III Quadratic factors in the denominator

11. Application
Solve

12. Differential respect to s

13. Integral of Transform
Integration by part

14. Diameter of Column = ?

15. input
Output
BV Problem

17. Integrating Factor
55,1

18. MATLAB
Safety

19. The Step Function
Unit Step Function

20. Unit Impulse Function
L’Hopital’s Rule, diff respect to c

21. Example
Steady State
Unsteady State

22. 8, 12, 61 with shifting

24. Convolution
Example

25. 23

26. Inversion by elementary Integration8

27. Inversion by Contour IntegralIF
THEN

31. Example