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ENGR5001 / Week 3
ENGR201 Laplace deck examples, Laplace transform of derivativesTutorialOld spec ENGR201Third6 min

ENGR201 (old spec) Laplace transforms deck, "example to verify" and Example 3 (pages 18-19)

Use the derivative rules to find the transforms below, and verify each by differentiating first and using the table directly.

Formulas you may need
  • L[f′(t)]=sF(s)−f(0)\mathcal{L}[f'(t)] = sF(s) - f(0); L[f′′(t)]=s2F(s)−sf(0)−f′(0)\mathcal{L}[f''(t)] = s^2F(s) - sf(0) - f'(0) (learn this)
  • L[sin⁡t]=1s2+1\mathcal{L}[\sin t] = \dfrac{1}{s^2 + 1}, L[cos⁡t]=ss2+1\mathcal{L}[\cos t] = \dfrac{s}{s^2 + 1}, L[tn]=n!sn+1\mathcal{L}[t^n] = \dfrac{n!}{s^{n+1}} (learn this)
  1. (a)
    L[f′(t)]\mathcal{L}[f'(t)] for f(t)=cos⁡tf(t) = \cos t
  2. (b)
    L[f′(t)]\mathcal{L}[f'(t)] and L[f′′(t)]\mathcal{L}[f''(t)] for f(t)=t2f(t) = t^2