University:
Whitman College
Course:
MATH-244 | Differential Equations
Academic year:

2021
Views:

500

Pages:

1
Author:

uslunerayoed

Table of Laplace Transforms f (t) F (s) Notes 1. 1 1 s 2. eat 1 s−a s>a Sect 6.1 n! , sn+1 s>0 Sect 6.1 s>0 Sect 6.1 3. tn , 4. sin(at) a , s2 + a2 s>0 Sect 6.1 5. cos(at) s , s2 + a2 s>0 Sect 6.1 n pos int 6. eat sin(bt) b , (s − a)2 + b2 s>a Sect 6.1 7. eat cos(bt) s−a , (s − a)2 + b2 s>a Sect 6.1 8. tn eat , 9. uc (t) or u(t − c) 10. uc (t)f (t − c) n pos int 11. ect f (t) n! , (s − a)n+1 s>a Sect 6.1 e−cs s Sect 6.3 e−cs F (s) Sect 6.3 F (s − c) Sect 6.3 12. f (t) ∗ g(t) F (s)G(s) Sect 6.6 13. δ(t − c) e−cs Sect 6.5 14. f (n) (t) sn F (s) − sn−1 f (0) − . . . − f n−1 (0) Sect 6.2 F (n) (s) Sect 6.2 15. (−t)n f (t) Note: uc (t) is the Heaviside function, and the asterisk (∗) denotes convolution.

Table of Laplace Transforms 2019

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