Scribd
Upload
3K views1 page

Table of Laplace Transforms: Heaviside Function Dirac Delta Function

This document provides a table of Laplace transforms that lists common functions and their corresponding Laplace transforms. Some examples included are: the Laplace transform of 1 is 1/s; the Laplace transform of et is 1/(s-a); the Laplace transform of sin(at) is a/(s2+a2); and the Laplace transform of a unit step function uc(t) is e-cs/s. The table contains 36 entries that define various functions and their associated Laplace transforms.

Uploaded by

Siraj AL sharif
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
3K views1 page

Table of Laplace Transforms: Heaviside Function Dirac Delta Function

This document provides a table of Laplace transforms that lists common functions and their corresponding Laplace transforms. Some examples included are: the Laplace transform of 1 is 1/s; the Laplace transform of et is 1/(s-a); the Laplace transform of sin(at) is a/(s2+a2); and the Laplace transform of a unit step function uc(t) is e-cs/s. The table contains 36 entries that define various functions and their associated Laplace transforms.

Uploaded by

Siraj AL sharif
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

Table of Laplace Transforms

f ( t ) = L -1 {F ( s )} F ( s ) = L { f ( t )} f ( t ) = L -1 {F ( s )} F ( s ) = L { f ( t )}
1 1
1. 1 2. e at
s s-a
n! G ( p + 1)
3. t n , n = 1, 2,3,K 4. t p , p > -1
s n +1 s p +1
p 1 × 3 × 5L ( 2n - 1) p
, n = 1, 2,3,K
n - 12
5. t 3 6. t n+ 1
2s 2
2n s 2
a s
7. sin ( at ) 8. cos ( at )
s + a2
2
s + a2
2

2as s2 - a2
9. t sin ( at ) 10. t cos ( at )
(s + a2 ) (s + a2 )
2 2 2
2

2a 3 2as 2
11. sin ( at ) - at cos ( at ) 12. sin ( at ) + at cos ( at )
(s + a )
2 2 2
(s + a )
2 2 2

s(s - a ) 2 2
s ( s + 3a )
2 2

13. cos ( at ) - at sin ( at ) 14. cos ( at ) + at sin ( at )


(s + a )
2 2 2
(s + a )
2 2 2

s sin ( b ) + a cos ( b ) s cos ( b ) - a sin ( b )


15. sin ( at + b ) 16. cos ( at + b )
s2 + a2 s2 + a2
a s
17. sinh ( at ) 18. cosh ( at )
s - a2
2
s - a2
2

b s-a
19. e at sin ( bt ) 20. e at cos ( bt )
(s - a) (s - a)
2 2
+ b2 + b2
b s-a
21. e at sinh ( bt ) 22. e at cosh ( bt )
(s - a) (s - a)
2 2
-b 2
- b2
n! 1 æsö
23. t ne at , n = 1, 2,3,K 24. f ( ct ) Fç ÷
(s - a)
n +1
c ècø
uc ( t ) = u ( t - c ) e - cs d (t - c )
25. 26. e - cs
Heaviside Function s Dirac Delta Function
27. uc ( t ) f ( t - c ) e F (s)
- cs
28. uc ( t ) g ( t ) e - cs L { g ( t + c )}
ect f ( t ) F ( s - c) t n f ( t ) , n = 1, 2,3,K ( -1) F ( n) ( s )
n
29. 30.
1 ¥ t F (s)
31. f (t ) ò F ( u ) du 32. ò f ( v ) dv
t s 0
s
T
t
ò e - st f ( t ) dt
33. ò f ( t - t ) g (t ) dt F (s)G (s) 34. f (t + T ) = f (t ) 0
0
1 - e - sT
35. f ¢ (t ) sF ( s ) - f ( 0 ) 36. f ¢¢ ( t ) s 2 F ( s ) - sf ( 0 ) - f ¢ ( 0 )
37. f ( n) ( t ) s n F ( s ) - s n-1 f ( 0 ) - s n- 2 f ¢ ( 0 )L - sf ( n- 2) ( 0 ) - f ( n-1) ( 0 )

You might also like