Tabla De Transformadas De Laplace 64a42

Differential Equations

f (t ) = L

−1

{F ( s )}

1.

1

3.

t n , n = 1, 2,3,…

5.

1 s n! s n +1

π

t

3 2

7.

sin ( at )

9.

t sin ( at )

11.

Table of Laplace Transforms F ( s ) = L { f ( t )} f ( t ) = L −1 { F ( s )}

sin ( at ) − at cos ( at )

2s a 2 s + a2 2as

(s

2

+ a2 )

2

(s + a ) s(s − a ) (s + a )

15.

sin ( at + b )

17.

sinh ( at )

19.

eat sin ( bt )

21.

eat sinh ( bt )

23.

t ne at , n = 1, 2,3,…

(s − a)

25.

uc ( t ) = u ( t − c )

(s − a)

2

20.

eat cos ( bt )

−b

22.

eat cosh ( bt )

24.

f ( ct )

26.

δ (t − c )

b

(s − a)

2

n! n +1

1 f (t ) t

∞

31.

∫

s

sin ( at ) + at cos ( at )

+ b2

2

n+ 1

2n s 2 s 2 s + a2 s2 − a2

(s

cosh ( at )

F ( s − c)

© 2005 Paul Dawkins

t cos ( at )

18.

ect f ( t )

f ( n) ( t )

10.

cos ( at + b )

29.

37.

cos ( at )

, n = 1, 2,3,…

16.

uc ( t ) f ( t − c )

f ′ (t )

8.

n − 12

cos ( at ) + at sin ( at )

27.

35.

t

14.

s sin ( b ) + a cos ( b ) s2 + a2 a 2 s − a2 b

Heaviside Function

0

6.

s p +1 1 ⋅ 3 ⋅ 5 ( 2n − 1) π

+ a2 )

2

F ( u ) du

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

2

(s − a)

t n f ( t ) , n = 1, 2,3,…

2

− b2

e − cs

e − cs L { g ( t + c )}

( −1)

n

F ( n) ( s )

F (s) s

f ( v ) dv

F (s)G ( s)

34.

f (t + T ) = f (t )

sF ( s ) − f ( 0 )

36.

f ′′ ( t )

s n F ( s ) − s n −1 f ( 0 ) − s n − 2 f ′ ( 0 ) 56

+ b2

1 ⎛s⎞ F⎜ ⎟ c ⎝c⎠

30.

0

2

s−a

uc ( t ) g ( t )

∫

2 2

2

(s − a)

Dirac Delta Function

t

2

s cos ( b ) − a sin ( b ) s2 + a2 s 2 s − a2 s−a

28.

32.

2

2as 2 2

2 2

2

e − cs s − cs e F (s)

∫

t p , p > -1

1 s−a Γ ( p + 1)

2

cos ( at ) − at sin ( at )

f ( t − τ ) g (τ ) dτ

4.

12.

2 2

2

13.

33.

eat

2a3 2

t

2.

F ( s ) = L { f ( t )}

∫

T 0

e− st f ( t ) dt

1 − e− sT s 2 F ( s ) − sf ( 0 ) − f ′ ( 0 )

− sf ( n − 2) ( 0 ) − f ( n −1) ( 0 )

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