The Laplace Transform

  • Ram P. Kanwal


The main applications of the Laplace transform are directed toward problems in which the time t is the independent variable. We shall therefore use this variable in this chapter. Let f(t) be a complex-valued function of the real variable t such that f(t)e -ct is abolutely integrable over 0 < t < ∞, where c is a real number. Then the Laplace transform of f(t), t ≥ 0, is defined as
$$ \tilde f(s) = \mathcal{L}\left\{ {f(t)} \right\} = \int_0^\infty {f(t)e^{ - st} dt, Re s > c,} $$
where s = σ + iω. The Laplace transform defined by (1) has the following basic properties.


Laplace Transform Heaviside Function Main Application Residue Theorem Inhomogeneous Equation 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Ram P. Kanwal
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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