Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below: 1 + e^(-3t) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. {(1 + e^(-t))} = ? Table of Laplace Transforms Properties of Laplace Transforms X f(t) F(s) {f+g} = {F} + {G} {(cf)} = c{F} for any constant c {e^(at)} = {F(s-a)} {f'} = s{F} - f(0) {f''} = s^2{F} - sf(0) - f'(0) {f'''} = s^3{F} - s^2f(0) - sf'(0) - f''(0) {f^(n)} = s^n{F} - s^(n-1)f(0) - s^(n-2)f'(0) - ... - f^(n-1)(0) {t^n} = n!/(s^(n+1)) sin(bt) b/(s^2 + b^2) cos(bt) s/(s^2 + b^2) sinh(bt) b/(s^2 - b^2) cosh(bt) s/(s^2 - b^2) Title_with_topic: Finding the Laplace Transform using Tables of Laplace Transforms and Properties
Added by Kelly H.
Close
Step 1
The Laplace transform of a function f(t) is denoted as F(s) and is defined as: F(s) = L{f(t)} = ∫[0,∞] e^(-st) f(t) dt Show more…
Show all steps
Your feedback will help us improve your experience
Benjamin Densmore and 81 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. t e^{5t} cos 7t L{t e^{5t} cos 7t} =
Sri K.
Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. Note that an appropriate trigonometric identity may be necessary. sin 7t sin 3t L{sin 7t sin 3t} =
Adi S.
Table of Laplace Transforms f(t)=mathcal{L}^{-1}{F(s)} F(s)=mathcal{L}{f(t)} f(t)=mathcal{L}^{-1}{F(s)} F(s)=mathcal{L}{f(t)} 1. 1 frac{1}{s} 2. e^{at} frac{1}{s-a} 3. t^n, n=1,2,3,... frac{n!}{s^{n+1}} 4. t^p, p > -1 frac{Gamma(p+1)}{s^{p+1}} 5. sqrt{t} frac{sqrt{pi}}{2s^{frac{3}{2}}} 6. t^{n-frac{1}{2}}, n=1,2,3,... frac{1cdot3cdot5cdots(2n-1)sqrt{pi}}{2^n s^{n+frac{1}{2}}} 7. sin(at) frac{a}{s^2+a^2} 8. cos(at) frac{s}{s^2+a^2} 9. t sin(at) frac{2as}{(s^2+a^2)^2} 10. t cos(at) frac{s^2-a^2}{(s^2+a^2)^2} 11. sin(at) - at cos(at) frac{2a^3}{(s^2+a^2)^2} 12. sin(at) + at cos(at) frac{2as^2}{(s^2+a^2)^2} 13. cos(at) - at sin(at) frac{s(s^2-a^2)}{(s^2+a^2)^2} 14. cos(at) + at sin(at) frac{s(s^2+3a^2)}{(s^2+a^2)^2} 15. sin(at+b) frac{s sin(b) + a cos(b)}{s^2+a^2} 16. cos(at+b) frac{s cos(b) - a sin(b)}{s^2+a^2} 17. sinh(at) frac{a}{s^2-a^2} 18. cosh(at) frac{s}{s^2-a^2} 19. e^{at} sin(bt) frac{b}{(s-a)^2+b^2} 20. e^{at} cos(bt) frac{s-a}{(s-a)^2+b^2} 21. e^{at} sinh(bt) frac{b}{(s-a)^2-b^2} 22. e^{at} cosh(bt) frac{s-a}{(s-a)^2-b^2} 23. t^n e^{at}, n=1,2,3,... frac{n!}{(s-a)^{n+1}} 24. f(ct) frac{1}{c}F(frac{s}{c}) 25. u_c(t) = u(t-c) Heaviside Function frac{e^{-cs}}{s} 26. delta(t-c) Dirac Delta Function e^{-cs} 27. u_c(t)f(t-c) e^{-cs}F(s) 28. u_c(t)g(t) e^{-cs}mathcal{L}{g(t+c)} 29. e^{at}f(t) F(s-a) 30. t^n f(t), n=1,2,3,... (-1)^n F^{(n)}(s) 31. frac{1}{t}f(t) int_s^infty F(u)du 32. int_0^t f(v)dv frac{F(s)}{s} 33. int_0^t f(t- au)g( au)d au F(s)G(s) 34. f(t+T) = f(t) frac{int_0^T e^{-st}f(t)dt}{1-e^{-sT}} 35. f'(t) sF(s)-f(0) 36. f''(t) s^2F(s)-sf(0)-f'(0) 37. f^{(n)}(t) s^n F(s)-s^{n-1}f(0)-s^{n-2}f'(0)-cdots-sf^{(n-2)}(0)-f^{(n-1)}(0)
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD