Partial Differential Equations I

  • Brian Davies
Part of the Texts in Applied Mathematics book series (TAM, volume 41)


Partial differential equations of the form
$$k{\partial \over {\partial t}}u(r,t) = \nabla ^2 u(r,t)$$
(diffusion equation) and
$${{\partial ^2 } \over {\partial t^2 }}u(r,t) = c^2 \nabla ^2 u(r,t)$$
(wave equation) are amenable to the use of the Laplace transform.1 Indeed, on taking the Laplace transform of the former, we get.
$$ \left( {kpI - \nabla ^2 } \right)U\left( {r,p} \right) = ku\left( {r,0} \right). $$


Partial Differential Equation Transmission Line Diffusion Equation Finite Line Transmission Line Coaxial 
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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Brian Davies
    • 1
  1. 1.Mathematics Department, School of Mathematical SciencesAustralian National UniversityCanberraAustralia

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