Step functions

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Intros
Lessons
  1. What is the Heaviside Step Function?
  2. What are some uses of the Heaviside Step Function and what is the Laplace Transform of a Heaviside Step Function?
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Examples
Lessons
  1. Determining Heaviside Step Functions

    Write the following graph in terms of a Heaviside Step Function

    graph of a Heaviside Step Function

    1. Determining the Laplace Transform of a Heaviside Step Function

      Find the Laplace Transform of each of the following Step Functions:

      1. f(t)=6u3(t)e3t15u5(t)+3(t7)2u7(t)f(t) = 6u_{3}(t) - e^{3t - 15}u_{5}(t) + 3(t - 7)^{2}u_{7}(t)
      2. g(t)=sin(t)uπ(t)+2t2u4(t)g(t) = -\sin{(t)}u_{\pi}(t) + 2t^{2}u_{4}(t)
    2. Determining the Inverse Laplace Transform of a Heaviside Step Function

      Find the inverse Laplace Transform of the following function:

      F(s)=4e3s(s2)(s+3)F(s) = \frac{4e^{-3s}}{(s - 2)(s + 3)}