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Convolution Integrals Differential Equations - Notes Systems of DE's

Table of Laplace Transforms

 

 

 

 

 

 

1.

1

 

2.

 

 

3.

 

 

4.

, p > -1

 

5.

 

 

6.

 

 

7.

 

 

8.

 

 

9.

 

 

10.

 

 

11.

 

 

12.

 

 

13.

 

 

14.

 

 

15.

 

 

16.

 

 

17.

 

 

18.

 

 

19.

 

 

20.

 

 

21.

 

 

22.

 

 

23.

 

 

24.

 

 

25.

 

Heaviside Function

 

26.

 

Dirac Delta Function

 

27.

 

 

28.

 

 

29.

 

 

30.

 

 

31.

 

 

32.

 

 

33.

 

 

34.

 

 

35.

 

 

36.

 

 

37.

 

 

 

Table Notes

  1. This list is not a complete listing of Laplace transforms and only contains some of the more commonly used Laplace transforms and formulas.

 

  1. Recall the definition of hyperbolic functions.

 

 

     

  1. Be careful when using “normal” trig function vs. hyperbolic functions.  The only difference in the formulas is the “+ a2” for the “normal” trig functions becomes a “- a2” for the hyperbolic functions!

 

  1. Formula #4 uses the Gamma function which is defined as

 

 

            If n is a positive integer then,

 

 

 

The Gamma function is an extension of the normal factorial function.  Here are a couple of quick facts for the Gamma function

 

                                      

Convolution Integrals Differential Equations - Notes Systems of DE's

Online Notes / Differential Equations (Notes) / Laplace Transforms / Table Of Laplace Transforms

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