Tables of Integral Transformations - Heat Conduction: Mathematical Models and Analytical Solutions - page 476

Tabl e C. 2 countinued

Inverse Image Functions Image Functions

ω

sin ω t

s 2 + ω

2

s

cos ω t

s 2

2

+ ω

k

sh kt

s 2 − k 2

s

ch kt

s 2 − k 2

s

1
√ t

√ π
2 √ s 3

√ t

Γ ( n + 1 )
( s − α )

t n e α t

n + 1

ω
( s − α )

e α t sin ω t

2

+ ω

2

s − α

e α t cos ω t

( s − α )

2

+ ω

2

δ ( t ) 1

2α s

t sin α t

2

s 2

2

( + α )

s 2

2

− α

t cos α t

2

( s 2 + α

2

)

arctan s

1
t

sin α t

2 α s

t sh α t

2

( s 2

2

− α )

s 2

2

+ α

t ch α t

2

( s 2 − α

2

)